ICS 91.080.40  
 
Refer ence number  
DRS 142: 2020  
© RSB 2020  
  
 RWANDA 
STANDARD  DRS  
142  
 
second  edition  
2020 -mm-dd 
 
Design of concrete structures — General 
rules and rules for buildings — Code of 
practice  
 
 DRS 142: 2020  
©RSB 2020  - All rights reserved                  ii 
 In order to match with technological development and to keep continuous progress in industries, 
standard s are subject to periodic review. Users shall ascertain that they are in possession of the latest 
edition  
 
 
 
 
 
 
 
 
© RSB 2020  
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized 
in any form or by any m eans, electronic or mechanical, including photocopying and microfilm, without 
prior written permission from R SB. 
Requests for permission to reproduce this document should be addressed to : 
Rwanda Standards  Board  
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Website: www.rsb.gov.rw  
ePortal: www.portal.rsb.gov.rw   DRS 142: 2020  
iii                ©RSB 2020  - All rights reserved  
 Contents  Page 
Foreword  ................................ ................................ ................................ ................................ ..........................  viii 
1 Scope  ................................ ................................ ................................ ................................ ......................  1 
2 Normative references  ................................ ................................ ................................ ............................  1 
3 Terms and definitions  ................................ ................................ ................................ ...........................  2 
4 Symbols  ................................ ................................ ................................ ................................ ..................  5 
5 Basis of design  ................................ ................................ ................................ ................................ .... 10 
5.1 Requirements  ................................ ................................ ................................ ................................ ....... 10 
5.1.1  Basic  requirements  ................................ ................................ ................................ ............................  10 
5.1.2  Reliability management  ................................ ................................ ................................ ......................  10 
5.1.3  Design working life, durability and quality management  ................................ ................................  10 
5.2 Requirements of limit state design  ................................ ................................ ................................ .... 10 
5.2.1  General  ................................ ................................ ................................ ................................ .................  10 
5.2.2  Stability  ................................ ................................ ................................ ................................ .................  10 
5.2.3  Robustness  ................................ ................................ ................................ ................................ ..........  10 
5.2.4  Special hazards  ................................ ................................ ................................ ................................ ... 11 
5.2.5  Loads and strength of materials  ................................ ................................ ................................ ........  11 
5.3 Basic variables  ................................ ................................ ................................ ................................ .... 12 
5.3.1  Actions and environmental influences  ................................ ................................ .............................  12 
5.3.2  Material and product properties  ................................ ................................ ................................ ........  13 
5.3.3  Shrinkage and creep  ................................ ................................ ................................ ...........................  13 
5.3.4  Deformations of concrete  ................................ ................................ ................................ ...................  14 
5.3.5  Geometric data  ................................ ................................ ................................ ................................ .... 14 
5.4 Verificatio n by the partial factor method  ................................ ................................ ..........................  14 
5.4.1  Design values  ................................ ................................ ................................ ................................ ...... 14 
5.4.2  Combinations of actions ................................ ................................ ................................ .....................  16 
5.4.3  Verification of static equilibrium - EQU  ................................ ................................ .............................  16 
5.5 Design assisted by testing  ................................ ................................ ................................ .................  16 
5.6 Supplementary requiremen ts for foundations  ................................ ................................ .................  16 
5.7 Requirements for fastenings  ................................ ................................ ................................ ..............  16 
6 Materials  ................................ ................................ ................................ ................................ ...............  17 
6.1 Concrete  ................................ ................................ ................................ ................................ ...............  17 
6.1.1  General  ................................ ................................ ................................ ................................ .................  17 
6.1.2  Strength  ................................ ................................ ................................ ................................ ................  17 
6.1.3  Elastic def ormation  ................................ ................................ ................................ .............................  19 
6.1.4  Creep and shrinkage  ................................ ................................ ................................ ...........................  20 
6.1.5  Stress -strain relation for non -linear structural analysis  ................................ ................................ . 24 
6.1.6  Design compressive and tensile strengths  ................................ ................................ ......................  25 
6.1.7  Stress -strain relations for the design of cross -sections  ................................ ................................ . 25 
6.1.8  Flexural tensile strength  ................................ ................................ ................................ .....................  28 
6.1.9  Confined concrete  ................................ ................................ ................................ ...............................  28 
6.2 Reinforcing steel  ................................ ................................ ................................ ................................ . 29 
6.2.1  General  ................................ ................................ ................................ ................................ .................  29 
6.2.2  Properties  ................................ ................................ ................................ ................................ .............  29 
6.2.3  Strength  ................................ ................................ ................................ ................................ ................  30 
6.2.4  Ductility characteristics  ................................ ................................ ................................ ......................  30 
6.2.5  Welding  ................................ ................................ ................................ ................................ .................  30 
6.2.6  Fatigue  ................................ ................................ ................................ ................................ ..................  31 
6.2.7  Design assumptions  ................................ ................................ ................................ ...........................  31 DRS 142: 2020  
©RSB 2020  - All rights reserved                  iv 
 6.3 Prestressing steel  ................................ ................................ ................................ ...............................  32 
6.3.1  General  ................................ ................................ ................................ ................................ .................  32 
6.3.2  Properties  ................................ ................................ ................................ ................................ ............  32 
6.3.3  Strength  ................................ ................................ ................................ ................................ ...............  34 
6.3.4  Ductility characteristics  ................................ ................................ ................................ .....................  34 
6.3.5  Fatigue  ................................ ................................ ................................ ................................ .................  35 
6.3.6  Design assumptions  ................................ ................................ ................................ ...........................  35 
7 Durability and cover to reinforcement  ................................ ................................ ..............................  35 
7.1 General  ................................ ................................ ................................ ................................ .................  35 
7.2 Environmental conditions  ................................ ................................ ................................ ..................  36 
7.3 Requirements for durability  ................................ ................................ ................................ ...............  38 
7.4 Methods of verification  ................................ ................................ ................................ ......................  39 
7.4.1  Concrete cover  ................................ ................................ ................................ ................................ .... 39 
8 Structural analysi s ................................ ................................ ................................ ..............................  42 
8.1 General  ................................ ................................ ................................ ................................ .................  42 
8.1.1  General requirements  ................................ ................................ ................................ .........................  42 
8.1.2  Special requir ements for foundations  ................................ ................................ ..............................  43 
8.2 Idealization of the structure  ................................ ................................ ................................ ...............  43 
8.2.1  Structural models for overall analysis  ................................ ................................ .............................  43 
8.2.2  Geometric data  ................................ ................................ ................................ ................................ .... 44 
8.2.3  Linear elastic analysis  ................................ ................................ ................................ ........................  47 
8.3 Linear elastic analysis with l imited redistribution  ................................ ................................ ..........  47 
8.4 Plastic analysis  ................................ ................................ ................................ ................................ ... 48 
8.4.1  General  ................................ ................................ ................................ ................................ .................  48 
8.4.2 Plastic analysis for beams, frames and slabs  ................................ ................................ .................  49 
8.5 Non-linear analysis  ................................ ................................ ................................ .............................  51 
8.6 Analysis of second order effects with axial load  ................................ ................................ ............  51 
8.6.1  General  ................................ ................................ ................................ ................................ .................  51 
8.6.2  Simplified criteria for second order effects  ................................ ................................ .....................  52 
8.6.3  Slenderness and effective length of isolated members  ................................ ................................ . 53 
8.6.4  Global second order effects in buildings  ................................ ................................ .........................  54 
8.6.5  Creep  ................................ ................................ ................................ ................................ ....................  55 
8.6.6  Methods of analysis  ................................ ................................ ................................ ...........................  56 
8.6.7  General method  ................................ ................................ ................................ ................................ ... 56 
8.6.8  Method based o n nominal stiffness ................................ ................................ ................................ .. 57 
8.6.9  Analysis for some particular structural members  ................................ ................................ ...........  60 
9 Ultimate Limit States (ULS)  ................................ ................................ ................................ ................  60 
9.1 Bending with or without axial force  ................................ ................................ ................................ .. 60 
9.2 Shear  ................................ ................................ ................................ ................................ ....................  61 
9.2.1  General verification proced ure ................................ ................................ ................................ ..........  61 
9.2.2  Members not requiring design shear reinforcement  ................................ ................................ ...... 62 
9.2.3  Members requiring design shear reinforcement  ................................ ................................ .............  64 
9.2.4  Shear between web and flanges  ................................ ................................ ................................ ....... 67 
9.3 Torsion  ................................ ................................ ................................ ................................ .................  68 
9.3.1  General  ................................ ................................ ................................ ................................ .................  68 
9.3.2  Warping torsion  ................................ ................................ ................................ ................................ .. 69 
9.4 Punching  ................................ ................................ ................................ ................................ ..............  69 
9.4.1  General  ................................ ................................ ................................ ................................ .................  69 
9.4.2  Load distribution and basic control perimeter  ................................ ................................ ................  70 
9.4.3  Punching shear calculation  ................................ ................................ ................................ ...............  73 
9.4.4 Punching shear resistance of slabs and column bases without shear reinforcement  ...............  78 
9.4.5  Punching shear resistance of slabs and column bases with shear reinforcement  .....................  80 
9.5 9.5   Anchorage of longitudinal reinforcement  ................................ ...... Error! Bookmark not defined.  
9.5.1  General  ................................ ................................ ................................ ....... Error! Bookmark not defined.  DRS 142: 2020  
v                ©RSB 2020  - All rights reserved  
 9.6 Anchorages and lap s ................................ ................................ ................................ ..........................  82 
9.7 Fatigue  ................................ ................................ ................................ ................................ ..................  84 
9.7.1  General  ................................ ................................ ................................ ................................ .................  84 
9.7.2  Verification conditions  ................................ ................................ ................................ ........................  84 
9.7.3  Internal forces and stresses for fatigue verification  ................................ ................................ ........  84 
10 SERVICEABILITY LIMIT STATES (SLS)  ................................ ................................ .............................  85 
10.1  General  ................................ ................................ ................................ ................................ .................  85 
10.2  Deflection  ................................ ................................ ................................ ................................ .............  85 
10.3  Crack control  ................................ ................................ ................................ ................................ ....... 86 
10.3.1  Reinforced concrete  ................................ ................................ ................................ ............................  86 
10.3.2  Prestressed concrete  ................................ ................................ ................................ ..........................  87 
10.3.3  Vibration  ................................ ................................ ................................ ................................ ...............  87 
10.4  Other considerations  ................................ ................................ ................................ ..........................  87 
10.4.1  Fire resistance  ................................ ................................ ................................ ................................ ..... 87 
10.5  Loads and strength of materials  ................................ ................................ ................................ ........  88 
10.5.1  Loads  ................................ ................................ ................................ ................................ ....................  88 
10.6  Strength of materials ................................ ................................ ................................ ...........................  89 
10.6.1  Characteristic strength  of materials  ................................ ................................ ................................ .. 89 
10.6.2  Partial safety factors for strength of materials γm ................................ ................................ ...........  89 
10.7  Values for the ultimate limit state (loads and m aterials)  ................................ ................................ . 89 
10.7.1  Design loads  ................................ ................................ ................................ ................................ ........  89 
10.7.2  Materials  ................................ ................................ ................................ .....Error! Bookmark not defined.  
10.8  Values fo r serviceability limit states (loads and materials)  ................................ ............................  90 
10.8.1  Design loads  ................................ ................................ ................................ ................................ ........  90 
10.8.2  Materials  ................................ ................................ ................................ ................................ ...............  90 
11 Detailing of  reinforced concrete members  ................................ ................................ ......................  90 
11.1  General  ................................ ................................ ................................ ................................ .................  90 
11.1.1  Basis of limit states design  ................................ ................................ ................................ ................  91 
11.1.2  11.1.2  Stability  ................................ ................................ ................................ ................................ ..... 91 
11.1.3  Durability and fire resistance  ................................ ................................ ................................ .............  91 
11.1.4 Loads  ................................ ................................ ................................ ................................ ....................  91 
11.1.5  Strength of materials ................................ ................................ ................................ ...........................  92 
11.2  Bar spacing  ................................ ................................ ................................ ................................ ..........  93 
11.3  Permissible mandrel diameters for bent bars  ................................ ................................ ..................  93 
11.4  Analysis of structures and structural frames  ................................ ................................ ...................  93 
11.4.1  Analysis of complete str uctures and complete structural frames  ................................ .................  93 
11.4.2  Analysis of structural frames supporting vertical loads only  ................................ ........................  94 
11.4.3  Redistributi on of moments  ................................ ................................ ................................ .................  95 
11.4.4  Column and beam construction  ................................ ................................ ................................ ........  96 
11.5  Beams  ................................ ................................ ................................ ................................ ...................  96 
11.5.1  General  ................................ ................................ ................................ ................................ .................  96 
11.5.2  Longitudinal reinforcement of beams  ................................ ................................ ...............................  97 
11.5.3  Torsion reinforcement  ................................ ................................ ................................ ......................  103 
11.5.4  Surface reinforcement  ................................ ................................ ................................ ......................  103 
11.5.5  Indirect supports  ................................ ................................ ................................ ...............................  103 
11.5.6  Moments of resistance at ultimate l imit state for beams  ................................ ..............................  104 
11.5.7  Shear resistance of beams  ................................ ................................ ................................ ...............  108 
11.5.8  Deflection of beams  ................................ ................................ ................................ ..........................  115 
11.6  Solid slabs  ................................ ................................ ................................ ................................ ..........  120 
11.6.1  Design of solid slabs ................................ ................................ ................................ .........................  120 
11.6.2  Moments and forces in solid slabs  ................................ ................................ ................................ .. 120 
11.6.3  One-way spanning slabs of approximately equal span  ................................ ................................  122 
11.6.4  Solid slabs spanning in two directions at right angles (uniformly distrib uted loads)  ...............  122 
11.6.5  11.6.5 Shear resistance of solid slabs ................................ ................................ .............................  128 
11.6.6  Deflection of solid slabs  ................................ ................................ ................................ ...................  131 DRS 142: 2020  
©RSB 2020  - All rights reserved                  vi 
 11.6.7  Crack control in solid slabs  ................................ ................................ ................................ .............  131 
11.6.8  Ribbed slabs (with solid or hollow blocks or with voids) ................................ .............................  132 
11.6.9  Cover to reinforcement  ................................ ................................ ................................ ....................  134 
11.7  Flat slabs  ................................ ................................ ................................ ................................ ...........  135 
11.7.1  General  ................................ ................................ ................................ ................................ ...............  135 
11.7.2  Shear in flat slabs  ................................ ................................ ................................ .............................  138 
11.7.3  Deflection of panels  ................................ ................................ ................................ ..........................  142 
11.7.4  Crack control in panels  ................................ ................................ ................................ ....................  142 
11.7.5  Analysis and design of flat slab structures  ................................ ................................ ...................  142 
11.8  Columns  ................................ ................................ ................................ ................................ .............  147 
11.8.1  General  ................................ ................................ ................................ ................................ ...............  147 
11.8.2  Longitudinal reinforcement  ................................ ................................ ................................ .............  147 
11.8.3  Transverse reinforcement  ................................ ................................ ................................ ................  148 
11.8.4  Size and reinforcement of columns  ................................ ................................ ................................  148 
11.8.5  Braced and unbraced columns  ................................ ................................ ................................ ....... 148 
11.8.6  Short and slender columns  ................................ ................................ ................................ .............  148 
11.8.7  Slenderness limits for columns  ................................ ................................ ................................ ...... 148 
11.8.8  Effective height of a column  ................................ ................................ ................................ ............  149 
11.9  Walls  ................................ ................................ ................................ ................................ ...................  151 
11.9.1  General  ................................ ................................ ................................ ................................ ...............  151 
11.9.2  Forces in lateral supports  ................................ ................................ ................................ ................  151 
11.9.3  Resistance of lateral supports to rotation  ................................ ................................ .....................  151 
11.9.4  Vertical reinforcement  ................................ ................................ ................................ ......................  151 
11.9.5  Horizontal reinforcement  ................................ ................................ ................................ .................  152 
11.9.6  Transverse reinforcement  ................................ ................................ ................................ ................  152 
11.9.7  Forces and moments in reinforced concrete walls  ................................ ................................ ....... 152 
11.9.8  Short reinforced walls  ................................ ................................ ................................ ......................  153 
11.9.9  Slender reinforced walls  ................................ ................................ ................................ ..................  154 
11.10  Staircases  ................................ ................................ ................................ ................................ ..........  155 
11.10.1  General  ................................ ................................ ................................ ................................ ...............  155 
11.10.2  Design of staircases  ................................ ................................ ................................ .........................  156 
11.11  Foundations  ................................ ................................ ................................ ................................ ...... 156 
11.11.1  General  ................................ ................................ ................................ ................................ ...............  156 
11.11.2  Moments and forces in foundations  ................................ ................................ ...............................  156 
11.11.3  Design of  pad footings  ................................ ................................ ................................ .....................  157 
11.11.4  Distribution of reinforcement  ................................ ................................ ................................ ..........  157 
11.11.5  Design of pile caps  ................................ ................................ ................................ ...........................  158 
11.12  Considerations affecting design details  ................................ ................................ ........................  159 
11.12.1  Constructional deviations  ................................ ................................ ................................ ................  159 
11.12.2  Concrete cover  to reinforcement  ................................ ................................ ................................ .... 160 
11.12.3  Reinforcement (general considerations)  ................................ ................................ ........................  161 
11.12.4  Minimum areas of reinforcement in elements  ................................ ................................ ...............  161 
− 163 
11.12.5  Maximum areas of reinforcement in element  ................................ ................................ ................  164 
11.12.6  Spacin g of reinforcement  ................................ ................................ ................................ ................  165 
12 Design and detailing of Precast, composite and plain concrete constructions  ........................  166 
12.1  General  ................................ ................................ ................................ ................................ ...............  166 
12.1.1  Design objectives  ................................ ................................ ................................ .............................  166 
12.1.2  Limit states design  ................................ ................................ ................................ ...........................  166 
12.2  Precast concre te construction  ................................ ................................ ................................ ........  168 
12.2.1  Framed structures and continuous beams  ................................ ................................ ....................  168 
12.2.2  Slabs  ................................ ................................ ................................ ................................ ..................  168 
12.2.3  Continuous concrete nibs  ................................ ................................ ................................ ...............  168 
12.2.4  Allowance for construction inaccuracies  ................................ ................................ ......................  168 
12.2.5  Horizontal forces or rotation at a bearing  ................................ ................................ ......................  169 
12.2.6  Joints between precast units  ................................ ................................ ................................ ..........  169 DRS 142: 2020  
vii                ©RSB 2020  - All rights reserved  
 12.3  Structural connections between units  ................................ ................................ ............................  171 
12.3.1  General  ................................ ................................ ................................ ................................ ...............  171 
12.3.2  Continuity of reinforcement  ................................ ................................ ................................ .............  173 
12.3.3  Connections with structur al steel inserts  ................................ ................................ .......................  175 
12.3.4  Other types of connection  ................................ ................................ ................................ ................  175 
12.4  Composite concrete construction  ................................ ................................ ................................ ... 175 
12.4.1  General  ................................ ................................ ................................ ................................ ...............  175 
12.4.2  Shear  ................................ ................................ ................................ ................................ ...................  176 
12.4.3  Serviceability limit states  ................................ ................................ ................................ .................  176 
12.5  Plain concrete walls  ................................ ................................ ................................ ..........................  176 
12.5.1  General  ................................ ................................ ................................ ................................ ...............  176 
12.5.2  Structural stability  ................................ ................................ ................................ .............................  177 
12.5.3  Design of plain concrete walls  ................................ ................................ ................................ .........  177 
13 Fire resistance  ................................ ................................ ................................ ................................ ... 181 
13.1  General  ................................ ................................ ................................ ................................ ...............  181 
13.2  Beams  ................................ ................................ ................................ ................................ .................  183 
13.3  Floors  ................................ ................................ ................................ ................................ ..................  183 
13.4  Additional protection to floors  ................................ ................................ ................................ .........  184 
13.5  Columns  ................................ ................................ ................................ ................................ .............  184 
13.6  Walls  ................................ ................................ ................................ ................................ ...................  184 
13.6.1  Concrete walls containing at least  1,0 % of vertical reinforcement  ................................ .............  184 
13.6.2  Plain concrete walls  ................................ ................................ ................................ ..........................  184 
ANNEX A ................................ ................................ ................................ ................................ ..........................  185 
(Normative)  ................................ ................................ ................................ ................................ ......................  185 
Properties of reinforcement suitable for use with this code of practice  ................................ ..................  185 
A.1 General  ................................ ................................ ................................ ................................ ...............  185 
A.2 Strength  ................................ ................................ ................................ ................................ ..............  186 
 DRS 142: 2020  
©RSB 2020  - All rights reserved                  viii 
 Foreword   
Rwanda Standard s are prepared  by Technical Committees and approved by R wanda Standards Board (RSB) 
Board  of Directors in  accordance with the procedu res of RSB, in compliance with Annex 3 of the WTO/TBT 
agreement on the preparation, adoption and application of standards.  
The main task of technical committees is to prepare national standards.  Final Draft Rwanda S tandards 
adopted by Technical committ ees are ratified  by me mbers of RSB Board of Director s for publication and 
gazettment as Rwanda Standards.  
CD 142  was prepared by Technical Committee RSB/TC 09 on Civil engineering and building materials.  
In the preparation of this standard, reference was made to the following standard s: 
1) BS EN 1992 -1-1: 2004 Eurocode 2: Design of concrete structures − Part 1 -1: General rules and rules for 
buildings  
2) SANS 10100 -1: 2000, The structural use of concrete − Part 1: Design  
The assistance de rived from the above source is hereby acknowledged with thanks.  
This second edition  cancels and replaces the first editio n (RS  142: 2012), which has been technically revised.  
Committee membership  
The following organizations were represented on the Technical Committee on Civil Engineering and Building 
Materials  (RSB/TC 09) in the preparation of this standard.  
University of Rwa nda – College of Science and Technology (UR -CST)  
Institut d’ Enseignement Supérieur ( INES - Ruhengeri ) 
City of Kigali  
Green Effect Engineering  
Integrated Polytechnic Regional Centre –Kigali (IPRC)  
NPD Ltd  
REAL Contractors Ltd  
Rwanda Housing Authority (RHA)  DRS 142: 2020  
ix                ©RSB 2020  - All rights reserved  
 Rwanda Transport Development Agency (RTDA)  
Standard For Sustainability (SFS)  
Gasabo 3D  
Masss Design Group - Rwanda  
NPD Ltd  
Enterpris es-Generale -des-Constrictions - EGC  
TECOS Ltd  
Institution of Engineers Rwanda  
CIMERWA Ltd  
Rwanda Standards Board (RSB) – Secretariat  DRS 142: 2020  
©RSB 2020  - All rights reserved                  x 
 Introduction   
This standard is intended for clients, designers, contractors and regulatory authorities. it serve s as a reference 
documents for the following purposes :  
– as a means to prove compliance of building and civil engineering works with t he existing Rwanda urban 
planning and building codes ; 
– as a basis for specifying contracts for construction works and related engineering services ;  and 
– as a framework for drawing up harmonised technical specifications for construction products  
This cod e of practice also provide s common structural design rules for everyday use for the design of whole 
structures and component products of both a traditional and an innovative nature. Unusual forms of 
construction or design conditions are not specifically co vered and additional expert consideration will be 
required by the designer in such cases.  
 DRS 142: 2020  
1                ©RSB 2020  - All rights reserved  
 Design of concrete structures — General rules and rules for building  — 
Code of practice   
1 Scope   
This Draft Rwanda  standard gives a general basis for the design of s tructures in plain, reinforced, precast and 
prestressed concrete made with normal and light weight aggregates together with specific rules for buildings.  
2 Normative references  
The following documents are referred to in the text in such a way that some or al l of their content constitutes 
requirements of this document.  For dated references, only the edition cited applies. For undated references, 
the latest edition of the referenced document (including any amendments) applies.  
RS 112, Basis of structural design  
RS 103, Geotechnical design —General rules  
RS ISO 1920 -3, Testing of concrete — Part 3: Making and curing test specimens  
RS ISO 15630 -1, Steel for the reinforcement and prestressing of concrete — Test methods — Part 1: 
Reinforcing bars, wire rod and wire  
RS ISO 6934 -1, Steel for the prestressing of concrete — Part I:General requirements  
RS ISO 6934 -4, Steel for the prestressing of concrete — Part4: Strand  
RS ISO 6934 -5 Steel for the prestressing of concrete — Part 5: Hot -rolled steel bars with or without 
subsequent processing  
RS EAS 417 -1, Concrete — Part 1: Method of specifying and guidance for the specifier  
RS EAS 417 -2, Concrete — Part 2: Specification for constituent materials ,production of concrete and 
compliance of concrete  
RS 357 -2/EAS417 -2  
ISO 17 660-1, welding of reinforcing steel  — Part 1: Load bearing welded joints  
ISO 17660 -2, welding of reinforcing steel  — Part 2: Non load bearing welded joints  
  
©RSB 2020  - All rights reserved                  2 
 3 Terms and definitions  
For the purpose of this standard, the terms and definitions given in DRS 106 and the following apply.  
3.2   
precast structures  
structures characterized by structural elements manufactured elsewhere than in the final position in the 
structure. In the structure, elements are connected to ensure the required structural integrity  
3.3  
plain or lightly reinforced concrete members  
structural concrete members having no reinforcement (plain concrete ) 
3.4 
prestress  
process of prestressing that consists in applying forces to the concrete structure by stressing tendons relative 
to the concrete m ember and  is used to name all the permanent effects of the prestressing process, which 
comprise internal forces in the sections and deformations of the structure  
3.5 
wall 
vertical load -bearing member whose length exceeds four times its thickness  
3.6 
brace d wall  
wall where the reactions to lateral forces are provided by lateral support (at right angles to the plane of that 
wall, lateral stability to the structure as a whole is provided by walls or other suitable bracing design to resist 
all lateral forces)  
3.7 
unbraced wall  
wall providing its own lateral stability  
3.8 
short wall  
wall may be considered short where the ratio of its effective height to its thickness ( le/h) does not exceed 15 
(braced) or 10 (unbraced)  DRS 142: 2020  
3                ©RSB 2020  - All rights reserved  
 3.9 
slender wall  
wall other than a short wal l  
3.10 
effective height of reinforced wall  
for a reinforced wall that is constructed monolithically with the adjacent construction, the effective height( le) 
should be assessed as though the wall were a column being bent at right angles to the plane of th e wall  
3.11 
Ultimate limit states  
those concerning safety, and they correspond to the maximum load -carrying capacity of a structure. An 
ultimate limit state is reached when the structure is not strong enough to withstand the design loads, i.e. when 
the res istance of a critical section (or sections) to compression, tension, shear or torsion is insufficient. This 
will result in loss of equilibrium of the whole or of a part of the structure regarded as a rigid body, with the 
following symptoms being likely to occur:  
a) the rupture of one or more critical sections (due to overloading, fatigue, fire or deformation);  
b) overturning or buckling caused by elastic or plastic instability, sway, wind flutter or ponding;  
c) very large deformation, e.g. transformation of the str ucture into a mechanism.  
3.12 
biaxial bending  
simultaneous bending about two principal axes  
3.13 
braced members or systems  
structural members or subsystems, which in analysis and design are assumed not to contribute to the overall 
horizontal stability of a  structure  
3.14 
bracing members or systems  
structural members or subsystems, which in analysis and design are assumed to contribute to the overall 
horizontal stability of a structure   
©RSB 2020  - All rights reserved                  4 
 3.15 
buckling  
failure due to instability of a member or structure under p erfectly axial compression and without transverse 
load 
NOTE  “Pure buckling” as defined above is not a relevant limit state in real structures, due to imperfections and 
transverse loads, but a nominal buckling load can be used as a parameter in some methods  for second order analysis.  
3.16 
buckling load 
load at which buckling occurs; for isolated elastic members it is synonymous with the Euler load  
3.17 
effective length  
length used to account for the shape of the deflection curve; it can also be defined as bu ckling length, i.e. the 
length of a pin -ended column with constant normal force, having the same cross section and buckling load as 
the actual member  
3.18 
First order effects  
action effects calculated without consideration of the effect of structural defor mations, but including geometric 
imperfections  
3.19 
isolated member  
members that are isolated, or members in a structure that for design purposes may be treated as being 
isolated; examples of isolated members with different boundary conditions are shown in  Figure 14 . 
3.20 
nominal second order moment  
second order moment used in certain design methods, giving a total moment compatible with the ultimate 
cross section resistance .  
3.21 
second order effects  
additional action effects caused by structural deformat ions 
 DRS 142: 2020  
5                ©RSB 2020  - All rights reserved  
 4 Symbols  
A                 Accidental action  
A                 Cross sectional area  
Ac               Cross sectional area of concrete  
Ap               Area of a prestressing tendon or tendons  
As               Cross sectional area of reinforcement  
As,min           minimum cross sectional area of reinforcement  
Asw              Cross sectional area of shear reinforcement  
D                Diameter of mandrel  
Es                Design value of modulus of elasticity of reinforcing steel  
F                 Action 
Fd                Design value of an action  
Fk                Characteristic value of an action  
Gk               Characteristic permanent action  
Ι                  Second moment of area of concrete section  
L                 Length  
M                Bending moment  
MEd             Design value of the applied internal bending moment  
N                Axial force  
NEd              Design value of the appl ied axial force (tension or compression)  
P                 Prestressing force  
P0                Initial force at the active end of the tendon immediately after stressing  
Qk               Characteristic variable action  
R                Resistance  
S                 Internal forces and moments  
S                 First moment of area  
SLS            Serviceability limit state  
T                 Torsional moment   
©RSB 2020  - All rights reserved                  6 
 TEd              Design value of the applied torsional moment  
ULS            Ultimate limit state  
V                 Shear force  
VEd              Design value of the applied shear force  
a                 Distance  
b                 Overall width of a cross -section, or actual flange width in a T or L beam  
bw                Width of the web on T, I or L beams  
d                 Diameter ; Depth  
d                 Effective depth of a cross -section  
dg                Largest nominal maximum aggregate size  
e                 Eccentricity  
fc                 Compressive strength of concrete  
fcd                 Design val ue of concrete compressive strength  
fck                Characteristic compressive cylinder strength of concrete at 28 days  
fcm                Mean value of concrete cylinder compressive strength  
fctk                Characteristic axial tensile strength of concrete  
fctm               Mean value of axial tensile strength of concrete  
fp                 Tensile strength of prestressing steel  
fpk                Characteristic tensile strength of prestressing steel  
ft                  Tensile strength of reinforc ement  
ftk                Characteristic tensile strength of reinforcement  
fy                 Yield strength of reinforcement  
fyd                Design yield strength of reinforcement  
fyk               Characteristic yield strength of reinforcement  
fywd              Design yield of shear reinforcement  
h                 Height  
h                 Overall depth of a cross -section  
i                  Radius of gyration  DRS 142: 2020  
7                ©RSB 2020  - All rights reserved  
 k                 Coefficient ; Factor  
l                   (or l or L) Length; Span  
m                Mass  
r                  Radius  
1/r               Curvature at a particular section  
t                  Thickness  
t                  Time being considered  
t0                 The age of concrete at the time of loading  
u                 Perimeter of concr ete cross -section, having area A c 
u,v,w          Components of the displacement of a point  
x                 Neutral axis depth  
x,y,z            Coordinates  
z                 Lever arm of internal forces  
α                 Angle ; ratio  
β                 Angle ; ratio; coefficient  
γ                 Partial factor  
γA                Partial factor for accidental actions A  
γC                Partial factor for concrete  
γF                Partial factor for actio ns, F  
γF,fat                   Partial factor for fatigue actions  
γC,fat                   Partial factor for fatigue of concrete  
γG               Partial factor for permanent actions, G  
γM                Partial factor for a material property, taking acco unt of uncertainties in the material  
                    property itself, in geometric deviation and in the design model used  
γP                 Partial factor for actions associated with prestressing, P  
γQ                 Partial factor for variable actio ns, Q 
γS                 Partial factor for reinforcing or prestressing steel  
γS,fat                     Partial factor for reinforcing or prestressing steel under fatigue loading   
©RSB 2020  - All rights reserved                  8 
 γf                  Partial factor for actions without taking account of mod el uncertainties  
γg                  Partial factor for permanent actions without taking account of model uncertainties  
γm                 Partial factors for a material property, taking account only of uncertainties in the  material 
property   
εc                  Compressive strain in the concrete  
εc1                Compressive strain in the concrete at the peak stress fc 
εcu                 Ultimate compressive strain in the concrete  
εu                  Strain of reinforcement or prestressing steel at maxi mum load  
εuk                 Characteristic strain of reinforcement or prestressing steel at maximum load  
λ                   Slenderness ratio  
ν                   shear stress  
ξ                   Ratio of bond strength of prestressing and reinforcing stee l 
ρ                   Oven -dry density of concrete in kg/m3 
ρ1000             Value of relaxation loss (in %), at 1000 hours after tensioning and at a mean  
                     temperature of 20°C  
ρl                   Reinforcement ratio for longitudinal r einforcement  
ρw                  Reinforcement ratio for shear reinforcement  
σc                  Compressive stress in the concrete  
σcp                Compressive stress in the concrete from axial load or prestressing  
σcu                Compressive stress in the concrete at the ultimate compressive strain ε cu 
τ                   Torsional shear stress  
ϕ                   Diameter of a reinforcing bar or of a prestressing duct  
As                 area of tension reinforcement  
 
A   area of compression reinforc ement  
b    width or effective width of beam or flange in compression zone  
bw      average web width of flanged beam  
d    effective depth of tension reinforcement  
d́ /    depth to compression reinforcement  DRS 142: 2020  
9                ©RSB 2020  - All rights reserved  
 fcu     characteristic strength of concrete  
fy      characteristic strength of reinforcement,   
fyc = fy/(γ m + fy/2000)  
hf       thickness of beam flange  
M     design ultimate moment  
X      depth to neutral axis  
Z      lever arm  
βb (moment at beam after redistribution) (moment at beam before redistribu tion) from the  respective 
maximum moments diagrams  
βf factor given in table 16.  
l1   panel length, measured from centres of columns, in direction of span under consideration  
l2   panel width, measured from centres of columns at right angles to direction o f span under 
consideration lm average of l1 and l2 
hc   diameter of column or of column head (see figure 46) (which shall be taken as the diameter  of a circle 
of the same area as the cross -section of the head (see 11.7.1.3))  
n    total ultimate load per u nit area of panel (1 .4gk + 1.6qk) 
Ac     total area of concrete  
Acc   area of concrete in compression  
As      minimum recommended area of reinforcement  
Asc    area of steel in compression  
Ast     area of transverse steel in a flange  
b       width of sectio n 
bw     width or effective width of the rib (for a box, T -section or I -section, bw is taken as the average width 
of the concrete below the flange)  
fy       characteristic strength of reinforcement  
h       overall depth of the cross -section of a reinforced  element  
hf      depth of flange  
l        span of beam   
©RSB 2020  - All rights reserved                  10 
 5 Basis of design  
5.1 Requirements  
5.1.1  Basic requirements  
5.1.1. 1 The design of concrete structures shall be in accordance with the general rules given in RS 112. 
5.1.1. 2 The supplementary provisions for concre te structures given in this section shall also b e applied.  
5.1.2  Reliability management  
The rules for reliability management are given in RS 122. 
5.1.3  Design working life, durability and quality management  
The rules for design working life, durability and quality man agement are given in RS  112. 
5.2 Requirements of limit state design  
5.2.1  General  
All relevant limit states should be considered in the initial stages of the design so as to ensure an adequate 
degree of safety and serviceability. The general rule, however, will be t o design on the basis of the expected 
critical limit state and then to check that the remaining limit states will not be reached.  
5.2.2  Stability  
Structures should be so designed that adequate means exist to transmit the design ultimate self -weight load, 
wind lo ad and imposed loads safely from the highest supported level to the foundations. The layout of the 
structure and the interaction between the structural elements should be such as to ensure a stable design. 
The engineer responsible for the overall stability  of the structure should ensure the compatibility of the design 
and details of parts and components, even where all or part of the design and details thereof were undertaken 
by someone else.  
5.2.3  Robustness  
5.2.3.1  Structures should be so designed that they are  not unreasonably susceptible to the effects of 
accidents. In particular, situations should be avoided where damage to a small area of a structure or failure of 
a single element could lead to the collapse of major sections of the structure. In general, if any failure were to 
occur, it should be in the beams and not in the columns. Unreasonable susceptibility to the effects of 
accidents may generally be prevented if the factors given below are taken into consideration.  
5.2.3.2  Structures should be capable of  safely resisting the design ultimate horizontal load applied at each 
floor or roof level simultaneously.  Structures should have effective horizontal ties:  
a) around the periphery,  DRS 142: 2020  
11                ©RSB 2020  - All rights reserved  
 b) internally, and 
c) to columns and walls.  
5.2.3.3  The layout of storied buildings  should be checked to identify any key elements whose failure would 
cause the collapse of more than a limited portion close to these key elements. Where such elements are 
identified and the layout cannot be revised to avoid them, the design should take the ir importance into 
account. The likely consequences of a failure of a key element should be considered when appropriate design 
loads are chosen. In all cases, an element and its connections should be capable of withstanding a design 
ultimate load of 34 kN/ m2 (to which no partial safety factor should be applied) from any direction. The area to 
which this load is applied will be the projected area of the element (i.e. the area of the face presented to the 
load). A horizontal element, or part of a horizontal e lement that provides lateral supports vital to the stability of 
a vertical key element, should also be considered a key element.  
5.2.3.4  Storied buildings should be so detailed that any vertical load -bearing element other than a key 
element can be removed without causing the collapse of more than a limited portion close to that element. 
This is generally achieved by providing vertical ties. There may, however, be cases where it is inappropriate or 
impossible to provide effective vertical ties in all or even  in some of the vertical load -bearing elements.  
5.2.3.5  When this occurs, the removal of each such load -bearing element should be considered, in turn, and 
the elements normally supported by such load -bearing element should be designed to "bridge" the gap, 
possibly with the use of catenary action or non -linear deflection effects, and allowing for considerable 
deflection.  
5.2.4  Special hazards  
5.2.4.1  In designing a structure to support loads occurring in the course of normal function, ensure that there  
is a reason able probability that the structure will not collapse disastrously as a result of misuse or  accident.  
5.2.4.2  Consider whether, due to the nature of a particular occupancy or use of a structure (e.g. flour mill, 
chemical plant, etc.), it will be necessary in the design concept or during a design reappraisal to consider the 
effect of a particular hazard, to ensure that, in the event of an accident, there is a reasonable probability that 
the structure will withstand the accident, even if damage does occur. In  such cases, partial safety factors may 
be required.  
5.2.4.3  No structure can be expected to withstand the excessive loads or forces that could arise owing to 
an extreme cause (such as an explosion), but the structure should not be damaged to an extent tha t is 
disproportionate to the original cause.  
5.2.5  Loads and strength of materials  
Use the design strength of materials and the design loads appropriate for the ultimate limit state.  
NOTE  In all the above cases;  the principles for limit state design are given in  RS 1 12.  
©RSB 2020  - All rights reserved                  12 
 5.3 Basic variables  
5.3.1  Actions and environmental influences  
5.3.1.1  Thermal effects  
5.3.1.1.1  Thermal effects should be taken into account when checking serviceability limit states.  
5.3.1.1.2  Thermal effects should be considered for ultimate limit states only wh ere they are significant (e.g. 
fatigue conditions, in the verification of stability where second order effects are of importance, etc). In other 
cases they need not be considered, provided that the ductility and rotation capacity of the elements are 
suffic ient. 
5.3.1.1.3  Where thermal effects are taken into account they should be considered as variable  actions and 
applied with a partial factor and ψ factor.  
NOTE  The values of ψ factor are given in  RS 1 12.  
 
5.3.1.2  Differential settlements/movements  
5.3.1.2.1  Differential settlements/movements of the structure due to soil subsidence should be classified as a 
permanent action, Gset which is introduced as such in combinations of actions. In general, Gset is represented 
by a set of values corresponding to differences (compared to a reference level) of settlements/movements 
between individual foundations or part of f oundations, dset,i (i denotes the number of the individual foundation 
or part of foundation).  
NOTE  Where differential settlements are taken into account, appropriate estimate values of predicted  settlements 
may be used.  
5.3.1.2.2  The effects of differentia l settlements should generally be taken into account for the verification for 
serviceability limit states.  
5.3.1.2.3  For ultimate limit states they should be considered only where they are significant (e.g. fatigue 
conditions, in the verification of stabil ity where second order effects are of importance, etc). In other cases for 
ultimate limit states they need not be considered, provided that the ductility and rotation capacity of the 
elements are sufficient.  
5.3.1.2.4  Where differential settlements are tak en into account a partial safety factor for settlement effects 
should be applied.  
5.3.1.3  Prestress  
5.3.1.3.1  The prestress considered in this standard is applied by tendons made of high -strength steel (wires, 
strands or bars).  
5.3.1.3.2  Tendons may be embedded in  the concrete. They may be pre -tensioned and bonded or post -
tensioned and bonded or unbonded.  DRS 142: 2020  
13                ©RSB 2020  - All rights reserved  
 5.3.1.3.3  Tendons may also be external to the structure with points of contact occurring at deviators and 
anchorages.  
5.3.2  Material and product properties  
5.3.2.1  Prop erties of materials (including soil and rock) or products should be represented by characteristic 
values.  
5.3.2.2  When a limit state verification is sensitive to the variability of a material property, upper and lower 
characteristic values of the material  property should be taken into account.  
5.3.2.3  Where a low value of material or product property is unfavourable, the characteristic value should be 
defined as the 5  % fractile value.  
5.3.2.4  Where a high value of material or product property is unfavoura ble, the characteristic value should be 
defined as the 95  % fractile value.  
5.3.2.5  Material property values shall be determined from standardised tests performed under specified 
conditions.  
5.3.2.6  Where an upper estimate of strength is required ( e.g. for capacity design measures and for the 
tensile strength of concrete for the calculation of the effects of indirect actions) a characteristic upper value of 
the strength should be taken into account.  
5.3.2.7  The reductions of the material strength or produc t resistance to be considered resulting from the 
effects of repeated actions can lead to a reduction of the resistance over time due to fatigue.  
5.3.2.8  The structural stiffness parameters ( e.g. moduli of elasticity, creep coefficients) and thermal 
expansi on coefficients should be represented by a mean value. Different values should be used to take into 
account the duration of the load.  
NOTE  In some cases, a lower or higher value than the mean for the modulus of elasticity may have to be taken into 
account (e.g. in case of instability).  
5.3.3  Shrinkage and creep  
5.3.3.1  Shrinkage and creep are time -dependent properties of concrete. Their effects should  generally be 
taken into account for the verification of serviceability limit states.  
5.3.3.2  The effects of shrin kage and creep should be considered at ultimate limit states only where their 
effects are significant, for example in the verification of ultimate limit states of stability where second order 
effects are of importance. In other cases these effects need not  be considered for ultimate limit states, 
provided that ductility and rotation capacity of the elements are sufficient.  
5.3.3.3  When creep is taken into account; its design effects should be evaluated under the quasi permanent 
combination of actions irresp ective of the design situation considered i.e. persistent, transient or accidental.  
NOTE  In most cases; the effects of creep may be evaluated under permanent loads and the mean value of prestress   
©RSB 2020  - All rights reserved                  14 
 5.3.4  Deformations of concrete  
5.3.4.1  The consequences of deforma tion due to temperature, creep and shrinkage shall be considered in 
design.  
5.3.4.2  The in fluence of these effects is normally accommodated by complying with the application rules of 
this Standard. Consideration should also be given to:  
a) minimising deformat ion and cracking due to early -age movement, creep and shrinkage  through the 
composition of the concrete mix;  
b) minimising restraints to deformation by the provision of bearings or joints;  
c) if restraints are present, ensuring that their influence is taken into  account in design  
5.3.5  Geometric data  
5.3.5.1  General  
5.3.5.1.1  Geometric data shall be represented by their characteristic values, or ( e.g. the case of imperfections) 
directly by their design values.  
5.3.5.1.2  The dimensions specified in the design may be taken as ch aracteristic values.  
5.3.5.1.3  Where their statistical distribution is sufficiently known, values of geometrical quantities that 
correspond to a prescribed fractile of the statistical distribution may be used.  
5.3.5.1.4  Tolerances for connected parts that  are made from different materials shall be mutually compatible.  
5.4 Verification by the partial factor method  
5.4.1  Design values  
5.4.1.1  Partial factor for shrinkage action  
Where consideration of shrinkage actions is required for ultimate limit state a partial factor, γ SH, should be 
used. The recommended value for  γSH is 1.0.  
5.4.1.2  Partial factors for prestress  
5.4.1.2.1  Prestress in most situations is intended to be favourable and for the ultimate limit state verification 
the value of γ P,fav should be used. The design value of prestress may be based on  the mean value of the 
prestressing force (see RS  112). The recommended value for P,fav is 1.0. This value can also be used for 
fatigue verification.  
5.4.1.2.2  In the verification of the limit state for stability with external pr estress, where an increase of the value 
of prestress can be unfavourable, P,unfav should be used.  The recommended value for global analysis is 1.3.  DRS 142: 2020  
15                ©RSB 2020  - All rights reserved  
 5.4.1.2.3  In the verification of local effects ; P,unfav  should also be used. The recommended value of P,unfav is 
1.2. 
5.4.1.3  Partial factor for fatigue loads  
The partial factor for fatigue loads is F,fat . The recommended value of F,fat  is 1.0. 
5.4.1.4  Partial factors for materials  
5.4.1.4.1   Partial factors for materials for ultimate limit states, C and S should be us ed. The recommended 
values for ‘persistent and transient’ and ‘accidental, design situations are given in Table 1.  
5.4.1.4.2   For fatigue verification the partial factors for persistent design situations given in Table 1 are 
recommended for the values of C,fat and S,fat. 
5.4.2  Materials  
When assessing the strength of a structure or of any part thereof, take the appropriate values of γm as follows:  
a) reinforcement: γm = 1.15;  
b) concrete in flexure or axial load: γm = 1.50;  
c) shear strength without shear reinforcement  and shear taken by concrete in combination with shear 
reinforcement: γm = 1.40;  
d) bond strength: γm = 1.40;  
e) others (e.g. bearing stresses): γm > 1.50.  
NOTE  When considering the effects of excessive loads or localized damage, take values of γm as 1.3 for co ncrete and 1.0 
for steel.  
Table 1  — Partial factors for materials for ultimate limit states  
Design situations  C for concrete  S for reinforcing steel  S for prestressing steel  
Persistent and transient  1.5 1.15 1.15 
Accidental  1.2 1.0 1.0 
 
5.4.1.4.3   The values for partial factors for materials for serviceability limit state verification should be taken 
as those given in the particular clauses of this standard.  The recommended value for situations not covered by 
particular clauses of this standard is 1 .0. 
5.4.1.4.4   Lower values of C and S may be used if justified by measures reducing the uncertainty in the 
calculated resistance.   
©RSB 2020  - All rights reserved                  16 
 5.4.2.1  Partial factors for materials for foundations  
5.4.1.5.1   Design values of strength properties of the ground should be calcula ted in accordance with RS 112  
5.4.1.5.2  The partial factor for concrete γ C given in 5.4.1.4 (1)  should be multiplied by a factor, kf, for 
calculation of design resistance of cast in place piles without permanent casing.  The recommended value of kf 
is 1.1.  
5.4.3  Combinations of actions  
5.4.2.1  The gene ral formats for combinations of actions for the ultimate and serviceability limit states are 
given in RS 1 12. 
5.4.2. 2 For each permanent action either the lower or the upper design value (whichever gives the more 
unfavourable effect) should be applied thro ughout the structure (e.g. self -weight in a structure).  
5.4.4  Verification of static equilibrium - EQU  
The reliability format for the verification of static equilibrium also applies to design situations of EQU, such as 
holding down devices or the verification of  the uplift of bearings for continuous beams.  
5.5 Design assisted by testing  
5.5.1  The design of structures or structural elements may be assisted by testing.  
NOTE  Information is given RS 1 12. 
5.6 Supplementary requirements for foundations  
5.6.1  Where ground -struc ture interaction has significant influence on the action effects in the structure, the 
properties of the soil and the effects of the interaction shall be taken into account in accordance with RS 113. 
5.6.2  Where significant differential settlements are lik ely, their influence on the action effects in the 
structure should be checked.  
5.6.3  Concrete foundations should be sized in accordance with RS 1 13. 
5.6.4  Where relevant, the design should include the effects of phenomena such as subsidence, heave, 
freezin g, thawing, erosion, etc.  
5.7 Requirements for fastenings  
The local and structural effects of fasteners should be considered .The requirements for the design of 
fastenings for use in concrete should include the following types of fasteners:  
a) headed anchors,  DRS 142: 2020  
17                ©RSB 2020  - All rights reserved  
 b) expa nsion anchors,  
c) undercut anchors,  
d) concrete screws,  
e) bonded anchors,  
f) bonded expansion anchors and  
g) bonded undercut anchors.  
NOTE  Design of Fastenings for use in concrete includes the local transmission of loads into the structure.  
6 Materials  
6.1 Concrete  
6.1.1  General  
The following clauses give principles and rules for normal and high strength concrete.  
6.1.2  Strength  
6.1.2.1  The compressive strength of concrete is denoted by concrete strength classes which relate to the 
characteristic (5  %) cylinder strength fck or the cube st rength fck,cube , in accordance with RS EAS 417 -2. 
6.1.2.2  The strength classes in this code are based on the characteristic cylinder strength fck determined at 
28 days with a maximum value of Cmax. The recommended value of Cmax is C90/105 . 
6.1.2.3  The char acteristic strengths for fck and the corresponding mechanical characteristics  necessary for 
design, are given in Table 2.  
6.1.2.4  In certain situations (e.g. prestressing) it may be appropriate to assess the compressive strength for 
concrete before or afte r 28 days depending on the conditions under which test specimens were stored.  If the 
concrete strength is determined at an age t > 28 days the values α cc and α ct defined in 6.1.6 .1  and 6.1.6 .2  
should be reduced by a factor kt. The recommended value of kt is 0.85.  
6.1.2.5  It may be required to specify the concrete compressive strength, fck(t), at time t for a  number of 
stages (e.g. demoulding, transfer of prestress), where  
fck(t) = fcm(t) - 8 (MPa) for 3 < t < 28 days.  
fck(t) = fck for t ≥ 28 days  
More pr ecise values should be based on tests especially for t ≤ 3 days   
©RSB 2020  - All rights reserved                  18 
 6.1.2.6  The compressive strength of concrete at an age t depends on the type of cement, temperature and 
curing conditions. For a mean temperature of 20°C and curing in accordance with RS ISO 1 920-3, the 
compressive strength of concrete at various ages fcm(t) may be estimated from Expressions (6.1) and (6.2).  
 
fcm(t) = βcc(t) fcm                                                                                                          (6.1)                                                                                                                                                             
 
                                                                        ( 6.2)  
where:  
fcm(t) is the mean  concrete compressive strength at an age of t days  
fcm is the mean compressive strength at 28 days according to Table 2  
βcc(t)  is a coefficient which depends on the age of the concrete t 
t  is the age of the concrete in days  
s  is a coefficient which depends on the type of cement:  
           = 0.20 for cement of strength Classes CEM 42 .5 R, CEM 52 .5 N and CEM 52 .5 R 
          (Class R)  
           = 0.25 for cement of strength Classes CEM 32 .5 R, CEM 42 .5 N (Class N)  
           = 0.38 for cement of strength Classes CEM 32 .5 N (Class S)  
NOTE  exp{ } has the same meaning as e( ). 
6.1.2.7  Where the concrete does not conform with  the specification for compressive strength at 28 days, the 
use of Expressions (6.1) and (6.2) is not appropriate.  This clause should not be used retrospectively to justify 
a non conforming reference strength by a later increase of the strength.  
6.1.2.8  The tensile strength refers to the highest stress reached under concentric tensile loading.  For the 
flexural tensile strength reference should be made to 6.1.8 (1).  
6.1.2.9  Where the tensile strength is determined as the splitting tensile strength, fct,sp, an approximate value 
of the axial tensile strength, fct, may be taken as:  
fct = 0,9 fct,sp                                                                                                         (6.3)                                                                                                                                                         
6.1.2.10  The development of tensile strength with time is strongly influenced by curing and drying conditions 
as well as by the dimensions of the structural memb ers. As a first approximation it may be assumed that the 
tensile strength f ctm(t) is equal to:  DRS 142: 2020  
19                ©RSB 2020  - All rights reserved  
 fctm(t)=(βcc(t))α.fctm                                                                                                 (6.4)                                                                                                                                           
where 
βcc(t) follows from Expression (6.2) and  
α = 1 for t < 28 
α = 2/3 for t ≥ 28. The values for fctm are given in Table 2.  
NOTE  Where the development of the tensile strength with time is important; it is recommended that tests are carried 
out taking into account the exposure conditions and the dimensions of the structural member.  
6.1.3  Elastic deformation  
6.1.3.1  The elastic deformations of concrete largely depend on its composition (especially the aggregates). 
The values given in this Standard should be regarde d as indicative for general applications. However, they 
should be specifically assessed if the structure is likely to be sensitive to deviations from these general values.  
6.1.3.2  The modulus of elasticity of a concrete is controlled by the moduli of elast icity of its  components. 
Approximate values for the modulus of elasticity Ecm, secant value between σ c = 0 and 0 .4fcm, for concretes 
with quartzite aggregates, are given in Table 2. For sandstone aggregates the value should be reduced by 30  
%. For basalt a ggregates the value should be increased by 20  %. 
Table 2 — Strength and deformation characteristics for concrete  
Strength classes for concrete  Analytical relation  
/ Explanation  
fck (MPa)  12 16 20 25 30 35 40 45 50 55 60 70 80 90  
fck,cube 
(MPa)  15 20 25 30 37 45 50 55 60 67 75 85 95 105 2.8 
fcm (MPa)  20 24 28 33 38 43 48 53 58 63 68 78 88 98 fcm = fck+8 (MPa)  
fctm (MPa)  1.6 1.9 2.2 2.6 2.9 3.2 3.5 3.8 4.1 4.2 4.4 4.6 4.8 5.0 fctm=0 .30×fck(2/3) 
≤C50/60  
fctm=2 .12·In(1+(fcm/10)
) > C50/60  
fctk,0,05 
(MPa)  1.1 1.3 1.5 1.8 2.0 2.2 2.5 2.7 2.9 3.0 3.1 3.2 3.4 3.5 fctk;0,05 = 0,7×fctm  
5% fractile  
fctk,,095  
(MPa)  2.0 2.5 2.9 3.3 3.8 4.2 4.6 4.9 5.3 5.5 5.7 6.0 6.3 6.6 fctk;0 .95 = 1,3×fctm  
95 % fractile  
Ecm (GPa)  27 29 30 31 33 34 35 36 37 38 39 41 42 44 Ecm = 22[(fcm)/10]0 .3 
(fcm in MPa)  
c1 (0/00)  1.8 1.9 2.0 2.1 2.2 2.25 2.3 2.4 2.45 2.5 2.6 2.7 2.8 2.8 see Figure 3.2  
εc1 (0/00) = 0 .7 fcm0 .31 
cu1(0/00)  3.5 2.2 3.0 2.8 2.8 2.8 see Figure  2 
for fck ≥ 50 Mpa  
εc1(0/00)=2 .8+27[(98 -
fcm)/100]4  
cu2 (0/00)  2.0 2.2 2.3 2.4 2.5 2.6 see Figure 3  
for fck ≥ 50 Mpa   
©RSB 2020  - All rights reserved                  20 
 εc2(0/00)=2 .0+0.085(fc
k-50)0.53 
cu2 (0/00)  3.5 3.1 2.9 2.7 2.6 2.6 see Figure 3  
for fck ≥ 50 Mpa  
cu2(0/00)=2 .6+35[(90 -
fck)/100]4  
N 2.0 1.75 1.6 1.45 1.4 1.4 for fck≥ 50 Mpa  
n=1.4+23 .4[(90 - 
fck)/100]4  
cu3 (0/00)  1.75 1.8 1.9 2.0 2.2 2.3 see Figure 4  
for fck≥ 50 Mpa  
εc3(0/00)=1 .75+0 .55[(fc
k-50)/40]  
cu3 (0/00)  3.5 3.1 2.9 2.7 2.6 2.6 see Figure 4  
for fck ≥ 50 Mpa  
εcu3(0/00)=2 .6+35[(90 -
fck)/100]4  
6.1.3.3  Variation of the modulus of elasticity with time can be estimated by:  
Ecm(t) = (fcm(t) / fcm)0.3 Ecm                                                                                                 (6.5)                                                                                                                    
Where  
Ecm(t) and fcm(t) are the values at an age of t days and  
Ecm and fcm are the values determined at an age of 28 days.  
The relation between fcm(t) and fcm follows from Expression (6.1).  
6.1.3.4  Poisson’s ratio may be taken equal to 0.2 for uncracked concrete and 0 for cracked  concrete.  
6.1.3.5  Unless more accurate information is available, the linear coefficient of thermal expansion may be 
taken equal to 10 .10-6 K -1. 
6.1.4  Creep and shrinkage  
6.1.4.1  Creep and shrinkage of the concrete depend on the ambient humidity, the dimensions of the element 
and the composition of the concrete. Creep is also influenced by the maturity of the concrete when the load is 
first applied and de pends on the duration and magnitude of the loading.  
6.1.4.2  The creep coefficient, εcc (t,t0) is related to Ec, the tangent modulus, which may be taken as 1 .05 Ecm. 
Where great accuracy is not required, the value found from Figure 1 may be considered as th e creep 
coefficient, provided that the concrete is not subjected  to a compressive stress greater than 0 .45 fck (t0 ) at an 
age t0, the age of concrete at the time of loading.  
6.1.4.3  The creep deformation of concrete ε cc(∞,t0) at time t = ∞ for a constant compressive stress σ c applied 
at the concrete age t0, is given by:  DRS 142: 2020  
21                ©RSB 2020  - All rights reserved  
 εcc (∞,t0) = φ (∞, t0). (σ c /Ec)                                                                            (6.6)  
6.1.4.4  When the compressive stress of concrete at an age t0 exceeds the val ue 0.45 fck(t0) then creep non -
linearity should be considered. Such a high stress can occur as a result of pretensioning, e.g. in precast 
concrete members at tendon level. In such cases the non -linear notional creep coefficient should be obtained 
as follow s: 
φnl= φ(∞, t0) exp (1 .5 (kσ – 0,45))                                                                   (6.7)  
where:  
φnl  is the non -linear notional creep coefficient, which replaces φ (∞, t0) 
kσ  is the stress -strength ratio σc/f (t0), where σc is the compr essive stress and  
f 0 (t ) is the characteristic concrete compressive strength at the time of loading  
 
 
a) inside conditions - RH = 50%  
 
NOTE  
a) intersection point between lines 4 and 5 can also be above point 1  
b) for t0 > 100 it is sufficiently accurate to assu me t0 = 100 (and use the tangent line)  
  
©RSB 2020  - All rights reserved                  22 
 
 
b) outside conditions - RH = 80%  
Figure 1  — Method for determining the creep coefficient φ(∞, t0) for concrete  under  normal 
environmental conditions  
 
6.1.4.5  The values given in Figure 1 are valid for ambient temperatures between -40 °C and +40  °C and a 
mean relative humidity between RH = 40% and RH = 100%. The following symbols are used:  
φ (∞, t0) is the final creep coefficient  
t0 is the age of the concrete at time of loading in days  
h0 is the notional size = 2Ac /u, where Ac is the concrete cross -sectional area and u is the perimeter of  
that part which is exposed to drying  
S is Class S, acco rding to 6.1.2 (6)  
N is Class N, according to 6.1.2 (6)  
R  is Class R, according to 6.1.2 (6)  
6.1.4.6  The total shrinkage strain is composed of two components, the drying shrinkage strain and the 
autogenous shrinkage strain. The drying shrinkage strain dev elops slowly, since it is a function of the 
migration of the water through the hardened concrete. The autogenous shrinkage strain develops during 
hardening of the concrete: the major part therefore develops in the early days after casting. Autogenous 
shrin kage is a linear function of the concrete strength.  
6.1.4.7  It should be considered specifically when new concrete is cast against hardened concrete.  Hence the 
values of the total shrinkage strain ε cs follow from  
εcs = εcd + εca                                                                                                         (6.8)                                                                                                                                        
where:  
εcs is the total shrinkage strain  DRS 142: 2020  
23                ©RSB 2020  - All rights reserved  
 εcd is the drying shrinkage strain  
εca is the autogenous shrinkage strain  
The final value of the drying shrinkage strain, ε cd,∞ is equal to kh.εcd,0. εcd,0. may be taken from Table 3 
(expected mean values, with a coefficient of variation of about 30%).  
Table 3 − Nominal unrestrained drying shrinkage values ε cd,0 (in 0/00) for concrete  with cement CEM 
Class N  
fck/fck,cube  
(MPa)  Relative Humidity (in % ) 
20 40 60 80 90 100 
20/25  0.62 0.58 0.49 0.30 0.17 0.00 
40/50  0.48 0.46 0.38 0.24 0.13 0.00 
60/75  0.38 0.36 0.30 0.19 0.10 0.00 
80/95  0.30 0.28 0.24 0.15 0.08 0.00 
90/105  0.27 0.25 0.21 0.13 0.07 0.00 
The development of the drying shrinkage strain  in time follows from:  
εcd(t) = β ds(t, ts) . kh . εcd,0                                                                                                                                       (6.9) 
where:  
kh is a coefficient depending on the notional size h0 according to Table 4  
Table 4 — Values for kh in Expression (6.9)  
ho Kh 
100 1.0 
200 0.85 
300 0.75 
≥ 500  0.70 
 
                                                             ( 6.10)  
where:  
t  is the age of the concrete at the moment considered, in days  
ts is the age of the c oncrete (days) at the beginning of drying shrinkage (or swelling).  Normally this is at the end of curing.  
h0 is the notional size (mm) of the cross -section = 2 Ac /u  
©RSB 2020  - All rights reserved                  24 
 where:  
Ac  is the concrete cross -sectional area  
U  is the perimeter of that part of the cro ss section which is exposed to drying  
The autogenous shrinkage strain follows from:  
εca (t) = βas( t) εca(∞)                                                                                                      (6.11)  
where:  
εca(∞) = 2,5 ( fck – 10) 10-6                                                                                                (6.12)  
and 
βas(t) =1 – exp ( – 0,2t 0,5)                                                                                                 (6.13)  
where t is given in days.  
6.1.5  Stress -strain relation for non -linear structural analysis  
 
6.1.5.1  The relation between σ c and ε c shown in Figure 2 (compressive stress and shortening strain shown 
as absolute values) for short term uniaxial loading is described by the Expression (6.14):  
 
                                                                                                 (6.14)  
where:  
η εc /εc1 
εc1  is the strain at peak stress according to Table 1  
k 1.05 Ecm × |ε c1| /fcm (fcm according to Table 1)  
Expression (6.14) is valid for 0 < | ε c| < |εc u1| where ε cu1 is the nominal ultimate strain.  
6.1.5.2  Other id ealised stress -strain relation may be applied, if they adequately represent the behaviour of 
the concrete considered.  DRS 142: 2020  
25                ©RSB 2020  - All rights reserved  
 
 
Figure 2 — Schematic representation of the stress -strain relation for structural  analysis (the use 0,4 fcm 
for the definition of Ecm is approximate).  
6.1.6  Design compressive and tensile strengths  
6.1.6.1  The value of the design compressive strength is defined as  
fcd = α cc fck / C                                                                                                              (6.15)                                                                                                                                               
where , 
C  is the partial safety factor for concrete, see 5.4.1.4, and  
αcc  is the coefficient taking account of long term effects on the compressive strength and of unfavourable 
effects resulting from the way the load is applied.  
NOTE  The recommended value of α cc is 1. 
6.1.6.2  The value of the design tensile strength, fctd, is defined as  
fctd = α ct fctk,0,05 / C                                                                                                         (6.16)                                                                                                                                      
where: 
C  is the partial safety factor for concrete, see 5.4.1.4, and  
αct is a coefficient taking account of long term effects on the tens ile strength and of  unfavourable effects, 
resulting from the way the load is applied.  
NOTE  The recommended value of α ct is 1.0. 
6.1.7  Stress -strain relations for the design of cross -sections  
6.1.7.1  For the design of cross -sections, the following stress -strain r elationship may be used, see Figure 3 
(compressive strain shown positive):   
©RSB 2020  - All rights reserved                  26 
 
for 0  c  c2                                                                              (  6.17)  
                                                               (6.18)  
Where, 
n  is the exponent according to Table 2  
εc2  is the strain at reaching the maximum strength according to Table 2.  
εcu2  is the ultimate strain according to Table 2.  
 
Figure 3 — Parabola -rectangle diagram for concrete under compression  
6.1.7.2  Other simplified stress -strain relationships may be used if equivalent to or more  conser vative than 
the one defined in 6.1.7. 1, for instance bi -linear according to Figure 4  (compressive stress and shortening 
strain shown as absolute values) with values of ε c3 and ε cu3 according to Table 2.  DRS 142: 2020  
27                ©RSB 2020  - All rights reserved  
 
 
Figure 4 — Bi-linear stress -strain relation  
6.1.7.3  A rectangular stress distribution (as given in Figure 5) may be assumed. The factor λ,  defining the 
effective height of the compression zone and the factor η, defining the effective  strength, follow from:  
λ = 0 .8 for fck ≤ 50 MPa                                                                                         (6.19)  
λ = 0 .8 - (fck -50)/400 for 50 < fck ≤ 90 MPa                                                           (6.20)  
and 
η = 1 .0 for fck ≤ 50 MPa                                                                                          (6.21)  
η = 1 .0 - (fck -50)/200 for 50 < fck ≤ 90 MPa                                                            (6.22)  
NOTE  If the width of the compression zone decreases in the  direction of the extreme compression fibre, the value η 
fcd should be reduced by 10  %. 
 
Figure 5 — Rectangular stress distribution   
©RSB 2020  - All rights reserved                  28 
 6.1.8  Flexural tensile strength  
The mean flexural tensile strength of reinforced concrete members depends on the mean axial tensi le 
strength and the depth of the cross -section. The following relationship may be used:  
fctm,fl = max {(1,6 - h/1000) fctm; fctm }                                                                       (6.23)  
where:  
h  is the total member depth in mm  
fctm is the mean axial tensile strength following from Table 2.  
The relation given in Expression (6.23) also applies for the characteristic tensile strength values.  
6.1.9  Confined concrete  
6.1.9.1  Confinement of concrete results in a modification of the effective stres s-strain relationship:  higher 
strength and higher critical strains are achieved. The other basic material characteristics may be considered 
as unaffected for design.  
6.1.9.2  In the absence of more precise data, the stress -strain relation shown in Figure 6  (compressive strain 
shown positive) may be used, with increased characteristic strength and strains according to:  
fck,c = fck (1,000 + 5,0 σ 2/fck) for σ 2 ≤ 0,05 fck                                                              (6.24)                                                                                   
fck,c = fck (1,125 + 2,50 σ 2/fck) for σ 2 > 0,05 fck                                                            (6.25)                                                                                  
εc2,c = εc2 (fck,c/fck)2                                                                                                      (6.26)                                                                                                                                                 
εcu2,c = εcu2 + 0,2 σ 2/fck                                                                                                (6.27)                                                                                                                               
where , 
σ2 (= σ 3) is the effective lateral compressive stress at the ULS due to confinement and ε c2 and ε cu2 follow from 
Table 2. Confinement can be generated by adequately closed links or cross -ties, which reach the plastic 
condition due to lateral extension of the concrete . 
 
Figure 6 −Stress -strain relationship for confined concrete  
 DRS 142: 2020  
29                ©RSB 2020  - All rights reserved  
 6.2 Reinforcing steel  
6.2.1  Gener al 
6.2.1.1  The following clauses give principles and rules for reinforcement which is in the form of bars, de -
coiled rods, welded fabric and lattice girders. They do not apply to specially coated bars.  
6.2.1.2  The requirements for the properties of the rei nforcement are for the material as placed in the 
hardened concrete. If site operations can affect the properties of the reinforcement, then those properties shall 
be verified after such operations.  
6.2.2  Properties  
6.2.2.1  The behaviour of reinforcing steel is s pecified by the following properties:  
a) yield strength ( fyk or f0,2k) 
b) maximum actual yield strength ( fy,max) 
c) tensile strength ( ft) 
d) ductility ( εuk and ft/fyk) 
e) bendability  
f) bond characteristics  
g) section sizes and tolerances  
h) fatigue strength  
i) weldability  
j) shear an d weld strength for welded fabric and lattice girders  
6.2.2.2  This standard applies to ribbed and weldable reinforcement, including fabric. The  permitted welding 
methods are given in Table 5.  
NOTE  The properties of reinforcement required for use with this standard are given in Annex A.  
6.2.2.3   The application rules for design and detailing in this standard are valid for a specified yield strength 
range, fyk = 400 to 600 MPa.  
6.2.2.4  The surface characteristics of ribbed bars shall be such to ensure adequat e bond with the concrete.  
6.2.2.5  Adequate bond may be assumed by compliance with the specification of projected rib area, fR.  
©RSB 2020  - All rights reserved                  30 
 NOTE  Minimum values of the relative rib area, fR, are given in the Annex A . 
6.2.2.6  The reinforcement shall have adequate bendabi lity to allow the use of the minimum  mandrel 
diameters and to allow rebending to be carried out.  
NOTE  For bend and rebend requirements see Annex A . 
6.2.3  Strength  
6.2.3.1  The yield strength fk (or the 0.2% proof stress, f0,2k) and the tensile strength ftk are d efined 
respectively as the characteristic value of the yield load, and the characteristic maximum load in direct axial 
tension, each divided by the nominal cross sectional area.  
6.2.4  Ductility characteristics  
The reinforcement shall have adequate ductility as d efined by the ratio of tensile strength  to the yield stress, 
(ft/fy)k and the elongation at maximum force, ε uk . 
NOTE  Values of k= (ft/fy)k and εuk for Class A, B and C are given in Annex A.  
 
a) Hot rolled steel                                                         b) Cold worked  steel  
 
Figure 7  — Stress -strain diagrams o f typical reinforcing steel (absolute values are  shown for tensile 
stress and strain)  
6.2.5  Welding  
6.2.5.1  Welding processes for reinforcing bars shall be in accordance with Table 5.  
Table 5 — Permitted welding processes and examples of application  
Loading case  Welding method  Bars in tension1 Bars in compression1 
Predominantly  flash -welding  butt joint  DRS 142: 2020  
31                ©RSB 2020  - All rights reserved  
 static  
 manual metal arc welding 
and metal arc welding with 
filling electrode  butt joint with  ≥ 20 mm, splice, lap, cruciform  
joints3, joint with other steel members  
metal arc active welding  2 
 splice, lap, cruciform  3 joints & joint with other  
steel members  
- butt joint with  ≥ 20 mm  
friction welding  butt joint, joint with other steels  
resistance spot welding  lap joint  4 
cruciform joint  2, 4 
Not predominantly  
static  flash -welding  butt joint  
manual metal arc welding  - butt joint with  ≥ 14 mm 
metal arc active welding2 - butt joint with  ≥ 14 mm 
resistance spot welding  lap joint  4 
cruciform joint  2, 4 
1 Only bars with approximately the same nominal diameter may be welded together.  
2 Permitted ratio of mixed diameter bars ≥ 0 .57 
3 For bearing joints  ≤ 16 mm  
4 For bearing joints  ≤ 28 mm  
 
6.2.5.2  All welding of reinforcing bars  shall be carried out in accordance with ISO 17660 . 
6.2.5.3  The strength of the welded joints along the anchorage length of welded fabric shall be sufficient to 
resist the design forces.  
6.2.5.4  The strength of the welded joints of welded fabric may be ass umed to be adequate if each welded 
joint can withstand a shearing force not less than 25  % of a force equivalent to the specified characteristic 
yield stress times the nominal cross sectional area. This force should be based on the area of the thicker wire  
if the two are different.  
6.2.6  Fatigue  
Where fatigue strength is required it shall be verified in accordance with ISO 17660.  
NOTE  Information is given in Annex A . 
6.2.7  Design assumptions  
6.2.7.1  Design should be based on the nominal cross -section area of the reinfo rcement and the design 
values derived from the characteristic values given in 6.2.2.  
6.2.7.2  For normal design, the recommended value of a strain limit ( εud) is 0  9εuk and that of a maximum 
stress (K= ( ft/fy)k ) is given in Annex A . 
6.2.7.3  The mean value of density may be assumed to be 7850 kg/m3  
©RSB 2020  - All rights reserved                  32 
 6.2.7.4  The design value of the modulus of elasticity, Es may be assumed to be 200 GPa.  
6.3 Prestressing steel  
6.3.1  General 
6.3.1.1  This clause applies to wires, bars and strands used as prestressing tendons in concrete structures.  
6.3.1.2  Prestressing tendons shall have an acceptably low level of susceptibility to stress  corrosion.  
6.3.1.3  For steels complying with this s tandard, tensile strength, 0 .1% proof stress, and  elongation at 
maximum load are specified in terms of characteristic values; these values are designated respectively fpk, 
fp0,1k and εuk. 
6.3.1.4  Each product shall be clearly identifiable with respect to the classification system in 6.3.2  
6.3.1.5  The prestressing tendons shall be classified for relaxation purposes according to 6.3.2  
6.3.1.6  Each consignment shall be accompanied by a certificate containing all the information necessary for 
its identification with r egard to (i) - (iv) in 6.3.2.2  and additional information where necessary.  
6.3.1.7  There shall be no welds in wires and bars. Individual wires of strands may contain  staggere d welds 
made only before cold drawing.  
6.3.2   Properties  
6.3.2.1  The properties of prestressing steel are given in RS ISO 6934 -1 
6.3.2.2  The prestressing tendons (wires, strands and bars) shall be classified according to:  
a) Strength, denoting the value of the 0 .1% proof stress ( fp0.1k) and the value of the ratio of tensile 
strength to proof strength ( fpk /fp0.1k) and elongation at maximum load (ε uk) 
b) Class, indicating the relaxation behaviour  
c) Size 
d) Surface characteristics.  
6.3.2.3  The actual mass of the prestressing tendons shall not differ from the nominal mass by more than the 
limits specified in RS ISO 6934 -4  
6.3.2.4  In this standard, three classes of relaxation are defined:  
a) Class 1: wire or strand - ordinary relaxation  DRS 142: 2020  
33                ©RSB 2020  - All rights reserved  
 b) Class 2: wire or strand - low relaxation  
c) Class 3: hot rolled and processed bars ( see RS ISO 6934 -5) 
6.3.2.5  The design calculations for the losses due to relaxation of the prestressing steel should be based on 
the value of ρ1 000, the relaxation loss (in %) at 1  000 hours after tensioning and at a mean temperature of 20 
°C. 
NOTE  The value of ρ1 000 is expressed as a percentage ratio of the initial stress and is obtained for an initial stress 
equal to 0 .7fp, where fp is the a ctual tensile strength of the prestressing steel samples. For design calculations, the 
characteristic tensile strength ( fpk) is used and this has been taken into account in the following expressions.  
6.3.2.6  The values for ρ 1 000 can be either assumed equa l to 8  % for Class 1, 2, 5  % for Class 2, and 4  % for 
Class 3, or taken from the certificate.  
6.3.2.7  The relaxation loss may be obtained from the manufacturers test certificates or defined as the 
percentage ratio of the variation of the prestressing stres s over the initial prestressing stress, should be 
determined by applying one of the expressions below.  
Note  Expressions (6.27) and (6.28) apply for wires or strands for ordinary prestressing and low relaxation tendons 
respectively, whereas Expression (6.2 9) applies for hot rolled and processed bars.  
        (6.27)  
 
        (6.28)  
 
          (6.29)  
Where  
Δσpr is absolute value of the relaxation losses of the prestress  
σpi  For post -tensioning σpi  is the absolute value of the initial prestress σ pi = σ pm0  
For pre -tensioning;   
©RSB 2020  - All rights reserved                  34 
 σpi is the maximum tensile stress applied to the tendon minus  the immediate losses occurred during the 
stressing process  
t is the time after tensioning (in hours)  
μ  σpi /fpk, where fpk is the characteristic value of the tensile str ength of the prestressing steel  
ρ1c000  is the value of relaxation loss (in %), at 1  000 hours after tensioning and at a mean temperature of 20  
°C. 
6.3.2.8  The long term (final) values of the relaxation losses may be estimated for a time t equal to 500 000  
hours (i.e. around 57 years).  
6.3.2.9  Relaxation losses are very sensitive to the temperature of the steel. Where heat treatment 50  °C the 
relaxation losses should be verified.  
6.3.3  Strength  
6.3.3.1  The 0 .1% proof stress ( fp0.1k ) and the specified value of th e tensile strength ( fpk) are defined as the 
characteristic value of the 0 .1% proof load and the characteristic maximum load in axial tension respectively, 
divided by the nominal cross sectional area as shown in Figure 8.  
 
Figure 8 — Stress -strain diagram for typical prestressing steel (absolute values  are shown for tensile 
stress and strain)  
6.3.4  Ductility characteristics  
6.3.4.1  The prestressing tendons shall have adequate ductility, as specified in RS ISO 6934 -4. 
6.3.4.2  Adequate ductility in elongation may b e assumed if the prestressing tendons obtain the specified 
value of the elongation at maximum load given in RS ISO 6934 -4 . DRS 142: 2020  
35                ©RSB 2020  - All rights reserved  
 6.3.4.3  Adequate ductility in bending may be assumed if the prestressing tendons satisfy the  requirements 
for bendability of RS ISO 15630 -3. 
6.3.4.4  Stress -strain diagrams for the prestressing tendons, based on production data, shall be prepared and 
made available by the producer as an annex to the certificate accompanying the consignment (see 6.3.1 9). 
6.3.4.5  Adequate ductility in te nsion may be assumed for the prestressing tendons if f pk /fp0,1k ≥ k. 
NOTE  The recommended value of k is 1,1.  
6.3.5  Fatigue  
6.3.5.1  Prestressing tendons shall have adequate fatigue strength as per the requirements of Annex A of RS 
ISO 6934 -1) 
6.3.5.2  The fatigue stress range for prestressing tendons shall be in accordance wit h RS ISO 6934 -1  
6.3.6  Design assumptions  
6.3.6.1  Structural analysis is performed on the basis of the nominal cross -section area of the prestressing 
steel and the characteristic values fp0.1k, fpk and εuk. 
6.3.6.2  The design value for the modulus of elasticity,  Ep may be assumed equal to 205 GPa for wires and 
bars. The actual value can range from 195 GPa to 210 GPa, depending on the  manufacturing process. 
Certificates accompanying the consignment should give the  appropriate value.  
6.3.6.3  The design value for th e modulus of elasticity, Ep may be assumed equal to 195 GPa for strand. The 
actual value can range from 185 GPa to 205 GPa, depending on the manufacturing process. Certificates 
accompanying the consignment should give the appropriate value.  
6.3.6.4  The mea n density of prestressing tendons for the purposes of design may normally be taken as 7850 
kg/m3 
6.3.6.5  The values given above may be assumed to be valid within a temperature range between -40 °C and 
+100  °C for the prestressing steel in the finished stru cture.  
6.3.6.6.6  The design value for the steel stress, fpd, is taken as fp0.1k/γS . 
NOTE  The recommended value of ε ud is 0.9εuk. If more accurate values are not known the recommended values are 
εud = 0.02 and fp0.1k /fpk = 0.9. 
7 Durability and cover to reinforcement  
7.1 General  
7.1.1   A durable structure shall meet the requirements of se rviceability, strength and stability throughout its 
design working life, without significant loss of utility or excessive unforeseen maintenance (for general 
requirements see also RS 471).   
©RSB 2020  - All rights reserved                  36 
 7.1.2  The required protection of the structure shall be established  by considering its intended use, design 
working life (see RS 471), maintenance programme and actions.  
7.1.3  The possible significance of direct and indirect actions, environmental conditions and consequential 
effects shall be considered.  
7.1.4  Corrosion p rotection of steel reinforcement depends on density, quality and thickness of concrete 
cover and cracking . The cover density and quality is achieved by controlling the maximum water/cement ratio 
and minimum cement content (see EAS 417 -1) and may be relate d to a minimum strength class of concrete.  
7.1.5  Where metal fastenings are inspectable and replaceable, they may be used with protective coatings 
in exposed situations. Otherwise, they should be of corrosion resistant material.  
7.1.6  Further requirements to those given in this clause should be considered for special  situations (e.g. for 
structures of temporary or monumental nature, structures subjected to extreme or unusual actions etc.).  
7.2 Environmental conditions  
7.2.1  Exposure conditions are chemical and physical conditions to which the structure is  exposed in 
addition to the mechanical actions.  
7.2.2  Environmental conditions are classified according to Table 6 , based on RS EAS 417 -1. 
7.2.3  In addition to the conditions in Table 6 , particular forms of aggr essive or indirect action should be 
considered including chemical attack arising from:  
a) the use of the building or the structure (storage of liquids, etc)  
b) solutions of acids or sulfate salts (RS EAS 417 -1, ISO 9690)  
c) chlorides contained in the concrete (RS E AS 417 -1) 
d) alkali -aggregate reactions (RS EAS 417 -1) physical attack,   
e) arising from e.g.  
f) temperature change  
g) abrasion  
h) water penetration (RS EAS 417 -1). 
 
Table 6  — Exposure classes related to environmental conditions in accordance  With RS EAS 417 -1 
Class de signation  Description of the environment  Informative examples where DRS 142: 2020  
37                ©RSB 2020  - All rights reserved  
 exposure classes may occur  
1 no risk of corrosion or attack  
XO For concrete without reinforcement 
or embedded metal: all exposures 
except where  there is freeze/thaw, 
abrasion or chemical  attack . For 
concrete with reinforcement or 
embedded  metal: very dry  Concrete inside buildings with very 
low air humidity  
2 Corrosion induced by carbonation  
XC1 Dry or permanently wet  Concrete inside buildings with low air 
humidity  
Concrete permanently s ubmerged in 
water  
XC2 Wet, rarely dry  Concrete surfaces subject to long -
term watercontact  
Many foundations  
XC3 Moderate humidity  Concrete inside buildings with 
moderate or high air  
humidity  
External concrete sheltered from rain  
XC4 Cyclic wet and dry  Concrete surfaces subject to water 
contact, not  
within exposure class XC2  
3 Corrosion induced by chlorides  
XD1 Moderate humidity  Concrete surfaces exposed to 
airborne chlorides  
XD2 Wet, rarely dry  Swimming pools  
Concrete components exposed to 
industrial w aters  
containing chlorides  
XD3 Cyclic wet and dry  Parts of bridges exposed to spray 
containing chlorides  
Pavements  
Car park slabs  
4 Freeze/Thaw Attack  
XF1 Moderate water saturation, without 
de-icing 
agent  Vertical concrete surfaces exposed 
to rain and f reezing  
XF2 Moderate water saturation, with de -
icing agent  Vertical concrete surfaces of road 
structures exposed to freezing and 
airborne de -icing agents  
XF3 High water saturation, without de -
icing agents  Horizontal concrete surfaces 
exposed to rain and freezing  
XF4 High water saturation with de -icing 
agents or  
sea water  Road and bridge decks exposed to 
de-icing agents  
Concrete surfaces exposed to direct 
spray containing de -icing agents and 
freezing   
©RSB 2020  - All rights reserved                  38 
 splash zone of marine structures 
exposed to freezing  
5 Chemical attack  
XA1 Slightly aggressive chemical 
environment  
according to RS EAS417 -1, Table A1  Natural soils and ground water  
XA2 Moderately aggressive chemical 
environment  
according to RS EAS 417 -1, Table 
A1 Natural soils and ground water  
XA3 Highly  aggressive chemical 
environment  
according to RS EAS 417 -1, Table 
A1 Natural soils and ground water  
7.2.4  The composition of the concrete affects both the protection of the reinforcement and the resistance of 
the concrete to attack. This may lead to the c hoice of higher strength classes than required for the structural 
design. In such cases the value of fctm should be associated with the higher strength in the calculation of 
minimum reinforcement and crack width control.  
7.3 Requirements for durability  
7.3.1  In order to achieve the required design working life of the structure, adequate measures shall be 
taken to protect each structural element against the relevant environmental actions.  
7.3.2  The requirements for durability shall be included when considering t he following:  
a) Structural conception,  
b) Material selection,  
c) Construction details,  
d) Execution,  
e) Quality Control,  
f) Inspection,  
g) Verifications,  
h) Special measures (e.g. use of stainless steel, coatings, cathodic protection).  DRS 142: 2020  
39                ©RSB 2020  - All rights reserved  
 7.4 Methods of verification  
7.4.1  Concrete cover  
7.4.1.1  Gene ral 
7.4.1.1.1  The concrete cover is the distance between the surface of the reinforcement closest to the nearest 
concrete surface (including links and stirrups and surface reinforcement where relevant) and the nearest 
concrete surface.  
7.4.1.1.2  The nomina l cover shall be specified on the drawings. It is defined as a minimum cover, cmin , plus an 
allowance in design for deviation, Δcdev: 
cnom = cmin + Δcdev                                                                                                            (7.1)                                                                                                                                           
7.4.1.2  Minimum cover, cmin 
7.4.1.2.1  Minimum concrete cover, cmin, shall be provided in order to ensure:  
a) the safe transmission of bond forces  
b) the protection of the steel against corrosion (durability)  
c) an adequate fire resistance  
7.4.1.2.2  The greater value for cmin satisfying the requirements for both bond and environmental conditions 
shall be used.  
cmin = max { cmin,b; cmin,dur + Δcdur,γ - Δcdur,st - Δcdur,add ; 10 mm}                                             (7.2)                              
where:  
cmin,b   is  the  minimum cover due to bond requirement,  
cmin,dur  is the  minimum cover due to environmental conditions,  
Δcdur,γ  is the additive safety element,  
Δcdur,st is the reduction of minimum cover for use of stainless steel,  
Δcdur,add is the reduction of minimum cover for use of additional protection,  
7.4.1.2.3  In order to transmit bond forces safely and to ensure adequa te compaction of the concrete, the 
minimum cover should not be less than cmin,b   given in Table 7.  
©RSB 2020  - All rights reserved                  40 
 Table 7  — Minimum cover, cmin,b, requirements with regard to bond  
Bond Requirement  
Arrangement of bars  Minimum cover cmin,b* 
Separated  Diameter of bar  
Bundled  Equivalent diameter ( ϕn) 
* If the nominal maximum aggregate size is greater than 32 mm, cmin,b should be increased by 5 mm.  
NOTE  The values of cmin,b for post -tensioned circular and rectangular ducts for bonded tendons, and the 
recommended values for pre -tensioned tendon are : 
1.5 x diameter of strand or plain wire  
2.5 x diameter of indented wire.  
The recommended values for post -tensioned ducts are:  
circular ducts: diameter rectangular ducts:  greater of the smaller dimension or half the greater dimension  
There is no requireme nt for more than 80 mm for either circular or rectangular ducts.  
7.4.1.2.4  The minimum cover values for reinforcement and pre -stressing tendons in normal weight concrete 
taking account of the exposure classes and the structural classes is given by cmin,dur . 
Table 8  — Recommended structural classification  
Structural Class  
Criterion  Exposure class according to table 6  
XO XC1 XC2/XC3  XC4 XD1 XD2/XS1  XD3/XS2/XS3  
Design Working Life of 
100 years  increase  
class by 2  increase  
class by 2  increase  
class by 2  increase  
class by 2  increase  
class by 2  increase  
class by 2  increase  
class by 2  
Strength Class 1) 2)  ≥ C30/37  
reduce  
class by 1  ≥ C30/37  
reduce  
class by 1  ≥ C35/45  
reduce  
class by 1  ≥ C40/50  
reduce  
class by 1  ≥ C40/50  
reduce  
class by 1  ≥ C40/50  
reduce  
class by 1  ≥ C45/55  
reduce class 
by 2 
Member with slab 
geometry  
(position of 
reinforcement  
not affected by 
construction  
process)  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  reduce class 
by 
1 
Special quality  
control of the concrete  
production ensured  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  reduce  
class by 1  
1 The strength class and w/c ratio are considered to be related values. A special composition (type of cement, w/c value, fine fillers) with the 
intent to produce low permeab ility may be considered.  
2 The limit may be reduced by one strength class if air entrainment of more than 4% is applied.  DRS 142: 2020  
41                ©RSB 2020  - All rights reserved  
  
Table 9 — Values of minimum cover, cmin,dur , requirements with regard to durability for  reinforcement 
steel  
Environmental Requiremen t for cmin,  dur (mm)  
Structural 
steel  Exposure Class according to Table 6  
X0 XC1 XC2/XC3  XC4 XD1/XS1  XD2/XS2  XD3/XS3  
S1 10 10 10 15 
 20 25 30 
S2 10 10 15 20 25 30 35 
S3 10 10 20 25 30 35 40 
S4 10 15 25 30 35 40 45 
S5 15 20 30 35 40 45 50 
S6 20 25 35 40 45 50 55 
Table 10 — Values of minimum cover, cmin,dur , requirements with regard to durability for  pre-stressing 
steel  
Environmental requirement for cmin,  dur (mm)  
Structural 
steel  Exposure Class according to Table 6  
X0 XC1 XC2/XC3  XC4 XD1/XS1  XD2/XS2  XD3/XS3  
S1 10 15 20 25 
 30 25 30 
S2 10 15 25 30 35 40 45 
S3 10 20 30 35 40 45 50 
S4 10 25 35 40 45 50 55 
S5 15 30 40 45 50 55 60 
S6 20 35 45 50 55 60 65 
 
7.4.1.2.5  The concrete cover should be increased by the additive safety element Δcdur,γ . 
NOTE  The recommended value of Δcdur,γ is 0 mm.  
7.4.1.2.6   Where stainless steel is used or where other special measures have been taken, the  minimum cover 
may be reduced by Δcdur,st. For such situations the effects on all relevant  material proper ties should be 
considered, including bond.  
NOTE  The recommended value of Δcdur,st  without further specification, is 0 mm.   
©RSB 2020  - All rights reserved                  42 
 7.4.1.2.7   For concrete with additional protection (e.g. coating) the minimum cover may be reduced by  
Δcdur,add . 
NOTE  The recommended  value of Δcdur,add , without further specification, is 0 mm.  
7.4.1.2.8  Where in -situ concrete is placed against other concrete elements (precast or in -situ) the minimum 
concrete cover of the reinforcement to the interface may be reduced to a value correspo nding to the 
requirement for bond (see (3) above) provided that:  
a) the strength class of concrete is at least C25/30,  
b) the exposure time of the concrete surface to an outdoor environment is short (< 28 days),  
c) the interface has been roughened.  
7.4.1.2.9   For u neven surfaces (e.g. exposed aggregate) the minimum cover should be increased by at least 
5mm.  The cover should be increased so that the nominal cover is taken from the highest point of the uneven 
surface. Also include minimum cover requirements of 40mm if  casting against prepared ground/blinding and 
75mm when casting directly against unprepared soil.  
7.4.1.2.10  Where freeze/thaw or chemical attack on concrete (Classes XF and XA) is expected special 
attention should be given to the concrete composition (see  RSEAS417 -1). Cover in accordance with 7.4 will 
normally be sufficient for such situations.  
7.4.1.2.11  For concrete abrasion special attention should be given on the aggregate according to EAS 131 -
1.  
8 Structural analysis  
8.1 General  
8.1.1  General requirements  
8.1.1. 1 The purpose of structural analysis is to establish the distribution of either internal forces  ( moments, 
torsions, shear and axial loads) or stresses, strains and displacements, over the whole or part of a structure.  
NOTE  In most normal cases analysis wi ll be used to establish the distribution of internal forces and moments, and 
the complete verification or demonstration of resistance of cross sections is based on these action effects; however, for 
certain particular elements, the methods of analysis used  (e.g. finite element analysis) give stresses, strains and 
displacements rather than internal forces and moments. Special methods are required to use these results to obtain 
appropriate verification.  
8.1.1.2  Local analyses may be necessary where the assump tion of linear strain distribution is not valid:  
a) in the vicinity of supports  
b) local to concentrated loads  DRS 142: 2020  
43                ©RSB 2020  - All rights reserved  
 c) in beam -column intersections  
d) in anchorage zones  
e) at changes in cross section.  
8.1.1.3  The effect of the geometry and properties of the structure on its behaviour at each stage of 
construction shall be considered in the design.  
8.1.1.4  In buildings, the effects of shear and axial forces on the deformations of linear elements and slabs 
may be ignored where these are likely to be less than 10% of those due t o bending.  
8.1.2  Special requirements for foundations  
8.1.2.1  Where ground -structure interaction has significant influence on the action effects in the structure, the 
properties of the soil and the effects of the interaction shall be taken into account in accord ance with RS 472 . 
8.1.2.2  For the design of spread foundations, appropriately simplified models for the description of the soil -
structure interaction may be used.  
NOT E For simple pad footings and pile caps the effects of soil -structure interaction may usua lly be ignored.  
8.1.2.3  Interaction between the piles, the pile cap and the supporting soil.  
8.1.2.4  Where the piles are located in several rows, the action on each pile should be evaluated by 
considering the interaction between the piles.  
8.1.2.5  This int eraction may be ignored when the clear distance between the piles is greater than two times 
the pile diameter.  
8.2 Idealization of the structure  
8.2.1  Structural models for overall analysis  
8.2.1.1  The elements of a structure are classified, by consideration of thei r nature and function, as beams, 
columns, slabs, walls, plates, arches, shells etc. Rules are provided for the analysis of the commoner of these 
elements and of structures consisting of combinations of these elements.  
8.2.1.2  For buildings; the following p rovisions ( 8.2.1.3 to 8.2.1. 7) are applicable:  
8.2.1.3  A beam is a member for which the span is not less than 3 times the overall section depth.  Otherwise 
it should be considered as a deep beam.  
8.2.1.4  A slab is a member for which the minimum panel dimens ion is not less than 5 times the overall slab 
thickness.   
©RSB 2020  - All rights reserved                  44 
 8.2.1.5  A slab subjected to dominantly uniformly distributed loads may be considered to be one -way 
spanning if either:  
a) it possesses two free (unsupported) and sensibly parallel edges, or  
b) it is the ce ntral part of a sensibly rectangular slab supported on four edges with a ratio of the longer to 
shorter span greater than 2.  
8.2.1.6  Ribbed or waffle slabs need not be treated as discrete elements for the purposes of  analysis, 
provided that the flange or s tructural topping and transverse ribs have sufficient  torsional stiffness. This may 
be assumed provided that:  
a) the rib spacing does not exceed 1500 mm ; 
b) the depth of the rib below the flange does not exceed 4 times its width ; 
c) the depth of the flange is at le ast 1/10 of the clear distance between ribs or 50 mm ; 
d) whichever is the greater ; 
e) transverse ribs are provided at a clear spacing not exceeding 10 times the overall depth of the slab.  
The minimum flange thickness of 50 mm may be reduced to 40 mm where perman ent blocks are incorporated 
between the ribs.  
8.2.1.7  A column is a member for which the section depth does not exceed 4 times its width and the height is 
at least 3 times the section depth. Otherwise it should be considered as a wall.  
8.2.2  Geometric data  
8.2.2.1  Effec tive width of flanges (all limit states)  
8.2.2.1  In T beams the effective flange width, over which uniform conditions of stress can be assumed, 
depends on the web and flange dimensions, the type of loading, the span, the support conditions and the 
transver se reinforcement.  
8.2.2.2  The effective width of flange should be based on the distance l0 between points of zero moment, 
which may be obtained from Figure 8.  
 DRS 142: 2020  
45                ©RSB 2020  - All rights reserved  
 Figure 9  — Definition of l0, for calculation of effective flange width  
NOTE  The length of the c antilever, l3, should be less than half the adjacent span and the ratio of adjacent spans 
should lie between 2/3 and 1 .5. 
8.2.2.3  The effective flange width beff for a T beam or L beam may be derived as:  
beff =Σb eff,i +bw ≤ b                                                                                                   (8.1) 
where  
beff,i =0.2bi +0.1l0 ≤ 0.2l0                                                                                           (8.1a)                                                                                                                                                                    
and 
beff,i ≤ bi                                                                                                                   (8.1b)                                                                                                                                                                                     
Note  for the notations  refer to the Figures 9 and 10  
 
Figure 10 — Effective flan ge width parameters  
8.2.2.4  For structural analysis, where a great accuracy is not required, a constant width may be assumed 
over the whole span. The value applicable to the span section should be adopted.  
8.2.2.2  Effective span of beams and slabs in buildings  
NOT E The following provisions are provided mainly for member analysis. For frame analysis some of these 
simplifications may be used where appropriate.  
8.2.2.2.1  The effective span, leff, of a member should be calculated as follows:  
leff = ln + a1 + a2                                                                                                              (8.2) 
where:   
©RSB 2020  - All rights reserved                  46 
 ln  is the clear distance between the faces of the supports;  
values for a1 and a2 , at each end of the span, may be determined from the appro priate ai values in Figure 11 
where t is the width of the supporting element as shown.  
 
   (a) Non -continuous members                                              (b) Continuous members  
 
 
         (c) Supports considered fully restrained                         (d) Bearing provided  
 
 
          (e) Cantilever  
Figure 11  — Effective span ( leff ) for different support conditions  DRS 142: 2020  
47                ©RSB 2020  - All rights reserved  
 8.2.2.2.2  Continuous slabs and beams may generally be analysed on the assumption that the  supports 
provide no rotational restraint.  
8.2.2.2.3  Where a beam or slab is monolithic with its supports, the critical design moment at the support 
should be taken as that at the face of the support. The design moment and reaction transferred to the 
supporting element (e.g. column, wall, etc.) sh ould be generally taken as the greater of the elastic or 
redistributed values.  
8.2.2.2.4  The moment at the face of the support should not be less than 0 .65 that of the full fixed end 
moment.  
8.2.2.2. 5 Regardless of the method of analysis used, where a beam  or slab is continuous over a support which 
may be considered to provide no restraint to rotation (e.g. over walls), the design support moment, calculated 
on the basis of a span equal to the centre -to-centre distance between supports, may be reduced by an 
amount Δ M Ed as follows:  
ΔM Ed = FEd,sup t / 8                                                                                                   (8.3)  
where:  
FEd,sup is the design support reaction  
t    is the breadth of the support (see Figure 11b))  
NOTE  Where support bearings are used t should be taken as the bearing width.  
8.2.3  Linear elastic analysis  
8.2.3.1  Linear analysis of elements based on the theory of elasticity may be used for both the  serviceability 
and ultimate limit states.  
8.2.3.2  For the determin ation of the action effects, linear analysis may be carried out assuming:  
a) uncracked cross sections,  
b) linear stress -strain relationships  
c) mean value of the modulus of elasticity.  
8.2.3.3  For thermal deformation, settlement and shrinkage effects at the Ultima te Limit State (ULS), a 
reduced stiffness corresponding to the cracked sections, neglecting tension stiffening but  including the effects 
of creep, may be assumed. For the Serviceability Limit State (SLS) a  gradual evolution of cracking should be 
considered.  
8.3 Linear elastic analysis with limited redistribution  
8.3.1  The influence of any redistribution of the moments on all aspects of the design shall be  considered.   
©RSB 2020  - All rights reserved                  48 
 8.3.2  Linear analysis with limited redistribution may be applied to the analysis of structural  members for the 
verification of ULS.  
8.3.3  The moments at ULS calculated using a linear elastic analysis may be redistributed,  provided that 
the resulting distribution of moments remains in equilibrium with the applied loads.  
8.3.4  In continuous beams or sl abs which:  
a) are predominantly subject to flexure and  
b) have the ratio of the lengths of adjacent spans in the range of 0,5 to 2,  redistribution of bending 
moments may be carried out without explicit check on the rotation  capacity, provided that:  
δ ≥  k1 + k2xu /d    for  fck ≤ 50 MPa                                                                          (8.10a)  
δ ≥  k3 + k4xu /d    for  fck > 50 MPa                                                                           (8.10b)  
  ≥ k5     wher e Class B and Class C reinforcement is used (see Annex A)  
≥ k6       where Class A reinforcement is used (see Annex A)  
Where:  
ᵟ is the ratio of the redistributed moment to the elastic bending moment  
Xu is the depth of the neutral axis at the ultimate limit  state after redistribution  
D is the effective depth of the section  
NOTE   The recommended value for k 1 is 0.44, for k 2 is 1.25(0.6+0.0014/ εcu2), for k 3 = 0.54, for k 4 = 
1.25(0.6+0.0014/ εcu2), for k 5 = 0.7 and k 6 = 0.8. εcu2 is the ultimate strain according  to Table 2.  
8.3.5  Redistribution should not be carried out in circumstances where the rotation capacity cannot be 
defined with confidence (e.g. in the corners of prestressed frames).  
8.3.6  For the design of columns the elastic moments from frame action sh ould be used without any 
redistribution.  
8.4 Plastic analysis  
8.4.1  General  
8.4.1.1  Methods based on plastic analysis shall only be used for the check at ULS.  
8.4.1.2  The ductility of the critical sections shall be sufficient for the envisaged mechanism to be formed . DRS 142: 2020  
49                ©RSB 2020  - All rights reserved  
 8.4.1.3  The plastic analysis should be based either on the lower bound (static) method or on the upper 
bound (kinematic) method.  
8.4.1.4  The effects of previous applications of loading may generally be ignored, and a monotonic increase 
of the intensity o f actions may be assumed.  
8.4.2  Plastic analysis for beams, frames and slabs  
8.4.2.1  Plastic analysis without any direct check of rotation capacity may be used for the ultimate limit state if 
the conditions of 8. 4.1.2 are met.  
8.4.2.2  The required ductility may be deemed to be satisfied without explicit verification if all the following are 
fulfilled:  
a) the area of tensile reinforcement is limited such that, at any section  
xu/d ≤ 0.25 for concrete strength classes ≤ C50/60  
xu/d ≤ 0.15 for concrete strength classes ≥ C55/67  
b) reinforcing steel is either Class B or C  
c) the ratio of the moments at intermediate supports to the moments in the span should be between 0 .5 
and 2.  
8.4.2.3  Columns should be checked for the maximum plastic moments which can be transmitted by 
connec ting members. For connections to flat slabs this moment should be included in the punching shear 
calculation.  
8.4.2.4  When plastic analysis of slabs is carried out account should be taken of any non -uniform 
reinforcement, corner tie down forces, and torsio n at free edges.  
8.4.2.5  Plastic methods may be extended to non -solid slabs (ribbed, hollow, waffle slabs) if their response is 
similar to that of a solid slab, particularly with regard to the torsional effects.  
 
Figure 12  — Plastic rotation θs of reinforced concrete sections for continuous  beams and continuous 
one way spanning slabs.   
©RSB 2020  - All rights reserved                  50 
 8.4.2.6  In region of yield hinges, x /d should not exceed the value 0 .45 for concrete strength classes less 
than or equal to C50/60, and 0 .35 for concrete strength classes greater than or equal to C55/67.  
8.4.2.7  The rotation θ s should be determined on the basis of the design values for actions and materials 
and on the basis of mean values for prestressing at the relevant time.  
8.4.2.8  In the si mplified procedure, the allowable plastic rotation may be determined by multiplying the basic 
value of allowable rotation, θ pl,d, by a correction factor kλ that depends on the shear  slenderness.  
NOTE  The recommended values of θ pl,d for steel Classes B and  C (the use of Class A steel is not recommended for 
plastic analysis) and concrete strength classes less than or equal to C50/60 and C90/105 are given in Figure 13.  
8.4.2.9  The values for concrete strength classes C 55/67 to C 90/105 may be interpolated ac cordingly. The 
values apply for a shear sle nderness λ = 3 .0. For different values of shear slenderness θ pl,d should be 
multiplied by kλ: 
k λ =
                                                                                                           (8.11)  
Where λ is the ratio of the di stance between point of zero and maximum moment after redistribution and 
effective depth, d. 
As a simplification λ may be calculated for the concordant design values of the bending moment and shear :  
λ = MSd / (VSd ⋅ d)                                                                                                         (8.12)  
 
Figure 13 — Basic value of allowable rotation, θ pl,d, of reinforced concrete sections for Class B and C 
reinforcement. The values apply for a shear slenderness λ = 3 .0 DRS 142: 2020  
51                ©RSB 2020  - All rights reserved  
 8.5  Non-linea r analysis  
8.5.1  Non-linear methods of analysis may be used for both ULS and SLS, provided that  equilibrium and 
compatibility are satisfied and an adequate non -linear behaviour for materials is assumed. The analysis may 
be first or second order.  
8.5.2  At the ultimate limit state, the ability of local critical sections to withstand any inelastic  deformations 
implied by the analysis should be checked, taking appropriate account of  uncertainties.  
8.5.3  For structures predominantly subjected to static loads, th e effects of previous applications  of loading 
may generally be ignored, and a monotonic increase of the intensity of the actions may be assumed.  
8.5.4  The use of material characteristics which represent the stiffness in a realistic way but take  account of 
the uncertainties of failure shall be used when using non -linear analysis. Only those  design formats which are 
valid within the relevant fields of application shall be used.  
8.5.5  For slender structures, in which second order effects cannot be ignored, the  design method  given in 
5.8.6 may be used.  
8.6 Analysis of second order effects with axial load  
8.6.1  General  
8.6.1.1  This clause deals with members and structures in which the structural behaviour is  significantly 
influenced by second order effects (e.g. columns, w alls, piles, arches and shells).  
NOTE  Global second order effects are likely to occur in structures with a flexible bracing system.  
8.6.1.2  Where second order effects are taken into account, equilibrium and resistance shall be verified in the 
deformed stat e. Deformations shall be calculated taking into account the relevant effects of cracking, non -
linear material properties and creep.  
NOTE  In an analysis assuming linear material properties, this can be taken into account by means of reduced 
stiffness values , see 8.8.7.  
8.6.1.3  Where relevant, analysis shall include the effect of flexibility of adjacent members and foundations 
(soil-structure interaction).  
8.6.1.4  The structural behaviour shall be considered in the direction in which deformations can occur, a nd 
biaxial bending shall be taken into account when necessary.  
8.6.1.5  Uncertainties in geometry and position of axial loads shall be taken into account as  additional first 
order effects based on geometric imperfections.  
8.6.1.6  Second order effects may be  ignored if they are less than 10 % of the corresponding first order 
effects. Simplified criteria are given for isolated members in 8.8.3.1 and for structures in 8.8.3.3.   
©RSB 2020  - All rights reserved                  52 
 8.6.2  Simplified criteria for second order effects  
8.6.2.1  Slenderness criterion for isolated membe rs 
8.6.2.1.1   As an altern ative to 8.8..6 , second order effects may be ignored if the slenderness λ is below a 
certain value λ lim. 
NOTE  The recommended value of λlim   follows from:  
λlim = 20 ⋅A⋅B⋅C/
                                                                                                                 (8.13)  
where:  
A 1 / (1+0 .2φef) (if φ ef is not known, A = 0.7 may be used)  
B  1+ 2ω (if ω is not known, B = 1.1 may be used)  
C  1.7 - rm (if rm is not known, C = 0.7 may be used)  
φef effecti ve creep ratio;ω      Asfyd / (Acfcd); mechanical reinforcement ratio;  
As is the total area of longitudinal reinforcement  
n  NEd / (Acfcd); relative normal force  
rm  M01/M02; moment ratio  
M01, M02 are the first order end moments, 
  
If the end moments M01 an d M02 give tension on the same side, rm should be taken positive (i.e. C ≤ 1.7), otherwise 
negative (i.e. C > 1.7). 
In the following cases, rm should be taken as 1 .0 (i.e. C = 0.7): 
a) for braced members in which the first order moments arise only from or pre dominantly due to  imperfections or 
transverse loading;  
b) for unbraced members in general.  
8.6.2.1.2   In cases with biaxial bending, the slenderness criterion may be checked separately for each 
direction. Depending on the outcome of this check, second order e ffects (a) may be ignored in both directions, 
(b) should be taken into account in one direction, or (c) should be taken into account in both directions.  DRS 142: 2020  
53                ©RSB 2020  - All rights reserved  
 8.6.3  Slenderness and effective length of isolated members  
8.6.3.1  The slenderness ratio is defined as follow s: 
λ = l0 / i                                                                                                                                  (8.14)  
where:  
l0 is the effective length, see 8.8.3.2  
I is the radius of gyration of the uncracked concrete sect ion 
8.6.3.2  For a general definition of the effective length, see 8.8.1. Examples of effective length for isolated 
members with constant cross section are given in Figure 14.  
 
    a) l0 = l        b) l0 = 2l      c) l0 = 0,7 l          d) l0 = l / 2      e) l0 = l       f) l /2 <l0< l     g) l0 > 2l 
Figure 14  — Examples of different buckling modes and corresponding effective  lengths for isolated 
members  
8.6.3.3  For compression members in regular frames, the slenderness criterion (see 8.8.3.1) should be 
chec ked with an effective length l0 determined in the following way:  
                                         (8.15) 
Unbraced members (see Figure 5.7 (g)):   
©RSB 2020  - All rights reserved                  54 
 
                        (8.16)  
where:  
k1, k2 are the relative flexibilities of rotational restraints a t ends 1 and 2 respectively:  
k = (θ / M)⋅ (EΙ / l) 
θ  is the rotation of restraining members for bending moment M; see also Figure 14 (f) and (g)  
EΙ is the bending stiffness of compression member,  
L is the clear height of compression member between end restraints  
NOTE  k = 0 is the theo retical limit for rigid rotational restraint, and k = ∞ represents the limit for no restraint at all. 
Since fully rigid restraint is rare in practice, a minimum value of 0,1 is recommended for k1 and k2. 
8.6.3.4  If an adjacent compression member (column) i n a node is likely to contribute to the rotation  at 
buckling, then ( EΙ / l ) in the definition of k should be replaced by [( EΙ / l )a+(EΙ / l )b], a and b representing the 
compression member (column) above and below the node.  
8.6.3.5  In the definition of e ffective lengths, the stiffness of restraining members should include the  effect of 
cracking, unless they can be shown to be uncracked in ULS.  
8.6.3.6  For other cases than those in (2) and (3), e.g. members with varying normal force and/or  cross 
section, t he criterion in 8.8.3.1 should be checked with an effective length based on the  buckling load 
(calculated e.g. by a numerical method):  
 
                                                                                                        (8.17)  
where:  
EI is a representative bending stiffness  
NB is buckling load expressed in terms of this EI 
(in Expression (8.14), i should also correspond to this EI) 
8.6.4  Global second order effects in buildings  
8.6.4.1  As an alternative to 5.8.2 (6), global second order effect s in buildings may be ignored if  DRS 142: 2020  
55                ©RSB 2020  - All rights reserved  
 
                                                               ( 8.18)  
where:  
FV,Ed is the total vertical load (on braced and bracing members)  
ns is the number of storeys  
L is the total height of building above level of mo ment restraint  
Ecd is the design value of the modulus of elasticity of concrete, see 8.8.6 (3)  
Ic is the second moment of area (uncracked concrete section) of bracing member(s)  
NOTE  The recommended value of k1 is 0,31.  
Expression (8.18) is valid only if a ll the following conditions are met:  
a) torsional instability is not governing, i.e. structure is reasonably symmetrical  
b) global shear deformations are negligible (as in a bracing system mainly consisting of shea r walls 
without large openings)  
c) bracing members are rigidly fixed at the base, i.e. rotations are negligible  
d) the stiffness of bracing members is reas onably constant along the height  
e) the total vertical load increases by approximately the same amount per storey  (2) k1 in Expression 
(8.18) may be replaced by k2 if it can be verified that bracing members  are uncracked in ultimate limit 
state.  
NOTE  The recommended value of k2 is 0,62.  
8.6.5  Creep  
8.6.5.1  The effect of creep shall be taken into account in second order analysis, with due  consideration of 
both the ge neral conditions for creep and the duration of different  loads in the load combination considered.  
8.6.5.2  The duration of loads may be taken into account in a simplified way by means of an  effective creep 
ratio, φ ef, which, used together with the design l oad, gives a creep deformation  (curvature) corresponding to 
the quasi -permanent load:  
φef = φ(∞,t 0) ⋅M0Eqp / M0Ed                                                                                                                          (8.19)  
where:   
©RSB 2020  - All rights reserved                  56 
 φ(∞,t 0)  is the final creep coefficient according to 6.1.4  
M0Eqp is the first order bending moment in quasi -permanent load combination (SLS)  
M0Ed is the first order bending moment in design load combination (ULS)  
NOTE  It is also possible to base φ ef on total bend ing moments MEqp and MEd, but this requires iteration and a 
verification of stability under quasi -permanent load with φ ef = φ (∞,t 0). 
8.6.5.3  If M0Eqp / M0Ed varies in a member or structure, the ratio may be calculated for the section with 
maximum moment, or a representative mean value may be used.  
8.6.5.4  The effect of creep may be ignored, i.e. φ ef = 0 may be assumed, if the following three  conditions are 
met: 
φ (∞,t 0) ≤ 2 
λ ≤ 75  
M0Ed/NEd ≥ h 
Here M0Ed is the first order moment and h is the cross section depth in the corresponding direction.  
NOTE  If the conditions for neglecting second order effects according to 8.8.2 (6) or 8.8.3.3 are only just achieved, it 
may be too unconservative to neglect both second order effects and creep, unless the mechanical re inforcement ratio (ω, 
see 8.8.3.1 1 ) is at least 0,25.  
8.6.6  Methods of analysis  
8.6.6.1  The methods of analysis include a general method, based on non -linear second order  analysis, see 
8.8.6 and the following two simplified methods:  
a) Method based on nominal stiffne ss, see 8.8.7  
b) Method based on nominal curvature, see 8.8.8  
NOTE  Nominal second order moments provided by the simplified methods (a) and (b) are sometimes greater than 
those corresponding to instability. This is to ensure that the total moment is compatible  with the cross section resistance.  
8.6.6.2  Method (a) may be used for both isolated members and whole structures, if nominal  stiffness values 
are estimated appropriately; see 8.8.7.  
8.6.6.3  Method (b) is mainly suitable for isolated members; see 5.8.8. Ho wever, with realistic  assumptions 
concerning the distribution of curvature, the method in 8.8.8 can also be used for  structures.  
8.6.7  General method  
8.6.7.1  The general method is based on non -linear analysis, including geometric non -linearity i.e.  second 
order effects. The general rules for non -linear analysis given in 8.7 apply.  DRS 142: 2020  
57                ©RSB 2020  - All rights reserved  
 8.6.7.2  Stress -strain curves for concrete and steel suitable for overall analysis shall be used. The effect of 
creep shall be taken into account.  
8.6.7.3  With stress -strain diagrams bas ed on design values, a design value  of the ultimate load is obtained 
directly from the analysis. In Expression (6.14), and in the k value, fcm is then substituted by the design 
compressive strength fcd and Ecm is substituted by  
Ecd = Ecm / CE                                                                                                         (8.20)  
NOTE  The val ue recommended value of γ CE is 1,2.  
8.6.7.4  In the absence of more refined models, creep may be taken into account by multiplying all  strain 
values in the concrete stress -strain diagram according to 8.8.6 (3) with a factor (1 + φ ef), where φ ef is the 
effective creep ratio according to 8.8.4.  
8.6.7.5  The favourable effect of tension stiffening may be taken into account.  
NOTE  This effect is favourable, and may always be ignored, for simplicity.  
8.6.7.6  Normally, conditions of equilibrium and strain compatibi lity are satisfied in a number of  cross 
sections. A simplified alternative is to consider only the critical cross section(s), and to  assume a relevant 
variation of the curvature in between, e.g. similar to the first order moment or  simplified in another ap propriate 
way. 
8.6.8  Method based on nominal stiffness  
8.6.8.1  General  
8.6.8.2  In a second order analysis based on stiffness, nominal values of the flexural stiffness  should be 
used, taking into account the effects of cracking, material non -linearity and creep on  the ov erall behaviour. 
This also applies to adjacent members involved in the analysis, e.g.  beams, slabs or foundations. Where 
relevant, soil -structure interaction should be taken into account.  
8.6.8.3  The resulting design moment is used for the design of cross sections with respect to bending 
moment and axial force according to 9.1, as compared with 8 .8.5.1 . 
8.6.8.2  Nominal stiffness  
8.6.8.2.1  The following model may be used to estimate the nominal stiffness of slender compression  members 
with arbitrary cross section:  
EI = KcEcdIc + KsEsIs                                                                                               (8.21)  
where:  
Ecd is the design value of the modulus of elasticity of concrete, see 8.8.6 (3)  
Ic   is the moment of inertia of concrete cross  section   
©RSB 2020  - All rights reserved                  58 
 Es is the design value of the modulus of elasticity of reinforcement, 8.8.6 (3)  
Is is the second moment of area of reinforcement, about the centre of area of the  concrete  
Kc  is a factor for effects of cracking, creep etc, see 8 .8.7.2.2 or 8.8.7.2 .3 
Ks is a factor for contribution of reinforcement, see 8.8.7.2.2 or 8.8.7.2.3  
 
8.6.8.2.2  The following factors may be used in Expression (8 .21), provided ρ ≥ 0,002:  Ks = 1  
Kc = k1k2 / (1 + φ ef)                                                                                              (8.22)  
where:  
ρ is the geometric reinforcement ratio, As/Ac 
As is the total area of reinforcement  
Ac is the area of concrete section  
φef is the effective creep ratio, see 8.8.4  
k1 is a factor which depends on concrete strength class, Expression (8.23)  
k2  is a factor which depends on axial force and slenderness, Expression (8.24)  
                                                                            (8.23)  
                                                                               (8.24)  
where:  
n is the relative axial force, NEd / (Acfcd) 
λ is the slenderness ratio, see 8.8.3  
If the slenderness ratio λ is not defined, k2 may be taken as  
k2 = n⋅0.30 ≤ 0 .20                                                                                             (8.25)  
8.6.8.2.2   As a simplified alternative, provided ρ ≥ 0,01, the following factors may be used in  Express ion 
(8.21):  DRS 142: 2020  
59                ©RSB 2020  - All rights reserved  
 Ks = 0  
Kc = 0.3 / (1 + 0 .5φef)                                                                                         (8.26)  
 
NOTE  The simplified alternative may be suitable as a preliminary step, followed by a more accurate calculation 
accord ing to ( 8.8.8.2.2 ). 
8.6.8.2.3  In statically indeterminate structures, unfavourable effects of cracking in adjacent members  should 
be taken into account. Expressions (8.21 -8.26) are not generally applicable to such  members. However, as a 
simplification, ful ly cracked sections may be assumed. The stiffness  should be based on an effective concrete 
modulus:  
Ecd,eff = Ecd /(1+φ ef)                                                                                            (8.27)  
where:  
Ecd  is the design value of the modulus of elasticity according to 8.8.6 (3)  
φef  is the effective creep ratio; same value as for columns may be used  
8.6.8.3  Moment magnification factor  
8.6.8.3.1  The total design moment, including second order moment, may be expressed as a  magnification of 
the bending moments resulting from a first order analysis, namely:  
                                                                     (8.28)  
where:  
M0Ed  is the first order moment;  
β is a factor which depends on distribution of 1st and 2nd order moments;  
NEd  is the design value of axial load  
NB  is the buckling load based on nominal stiffness  
 
8.6.8.3.2  For isolated members with constant cross section and axial load, the second ord er moment  may 
normally be assumed to have a sine -shaped distribution. Then  
β = π2 / c0                                                                                                                     (8.29)                                                                                                                                                               
where:   
©RSB 2020  - All rights reserved                  60 
 c0   is a coefficient which depends on the distribution of first order moment (for instance,  
c0 = 8 for a constant first order moment, c0 = 9,6 for a parabolic and 12 for a  symmetric triangular distribution 
etc.).  
8.6.8.3.3   For members without transverse load, differing first order end moments M01 and M02 may be 
replaced by an equivalent constant first order moment M0e according to 8 .8.8.2 .2. Consistent with the 
assumption of a constant first order moment, c0 = 8 should be used.  
8.6.8.3.4  The value of c0 = 8 also applies to members bent in double curvature. It should be noted that in 
some cases, depending on slenderness and axial force, the  end moments(s) can be greater than the 
magnified equivalent moment.  
8.6.8.3. 5 Where 8 .8.7.3.2 or 8.8.7.3.3  is not applicable, β = 1 is normally a reasonable simplification.  
Expression (8.28) can then be reduced to:  
                                                                                       (8.30)  
NOTE  8.8.7.3.4  is also applicable to the global anal ysis of certain types of structures, e.g. structures braced by shear 
walls and similar, where the principal action effect is bending moment in bracing units.  
8.6.9  Analysis for some particular structural members  
8.6.9.1  Slabs supported on columns are defined as  flat slabs.  
8.6.9.2  Shear walls are plain or reinforced concrete walls that contribute to lateral stability of the structure.  
9 Ultimate Limit States (ULS)  
9.1 Bending with or without axial force  
9.1.1  This section applies to undisturbed regions of beams, slabs  and similar types of members for which 
sections remain approximately plane before and after loading. The discontinuity regions of beams and other 
members in which plane sections do not remain plane may be designed and detailed according to 9.5.  
9.1.2  When  determining the ultimate moment resistance of reinforced or prestressed concrete cross -
sections, the following assumptions are made:  
a) plane sections remain plane.  
b) the strain in bonded reinforcement or bonded prestressing tendons, whether in tension or in 
compression, is the same as that in the surrounding concrete.  
c) the tensile strength of the concrete is ignored.  DRS 142: 2020  
61                ©RSB 2020  - All rights reserved  
 d) the stresses in the concrete in compression are derived from the design stress/strain  relationship 
given in 6.1.7.  
e) the initial strain in prestress ing tendons is taken into account when assessing the  stresses in the 
tendons.  
9.1.3  The compressive  strain in the concrete shall be limited to ε cu2, or ε cu3, depending on the stress -strain 
diagram used, see 6.1.7 and Table 2. The strains in the reinforcing steel and the prestressing steel shall be 
limited to ε ud (where applicable); see 6.2.7 (2) and 6.3 .6 (7) respectively . 
9.1.4  For cross -sections with symmetrical reinforcement loaded by the compression force it is necessary to 
assume the minimum eccentricity, e0 = h/30 but not less than 20 mm where h is the depth of the section.  
9.2 Shear  
9.2.1  General verificati on procedure  
9.2.1.1  For the verification of the shear resistance the following symbols are defined:  
VRd,c is the design shear resistance of the member without shear reinforcement.  
VRd,s   is the design value of the shear force which can be sustained by th e yielding shear  reinforcement.  
VRd,max is the design value of the maximum shear force which can be sustained by the  member, limited by 
crushing of the compression struts.  
In members with inclined chords the following additional values are defined (see Fig ure 15):  
Vccd  is the design value of the shear component of the force in the compression area, in  the case of an 
inclined compression chord.  
Vtd  is the design value of the shear component of the force in the tensile reinforcement,  in the case of an 
inclined tensile chord.  
 
Figure 15  —Shear component for members with inclined chords  
9.2.1.2  The shear resistance of a member with shear reinforcement is equal to:   
©RSB 2020  - All rights reserved                  62 
 VRd = VRd,s + Vccd + Vtd                                                                                            (9.1) 
9.2.1.3  In regions of the member where VEd ≤ VRd,c no calculated shear reinforcement is necessary.  VEd is the 
design shear force in the section considered resulting from external loading and  prestressing (bonded or 
unbonded).  
9.2.1.4  When, on the basis of the design shear calculation, no shear rei nforcement is required,  minimum 
shear reinforcement should nevertheless be provided according to 9.2.2. The  minimum shear reinforcement 
may be omitted in members such as slabs (solid, ribbed or  hollow core slabs) where transverse redistribution 
of loads is  possible. Minimum reinforcement  may also be omitted in members of minor import ance (e.g. lintels 
with span ≤ 2 m) which do not  contribute significantly to the overall resistance and stability of the structure.  
9.2.1. 5 In regions where VEd > VRd,c according to expression (9.2), sufficient shear reinforcement should be 
provided in ord er that VEd ≤ VRd 
9.2.1.6  The sum of the design shear force and the contributions of the flanges, VEd - Vccd - Vtd, should not 
exceed the permitted maximum value VRd,max (see 9.2.3), anywhere in the member.  
9.2.1.7  The longitudinal tension reinforcement sh ould be able to resist the additional tensile force  caused by 
shear (see 9 .2.3.7 . 
9.2.1.8  For members subject to predominantly uniformly distributed loading the design shear force  need not 
to be checked at a distance less than d from the face of the suppor t. Any shear  reinforcement required should 
continue to the support. In addition it should be verified that the  shear at the support does not exceed VRd,max 
(see also 9 .2.2.6  and 9.2.3 .8. 
9.2.1.9  Where a load is applied near the bottom of a section, suffici ent vertical reinforcement to  carry the 
load to the top of the section should be provided in addition to any reinforcement  required to resist shear.  
9.2.2  Members not requiring design shear reinforcement  
9.2.2.1  The design value for the shear resistance VRd,c   is given by:  
VRd,c = [C Rd,ck(100 ρ l f ck)1/3 + k 1 σcp] bwd                                                       (9.2.a)  
with a minimum of  
VRd,c = (v min + k 1σcp) bwd                                                                                   (9.2.b)  
where:  
fck    is  in MPa  
 
Asl  is the area of the tensile reinforcement, which extends ≥ ( lbd + d) beyond the  section considered (see 
 Figure 15). (see Expression (9.1))  DRS 142: 2020  
63                ©RSB 2020  - All rights reserved  
 bw is the smallest width of the cross -section in the tensile area [mm]  
σcp = NEd/Ac < 0.2 fcd [MPa]  
NEd  is the a xial force in the cross -section due to loading or prestressing [in N] ( NEd>0 for compression). The 
influence of imposed deformations on may be ignored.  
AC is the area of concrete cross section [mm2] 
VRd,c is [N]  
NOTE  The recommended value for CRd,c is 0.18/ γc, that for vmin is given by Expression (9.3) and that for k1 is 0.15. 
vmin =0.035 k3/2 ⋅ fck1/2                                                                                            (9.3) 
 
 
Figure 16 — Definition of Asl in Expression (9.2)  
9.2.2. 2 The regions cracked in bending may be calculated using expression (9.2a). In regions  uncracked in 
bending (where the flexural tensile stress is smaller than fctk,0.05/γ c) the shear resistance should be limited by 
the tensile strength of the concrete. In these regions the shear resistance is given by:  
                                                        (9.4) 
where  
Ι is the second moment of area  
bw is the width of the cross -section at the centroidal axis, allowing for the presence of   ducts in accordan ce 
with Expressions (9.16) and (9.17)  
S is the first moment of area above and about the centroidal axis  
αI = lx/lpt2 ≤ 1.0 for pretensioned tendons  
    = 1.0 for other types of prestressing  
lx  is the distance of section considered from the starting point of the transmission  length   
©RSB 2020  - All rights reserved                  64 
 σcp is the concrete compressive stress at the centroidal axis due to axial loading and/or  prestressing (σ cp = 
NEd /Ac in MPa, NEd > 0 in compression)  
9.2.2.3  For cross -sections where the width varies over the height, the maximum principal stress may occur 
on an axis other than the centroidal axis. In such a case the minimum value of the shear resistance should be 
found by calculating V Rd,c at various axes in the cross -section.  
9.2.2.4  The calculation of the shear resistance accord ing to Expression (9.4) is not required for cross -
sections that are nearer to the support than the point which is the intersection of the elastic centroidal axis and 
a line inclined from the inner edge of the support at an angle of 45o. 
 
               (a) Beam with direct support                                        (b) Corbel  
                                      Figure 17  — Loads near supports  
 
9.2.3  Members requiring design shear reinforcement  
9.2.3.1  The design of members with shear reinforcement is based  on a truss model (Figure 18).  Limiting 
values for the angle θ of the inclined struts in the web are given in 9 .2.3.2. In Figure 18 the following notations 
are shown:  
Α  is the angle between shear reinforcement and the beam axis perpendicular to the  shear force (measured 
positive as sho wn in Figure 18)  
θ  is the angle between the concrete compression strut and the beam axis  perpendicular to the shear force  
Ftd  is the design value of the tensile force in the longitudinal reinforcement  
Fcd is the design value of the concrete compression f orce in the direction of the  longitudinal member axis.  
bw  is the minimum width between tension and compression chords  DRS 142: 2020  
65                ©RSB 2020  - All rights reserved  
 z   is the inner lever arm, for a member with constant depth, corresponding to the bending  moment in the 
element under consideration. In  the shear analysis of reinforced concrete without axial force, the approximate 
value z = 0.9d may normally be used.  
9.2.3.2  In el ements with inclined prestressing tendons, longitudinal reinforcement at the tensile chord θ 
should be provided to carry the longitudinal tensile force due to shear defined in (10) .‰  
 
 
  
 
Figure 18  — Truss model and notation for shear reinforced members  
 
9.2.3.3  The angle θ should be limited.  
NOTE  The recommended limiting values of cot θ are given in Expression (9.5).  
1 ≤ cot θ ≤ 2,5                                                                                                         (9.5)  
9.2.3.4  For members with vertical shear reinforcement, the shear resistance, VRd is the smaller value of:  
                                                                                     (9.6)  
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 NOTE  If Expression (6.10) is used the value of fywd should be reduced  to 0,8 fywk in Expression (9.7)  
and 
VRd,max = α cw bw z ν1 fcd/(cot θ + tan θ )                                                                         (9.7)  
where:  
Asw  is the cross -sectional area of the shear reinforcement  
s  is the spacing of the stirrups  
fywd  is the design yield strength of the shear reinforcement  
ν1   is a strength reduction factor for concrete cracked in shear  
αcw   is a coefficient taking account of the state of the stress in the compression chord  
NOTE 1 The recommended value of ν 1 and α cw is ν. 
NOTE 2 If the design stress of the shear reinforcement is below 80  % of the characteristic yield stress fyk, ν1 may be 
taken as:  
ν1 = 0.6 for fck ≤ 60 MPa                                                                                                             
ν1 = 0.9 – fck /200 > 0 .5 for fck ≥ 60 MPa                                                                                     
NOTE  The recommended value of α cw is as follows:  
1 for non -prestressed structures  
(1 + σ cp/fcd)      for 0 < σ cp ≤ 0.25 fcd                                                                         (9.8.a)  
1.25                for 0 .25 fcd < σ cp ≤ 0.5 fcd                                                                    ( 9.8.b)                                                                                                                            
2.5 (1 - σcp/fcd) for 0 .5 fcd < σ cp < 1.0 fcd                                                                      (9.11)                                                                                                                              
where:  
σ cp  is the mean compressive stress, measured positive, in the concrete due to the design axial force.  This 
should be obtained by averaging it over the concrete section taking account of the reinforcement.  The value of 
σcp need not be calculated at a distance less than 0.5 d cot θ from the edge of the support.  
NOTE 3 The maximum effective cross -sectional area of the shear reinforcement, Asw,max , for cot θ =1 is given by:  
                                                                                     (9.12)  
9.2.3. 5 For members with inclined shear reinforcement, the shear resistance is the smaller value of:  DRS 142: 2020  
67                ©RSB 2020  - All rights reserved  
 
                                                             (9.13)  
and 
                                          (9.14)  
NOTE  The maximum effective shear reinforcement, A sw,max for cot θ =1 follows from:  
                                                                                           (9.15)  
9.2.4  Shear between web and flanges  
9.2.4.1  A minimum amount of longitudinal reinforcement should be provided, as specified in 9.3.1.  
9.2.4.2  The longitudinal shear stress, vEd, at the junction between one side of a flange and the web is 
determined by the change of the normal (longitudinal) force in the part of the flange considered, according to:  
vEd = Δ Fd/(hf ⋅ Δx)                                                                                                                   (9.16)  
where:  
hf  is the thickness of flange at the junctions  
Δx  is the length under consideration, see Figure 19  
ΔFd is the change of the normal force in the flan ge over the length Δ x. 
  
©RSB 2020  - All rights reserved                  68 
   
  − compressive struts       
 −longitudinal bar anchored beyond this projected point  
Figure 19 — Notations for the connection between flange and web  
 
9.2.4.3  The maximum value that may be assumed for Δ x is half the distance betwe en the section where the 
moment is 0 and the section where the moment is maximum. Where point loads are applied the length Δ x 
should not exceed the distance between point loads.  
9.2.4.4  The transverse reinforcement per unit length Asf/sf may be determined as follows:  
                                                                                   (9.17)  
satisfied:  
vEd ≤ ν fcd sin θf cos θf                                                                                                   ( 9.18)  
NOTE  The re commended values of cot θ f in the calculation are in the following range:  
1.0 ≤ cot θ  f ≤ 2.0 for compression flanges (45° ≥θ f ≥ 26.5°) 
1.0 ≤ cot θ f ≤ 1.25 for tension flanges (45° ≥ θ f ≥ 38.6°) 
9.2.4.5  In the case of combined shear between the flange and  the web, and transverse bending,  the area of 
steel should be the greater than that given by Expression (9.17) or half that given by  Expression (9.17) plus 
that required for transverse bending.  
9.2.4.6  If vEd is less than or equal to kfctd no extra reinfor cement above that for flexure is required.  
NOTE  The recommended value of k is 0.4. 
9.2.4.7  Longitudinal tension reinforcement in the flange should be anchored beyond the strut  required to 
transmit the force back to the web at the section where this reinfor cement is  required (See Section (A - A) of 
Figure 19).  
9.3 Torsion  
9.3.1  General  
9.3.1.1  Where the static equilibrium of a structure depends on the torsional resistance of  elements of the 
structure, a full torsional design covering both ultimate and serviceability l imit states shall be made.  
9.3.1.2  Where, in statically indeterminate structures, torsion arises from consideration of compatibility only, 
and the structure is not dependent on the torsional resistance for its stability, then it will normally be 
unnecessar y to consider torsion at the ultimate limit state. In such cases a minimum reinforcement in the form 
of stirrups and longitudinal bars should be provided in order to prevent excessive cracking.  
9.3.1.3  The torsional resistance of a section may be calculate d on the basis of a thin -walled closed section, 
in which equilibrium is satisfied by a closed shear flow. Solid sections may be modeled by equivalent thin -DRS 142: 2020  
69                ©RSB 2020  - All rights reserved  
 walled sections. Complex shapes, such as T -sections, may be divided into a series of sub -sections, ea ch of  
which is modelled as an equivalent thin -walled section, and the total torsional resistance taken as the sum of 
the capacities of the individual elements.  
9.3.1.4  The distribution of the acting torsional moments over the sub -sections should be in prop ortion to their 
uncracked torsional stiffnesses. For non -solid sections the equivalent wall thickness should not exceed the 
actual wall thickness.  
9.3.1.5  Each sub -section may be designed separately.  
9.3.2  Warping torsion  
9.3.1.1  For closed thin -walled sections and solid sections, warping torsion may normally be  ignored.  
9.3.1.2  In open thin walled members it may be necessary to consider warping torsion. For very  slender 
cross -sections the calculation should be carried out on the basis of a beam -grid model  and fo r other cases on 
the basis of a truss model. In all cases the design should be carried out  according to the design rules for 
bending and longitudinal normal force, and for shear.  
9.4 Punching  
9.4.1  General  
9.4.1.1  The rules in this Section complement those given in 9.3 and cover punching shear in solid slabs, 
waffle slabs with solid areas over columns, and foundations.  
9.4.1.2  Punching shear can result from a concentrated load or reaction acting on a relatively small area, 
called the loaded area A load of a slab or a  foundation.  
9.4.1.3  An appropriate verification model for checking punching failure at the ultimate limit state is shown in 
Figure 20.  
 
basic control section   
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 a) Section  
 
b) Plan  
Figure 20 − Verification model for punching shear at the ultimate limit state  
 
rcont  - further control perimeter  
9.4.1.4  The shear resistance should be checked at the face of the column and at the basic control  perimeter 
u1. If shear reinforcement is required a fu rther perimeter u out,ef should be found where shear reinforcement is 
no longer required.  
9.4.1.5  The rules given in 9.4 are principally formulated for the case of uniformly distributed  loading. In 
special cases, such as footings, the load within the contro l perimeter adds to the  resistance of the structural 
system, and may be subtracted when determining the design  punching shear stress.  
9.4.2  Load distribution and basic control perimeter  
9.4.2.1  The basic control perimeter u1 may normally be taken to be at a dist ance 2,0 d from the  loaded area 
and should be constructed so as to minimise its length (see Figure 21).  The effective depth of the slab is 
assumed constant and may normally be taken as:  DRS 142: 2020  
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                                                                                    ( 9.19)  
where dy and dz are the effective depths of the reinforcement in two orthogonal directions.  
 
Figure 21  — Typical basic control perimeters around loaded areas  
9.4.2.2  Control perimeters at a distance less than 2 d should be considered where the concentrated  force is 
opposed by a high pressure (e.g. soil pressure on a base), or by the effects of a load or  reaction within a 
distance 2 d of the periphery of area of application of the force.  
9.4.2.3  For loaded areas situated near openings, i f the shortest distance between the perimeter of  the 
loaded area and the edge of the opening does not exceed 6 d, that part of the control  perimeter contained 
between two tangents drawn to the outline of the opening from the centre  of the loaded area is con sidered to 
be ineffective (see Figure 22).  
opening  
Figure 22  — Control perimeter near an opening  
 
9.4.2.4  For a loaded area situated near an edge or a corner, the control perimeter should be taken  as shown 
in Figure 23, if this gives a perimeter (excludi ng the unsupported edges) smaller than that obtained from (1) 
and (2) above.   
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Figure 23  — Basic control perimeters for loaded areas close to or at edge or corner  
9.4.2.5  For loaded areas situated near an edge or corner, i.e. at a distance smaller than d, special  edge 
reinforcement should always be provided.  
9.4.2.6  The control section is that which follows the control perimeter and extends over the  effective depth d. 
For slabs of constant depth, the control section is perpendicular to the middle  plane of t he slab. For slabs or 
footings of variable depth other than step footings, the effective  depth may be assumed to be the depth at the 
perimeter of the loaded area as shown in Figure 24  
 
Figure 24  − Depth of control section in a footing with variable depth  
9.4.2.7  Further perimeters, ui, inside and outside the basic control area should have the same  shape as the 
basic control perimeter.  
9.4.2.8  For slabs with circular column heads for which lH < 2hH (see Figure 25) a check of the  punching 
shear stresses according to 9.4.3 is only required on the control section outside the  column head. The 
distance of this section from the centroid of the column rcont may be taken as:  
rcont = 2d + l H + 0,5c                                                                                                (9.20)  
where , 
lH is the distance from the column face to the edge of the column head  
c is the diameter of a circular column  DRS 142: 2020  
73                ©RSB 2020  - All rights reserved  
 
 
Figure 25  — Slab with enlarged column head w here lH < 2.0 hH 
 
9.4.2.9  For a rectangular column with a rectangular head with lH < 2.0hH (see Figure 25) and overall  
dimensions l1 and l2 (l1 = c1 + 2lH1, l2 = c2 + 2lH2, l1 ≤ l2), the value rcont may be taken as the lesser of:  
rcont = 2d + 0.56
                                                                                  (9.21)                                                                                                                     
and  
rcont = 2d + 0.69 I1                                                                                                                (9.22)                                                                                                                                        
9.4.2.10  For slabs with e nlarged column heads where lH > 2hH (see Figure 25) control sections  both within the 
head and in the slab should be checked.  
9.4.2.11  The provisions of 9.4.2 and 9.4.3 also apply for checks within the column head with d taken as dH 
according to Figure 25.  
9.4.2.12  For circular columns the distances from the centroid of the column to the control sections  in Figure 
25 may be taken as:  
rcont,ext = lH + 2d + 0,5c                                                                                                      (9.23)  
rcont,int = 2(d + h H) +0,5c                                                                                                    (9.24)  
9.4.3  Punching shear calculation  
9.4.3.1  The design procedure for punching shear is based on checks at the face of the column  and at the 
basic control perimeter u1. 
If shear reinforcement is required a further perimeter uout,ef should be found where shear reinforcement is no 
longer required. The  following design shear stresses (MPa) along the control sections  are defined:  
vRd,c   is the design value of the punching shear resistance of a slab without punching shear  reinforcement 
along the control section considered.  
vRd,cs  is the design value of the punching shear resistance of a slab with punching shear  reinforcement 
along  the control section considered.   
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 vRd,max  is the design value of the maximum punching shear resistance along the control section considered.  
9.4.3.2  The following checks should be carried out:  
a) At the column perimeter, or the perimeter of the loaded area, t he maximum punching  shear stress 
should not be exceeded:  
vEd ≤ vRd,max  
b) Punching shear reinforcement is not necessary if:  
vEd ≤ vRd,c 
c) Where vEd exceeds the value vRd,c for the control section considered, punching shea r reinforcement 
should be provided acco rding to 9.4.5.  
9.4.3.3  Where the support reaction is eccentric with regard to the control perimeter, the maximum shear 
stress should be taken as:  
                                                                                                   (9.25)  
where 
d   is the mean effective depth of the slab, which may be taken as ( dy + dz)/2 where:  
dy, dz is the effective depths in the y - and z - directions of the control section  
ui  is the length of the control perimeter being considered  
β  is given by:  
                                                                                 (9.26)  
where  
u1  is the length of the basic control perimeter  
k is a coefficient dependent on the ratio between the column dimensions c1 and c2: its value is a function of 
the proportions of the unbalanced moment transmitted by  uneven shear and by bending and torsion (see 
Table 10).  
W1 corresponds to a distribution of shear as illustrated in Figure 6.19 and is a function of  the basic control 
perimeter u1: DRS 142: 2020  
75                ©RSB 2020  - All rights reserved  
 
                                                                                                      (9.27)  
dl  is a length increment of the perimeter  
e   is the distance of d l from the axis about which the moment MEd acts 
Table 11  — Values of k for rectangul ar loaded areas  
C1/C2  ≤ 0.5  1.0 2.0 ≥ 3.0  
K 0.45 0.60 0.70 0.80 
 
 
Figure 26  — Shear distribution due to an unba lanced moment at a slab -internal column connection  
9.4.3.4  For a rectangular column:  
                                                       (9.28)  
where:  
c1 is the column dimension parallel to the eccentricity of the load  
c2 is the column dimension perpendicular to the eccentricity of the load  
For internal circular columns β follows from:  
                                                                                           (9.29)  
Where   
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 D  is the diameter of the circular column  
e   is the eccentricity of the applied load e = M Ed / VEd 
9.4.3.5  For an internal rectangular column where the loading is eccentric to both axes, the following 
appro ximate expression for β may be used:  
                                                                             (9.30)  
where:  
ey  and  ez  are the eccentricities MEd/VEd along y and z axes respectively  
by  and  bz is the dimensions of the control perimeter (see Figure 21).  
NOTE ey results from a moment about the z axis and ez from a moment about the y axis.  
9.4.3.6  For edge column connections, where the eccentricity perpendicular to the slab edge  (resulting from a 
moment about an axis parallel to the slab edge) is toward the interior and there is no eccentricity parallel to 
the edge, the punching force may be considered to be uniformly distributed along the control perimeter u1* as 
shown in Figure 27(a).  
 
     a) edge column                                          b) corner column  
Figure 27  — Reduced basic control perimeter u1* 
 
9.4.3.7  Where there are eccentricities in both orthogonal directions, β may be determined using the following 
expression:  DRS 142: 2020  
77                ©RSB 2020  - All rights reserved  
 
                                                                                       (9.31)  
where,  
u1 is the basic control perimeter (see Figure 23)  
u1* is the reduced basic control perimeter (see Figure 27(a))  
epar is the eccentricity parallel to the slab edge resulting from a moment about an axis  perpendicular to the 
slab edge.  
k  may be determined from Table 11 with the ratio c1/c2 replaced by c1/2c2 
W 1  is calculated for the basic control perimeter u1 (see Figure 21).  
For a rectangular column as shown in Figure 27(a):  
                                                    (9.32 ) 
9.4.3.8  If the eccentricity perpendicular to the slab edge is not toward the interior, Expression (9.26) applies. 
When calculating W1 the distance e should be measured from the centroid axis of the control perimeter.  
9.4.3.9  For corner column connections , where the eccentricity is toward the interior of the slab, it is assumed 
that the punching force is uniformly distributed along the reduced control perimeter u1*, as defined in Figure 
27(b). The β-value may then be considered as:  
                                                                                                         (9.33)  
If the eccentricity is toward the exterior, Expression (9.21) applies.  
9.4.3.10  For structures where the lat eral stability does not depend on frame action between the slabs and the 
columns, and where the adjacent spans do not differ in length by more than 25%, approximate values for β 
may be used.  
NOTE  Recommended values of β are given in Figure 28.   
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Figure 28 — Recommended values for β  
 
9.4.4  Punching shear resistance of slabs and column bases without shear reinforcement  
9.4.4.1  The punching shear resistance of a slab should be assessed for the basic control section  according 
to 9.34. The design punching shear resistance [MPa] may be calculated as follows:  
                      (9.34)  
where:  
fck is in MPa  
 
ρly, ρlz relate to the bonded tension steel in y - and z - directions respectively. The values  
ρly and ρ lz should be calcul ated as mean values taking into account a slab width  equal to the column width 
plus 3 d each side.  
σcp = (σ cy + σ cz)/2 
where  DRS 142: 2020  
79                ©RSB 2020  - All rights reserved  
 σcy, σcz  are the normal concrete stresses in the critical section in y - and z directions  (MPa, positive if 
 compression):  
 
NEdy, NEdz are the longitudinal forces across the full bay for internal columns and the longitudinal force 
across the control section for edge columns. The force may be from a load or prestressing action.  
Ac  is the area of concrete according to the definition of  NEd 
NOTE  The recommended value for CRd,c is 0.18/ γ c, for vmin is given by Expression (9.3) and that for k1 is 0.1. 
9.4.4.2  The punching resistance of column bases should be verified at control perimeters within 2 d from the 
periphery of the column.  
9.4.4.2.1  For concentric loading the net applied forc e is  
VEd,red = VEd – ΔVEd                                                                                                               (9.35)                                                                                                                                        
where:  
VEd is the applied shear force  
ΔVEd is the net upward force within the control perimeter considered i.e. upwar d  pressure from soil minus 
self weight of base.  
vEd = VEd,red/ud    
                                                                                                                                              (9.36)                                                                                                   
                                                                     (9.37)  
Where:  
a  is the distance from the periphery of the column to the control perimeter considered  
CRd,c  is defined in 9.4.4.1  
Vmin   is defined in 9.4.4.1  
k  is defined in 9.4.4 .1 
9.4.4.2.2  For eccentric loading                                                                                                 
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                                                                                (9.38)  
Where  
k is defined in 9.4.3 (3) or 9.4.3 (4) as appropriate and W is similar to W1 but for  perimete r u. 
9.4.5  Punching shear resistance of slabs and column bases with shear reinforcement  
9.4.5.1  Where shear reinforcement is required it should be calculated in accordance with  Expression (9.39):  
vRd,cs = 0.75 vRd,c + 1.5 (d/sr) Asw fywd,ef (1/(u1d)) sinα                                       (9.39)  
where  
Asw is the area of one perimeter of shear reinforcement around the column [mm2] 
sr   is the radial spacing of perimeters of shear reinforcement [mm]  
fywd,ef  is the effective design strength of the  punching shear reinforcement, according to  fywd,ef = 250 + 0,25 
d ≤ fywd [MPa]  
d  is the mean of the effective depths in the orthogonal directions [mm]  
α is the angle between the shear reinforcement and the plane of the slab  
If a single line of bent -down bars is provided, then the ratio d/sr in expression (9.34) may be given the value 
0.67. 
9.4.5.2  Detailing requirements for punching shear reinforcement are given in 9.4.3.  
9.4.5.3  Adjacent to the column the punching shear resistance is limited to a maximum  of: 
                                                                                                 (9.40)  
where : 
for an interior column,    u0 = length of column periphery [mm]  
for an edge column,   u0 = c2 + 3d ≤ c2 + 2c1 [mm]  
for a corner column ,   u0 = 3d ≤ c1 + c2 [mm]  DRS 142: 2020  
81                ©RSB 2020  - All rights reserved  
 
 
c1, c2 are the column dimensions as shown in Figure 27  
for β,  see 9.4.3 (3), (4) and (5)  
NOTE  The recommended value of vRd,max is 0.5νfcd. 
9.4.5.4  The control perimeter at which shear reinforc ement is not required, uout (or uout,ef see Figure  6.22) 
should be calculated from expression (9.4 .1): 
uout,ef = βVEd / (vRd,c d)                                                                                                (9.41)  
9.4.5.5  The outermost pe rimeter of shear reinforcement should be placed at a distance not greater than kd 
within uout (or uout,ef, see Figure 29 ). 
where : 
for an interior column , u0 = length of column periphery [mm]  
for an edge column, u0 = c2 + 3d ≤ c2 + 2c1 [mm]  
for a corner col umn, u0 = 3d ≤ c1 + c2 [mm]  
c1, c2 are the column dimensions as shown in Figure 27  
ν, see Expression: v =0.6
            ( fck in MPa ) 
β, see 6.4.3 (3), (4) and (5)  
NOTE  The recommended value is 0 .5νfcd value of vRd,max . 
9.4.5.6  The control peri meter at which shear reinforcement is not required, uout (or uout,ef see Figure 29) 
should be calculated from Expression (9.42):  
uout,ef = βVEd / (vRd,c d)                                                                                         (9.42)   
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     Figure 29  — Control perimeters at internal columns  
NOTE  The recommended value of k is 1.5. 
9.5 Anchorages and laps  
9.6 Anchorage of longitudinal reinforcement  
9.6.1  General  
9.5.1.1  Reinforcing bars, wires or welded mesh fabrics shall be so anchored that the bond forces are safely 
transmitted to the concrete avoiding longitudinal cracking or spalling. Transverse reinforcement shall be 
provided if necessary.  
9.5.1.2  Methods of anchorage are shown in Figure 30.  
               
  
a) Basic tension anchor age length, lb,                     b) Equivalent anchorage length for standard bend  
             for any shape measured along the centreline  DRS 142: 2020  
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c) Equivalent anchorage length for standard loop   d) Equivalent an chorage length for standard hook  
 
e) Equivalent anchorage length for welded transverse bar  
Figure 30 — Methods of anchorage other than by a straight bar  
 
9.5.1.3  Bends and hooks do not contribute to compression anchorages.  
9.6.1  The design bond stress is limited to a value depending on the surface characteristics of the 
reinforcement, the tensile strength of the concrete and confinement of surrounding concrete. This depends on 
cover, transverse reinforcement and transverse pressure.  
9.6.2  The length necess ary for developing the required tensile force in an anchorage or lap is calculated 
on the basis of a constant bond stress.  
9.6.3  The anchorage of links and shear reinforcement should normally be effected by means of bends and 
hooks, or by welded transverse  reinforcement. A bar should be provided inside a hook or bend.  
9.6.4  The anchorage should comply with Figure 31. Welding should be carried out in accordance with ISO 
17660.  
NOTE  For definition of the bend angles see Figure 30.   
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Figure 31  — Anchorage of links  
NOTE  For c) and d) the cover should not be less than either 3 ϕ or 50 mm.  
9.7 Fatigue  
9.7.1  General  
When the imposed load on a structure is predominantly cyclic in character, take the effects of fatigue into 
consideration in satisfying limit state requirements.  
9.7.2  Verification conditions  
9.7.2.1  The resistance of structures to fa tigue shall be verified in special cases. This verification shall be 
performed separately for concrete and steel.  
9.7.2.2  A fatigue verification should be carried out for structures and structural components which are 
subjected to regular load cycles (e.g.  crane -rails, bridges exposed to high traffic loads).  
9.7.3  Internal forces and stresses for fatigue verification  
9.7.3.1  The stress calculation shall be based on the assumption of cracked cross sections  neglecting the 
tensile strength of concrete but satisfying  compatibility of strains.  
9.7.3.2  The effect of different bond behaviour of prestressing and reinforcing steel shall be taken into 
account by increasing the stress range in the reinforcing steel calculated under the assumption of perfect 
bond by the facto r, η, given by  
                                                                  (9.43)  
where:  DRS 142: 2020  
85                ©RSB 2020  - All rights reserved  
 As  is the area of reinforcing steel  
AP  is the area of prestressing tendon or tendons  
ϕs is the largest diameter of reinforcement  
ϕP is the diameter or equival ent diameter of prestressing steel  
ϕP 1.6 √AP for bundles  
ϕP   1.75 ϕwire for single 7 wire strands where ϕwire is the wire diameter  
ϕP   1.20 ϕwire for single 3 wire strands where ϕwire is the wire diameter  
ξ is the ratio of bond strength between bonded t endons and ribbed steel in concrete.  
10 Serviceability Limit States (SLS)  
10.1 General  
10.1.1  This section covers the common serviceability limit states.  Serviceability limit states are those that 
restrict stresses:  
a) deformation (deflection, rotation);  
b) local damage  (cracking, splitting, spalling);  
c) displacement (slip of connections);  
d) vibration; and  
e) corrosion . 
10.1.2  The above effects are likely to impair the normal use, occupancy, appearance or durability of the 
structure or of its structural or non -structural elemen ts, or they might affect the operation of equipment.  Effects 
such as temperature, creep, shrinkage, sway, settlement, and cyclic loading should be  considered, when 
relevant.  The design strength of materials and the design loads appropriate for serviceabili ty limit states 
should be use d. 
10.2 Deflection  
10.2.1  The deflection of the structure or of any part thereof should not exceed the permissible  value. 
Permissible values of deflection should comply with the requirements of the particular structure, taking the 
efficient functioning of the structure, possible damage to adjacent structures or aesthetic considerations into 
account.  As a guide, the limits given below can be regarded as reasonable.   
©RSB 2020  - All rights reserved                  86 
 10.2.2  The final deflection (including the effects of temperature, cre ep and shrinkage), measured  below the 
as-cast level of the support of floors, roofs and all other horizontal members, should not exceed span/250.  
10.2.3  Partitions and finishes will be affected only by that part of the deflection (including the  effects of 
temperature, creep and shrinkage) that takes place after the construction of the partitions or the application of 
the finishes. Information is lacking, but it is suggested that such deflection in the case of flexible partitions (e.g. 
dry-wall) be limited t o the lesser of span/350 or 20 mm. In the case of rigid brick walls or other brittle partitions, 
this deflection should be limited to the lesser of span/500 or 10 mm. Investigation is required in more 
complicated cases.  
10.2.4  If finishes are to be applied  to prestressed concrete elements, the total upward deflection  of the 
elements should not exceed span/300, unless uniformity of camber between adjacent elements can be 
ensured.  
10.2.5  Consider the effects of lateral deflections, particularly for tall slend er structures. The  acceleration 
associated with the deflections may be more critical than the deflection itself.  
10.2.6  In any calculation of deflections, take the design strength of materials and the design loads  as 
appropriate for a serviceability limit state.  
10.3 Crack control  
10.3.1  Cracking shall be limited to an extent that will not impair the proper functioning or durability of the 
structure or cause its appearance to be unacceptable.  
10.3.2  Cracking is normal in reinforced concrete structures subject to  bending, shear, torsion or tension 
resulting from either direct loading or restraint or imposed deformations.  
10.3.3  Cracks may be permitted to form without any attempt to control their width, provided they do not 
impair the functioning of the structure.  
10.3.4  A limiting value, wmax, for the calculated crack width, wk, taking into account the proposed function 
and nature of the structure and the costs of limiting cracking, should be established.  
10.3.5  The permissible width of cracks should be determined taking into account the requirements  (e.g. 
tightness, aesthetic appearance, etc.) of the particular structure.  
10.3.1  Reinforced concrete  
An assessment of the likely behaviour of a reinforced concrete structure enables identification of the sections 
where the eff ect of cracking should be considered. In general, the surface width of cracks should not exceed 
0.3 mm. Where elements are exposed to particularly aggressive environments,  the surface width of cracks at 
points nearest the main reinforcement should not, in  general, exceed 0,004 times the nominal cover to the 
main reinforcement. In a reinforced concrete structure under the effects of load and environment, the actual 
widths of cracks will vary considerably; the prediction of an absolute maximum width is there fore not possible, 
since the possibility of some cracks being even wider should be accepted unless special precautions are 
taken.  DRS 142: 2020  
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 10.3.2  Prestressed concrete  
10.3.2.1  In the assessment of the likely behaviour of a prestressed concrete structure, the flexural tens ile 
stress for structures of different classes should be limited as follows:  
a) class 1: no tensile stresses;  
b) class 2: tensile stresses, but no visible cracking; and  
c) class 3: tensile stresses, but surface width of cracks do not exceed 0,1 mm for elements  expo sed to 
particularly aggressive environment and do not exceed 0,2 mm for all other  elements.  
10.3.2.2  In either tall or long buildings, the effects of temperature, creep and shrinkage could, unless  
otherwise catered for, require the provision of movement jo ints both within the structure and between the 
structure and the cladding.  
 
10.3.2.3  In any calculations of crack widths ,take the design strength of the materials and the design loads as 
appropriate for a serviceability limit state.  
10.3.2.4  Sufficient no n-prestressed reinforcement should be provided to control cracking adequately.  
 
10.3.3  Vibration  
Where a structure is likely to be subjected to vibration from causes such as wind forces or machinery, take 
measures to prevent discomfort or alarm, damage to the str ucture, or interference with its proper function  
NOTE  In certain circumstances, it could be necessary to isolate the source of vibration or, alternatively, to isolate a part  or 
the whole of the structure. Special consideration could be necessary for flexi ble elements of structure.  
10.4 Other considerations  
10.4.1  Fire resistance  
Consider the following three conditions for structural elements that may be subjected to fire:  
a) retention of structural strength;  
b) resistance to penetration of flames; and  
c) resistance to heat tra nsmission.   
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 10.5 Loads and strength of materials  
10.5.1  Loads  
10.5.1.1  Nominal load  
The following nominal loads should be used in the design of a structure:  
a) nominal self -weight load Gn (i.e the weight of the structure complete with finishes, fixtures and 
partitions);  
b) nominal im posed load Qn; 
c) nominal wind load Wn; and  
d) earth and water pressure.  
10.5.1.2  Partial safety  factors for load γf 
10.5.1.2.1  The design load for a given type of limit state and loading is obtained from:  
a) Gn.γf = design self -weight load,  
b) Qn.γf = design imposed load,  
c) Wn.γf = design wind load,  
10.5.1.2.2  where γf is the appropriate partial safety factor for load, which is introduced to take account of 
possible unusual increases in load beyond those considered in the derivation of the  nominal loads,  
a) inaccurate assessment of  the effects of loading,  
b) unforeseen stress redistribution within the structure,  
c) the variations in dimensional accuracy achieved in construction,  
d) the importance of the limit state that is being considered.  
10.5.1.3  Load during construction  
The loading conditions du ring erection and construction should be considered in design and should be such 
that the structure's subsequent compliance with the limit state requirements is not impaired.  DRS 142: 2020  
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 10.6 Strength of materials  
10.6.1  Characteristic strength of materials  
Unless otherwise state d, the characteristic strength of materials means:  
a) the cube strength of concrete fcu,; 
b) the yield or proof stress of reinforcement fy, ; 
c) the ultimate strength of a prestressing tendon fpu below which not more than 5 % of the test results 
fall. 
10.6.2  Partial safet y factors for strength of materials γm 
For the analysis of sections, the design strength for a given material and limit state is derived from the 
characteristic strength divided by γm, where γm is the appropriate partial safety factor for material strength 
given in 10.7 and 10.8. Factor γm takes account of:  
a. differences between actual and laboratory values of strength;  
b. local weakness;  
c. inaccuracies in the assessment of the resistance of sections;  and 
d. the importance of the limit state that is being considered.  
10.7  Values for the ultimate limit stat e (loads and materials)  
10.7.1  Design loads  
10.7.1.1  The design load effect may be adjusted, at the discretion of the designer, by multiplying the design 
load by an importance factor γc to allow for the consequences of failure. In the case of critical structural 
elements for structures in which large crowds gather and where there would be very serious consequences in 
the event of a failure, a value of γc in the range 1,1 to 1,2 should be used. For structures with a very low 
degree of hazard to life and with less serious consequences of failure, a value of γc of 0,9 would be 
appropriate.  
10.7.1.2  In assessing the effect of loads on the whole structure or on any part of the structure, so arrange the 
loads as to cause the most severe stresses. It will only be necessary to use the factor 0 .9 if the self -weight 
load is an essential factor in the stability, e.g. for cantilevers or for wind forces. If a critical stability condition 
results in t he case of self -weight and wind loads combined and when (on selected parts of the structure) the 
self-weight load is increased, adopt the higher figure for the self -weight load, i.e. 1 .4 Gk. Generally, in the case 
of self -weight, imposed and wind loads com bined, assume that no variations in γf factors need be considered.  
10.7.1.3  Since the design of the whole or of any part of a structure may be controlled by any of the load 
combinations, consider each in design, and adopt the most severe.   
©RSB 2020  - All rights reserved                  90 
 10.7.1.4  If the p robable effect of excessive loads caused by misuse or accident has to be considered in the 
design, take the γf factor for the overload as 1 .05, and consider this only in conjunction with the sustained 
loads at the ULS. When considering the continued stabil ity of the structure after it has sustained localized 
damage, consider only the sustained portion of the loads at the ULS.  
NOTE  In general, the effect of creep, shrinkage and temperature will be of secondary importance for the ULS, and no 
specific calculat ions will be necessary.  
10.8 Values for serviceability limit states (loads and materials)  
10.8.1  Design loads  
10.8.1.1  General  
10.8.1.1.1  When assessing the deflection of a structure or of any part thereof, so arrange the imposed load 
as to cause the largest deflection.  The de sign loads given above apply when the immediate deflections of a  
structure are being estimated, but in most cases it is also necessary to estimate the additional time -dependent 
deflections due to creep, shrinkage and temperature.  
10.8.1.1.2  The deflection due to creep depends on the self -weight load and those imposed loads of long 
duration. Where the full imposed load is unlikely to be permanent, calculate the deflection due to creep on the 
assumption that only the self -weight load and that part of the impo sed load likely to be permanent are 
effective. This deflection could be upward. Consider the effects of temperature, including temperature 
gradients within the elements, when these effects exceed those known from experience to be inconsequential.  
10.8.1.1. 3 When an imposed load is predominantly cyclic in character, should give special attention to the 
assessment of the deflections.  
10.8.1.1.4  When assessing crack widths or other forms of local damage in a structure subjected to 
temperature, creep or shrinka ge effects exceeding those known from experience to be inconsequential, shall 
consider the resulting internal forces and their effect on the structure as a whole.  
10.8.2  Materials  
When assessing the deflections of a structure or of any part thereof, take the appr opriate values of γm as 1.0 
for both concrete and steel. Thus, take the properties of the materials relevant to deflection assessment, i.e. 
moduli of elasticity, creep, shrinkage, etc., as those associated with the characteristic strength of the materials 
. When assessing t he cracking strength of prestressed concrete elements by tensile stress criteria, γm should 
be taken as 1.3 for concrete in tension due to flexure and 1.0 for steel.  
11 Detailing of  reinforced concrete members  
11.1 General  
11.1.1  The requirements for safety, ser viceability and durability are satisfied by following the rules given in 
this section in addition to the general rules given elsewhere.  
11.1.2  The detailing of members should be consistent with the design models adopted.  The engineer will 
have to adopt a m ore suitable method, bearing in mind the nature of the structure in question.  DRS 142: 2020  
91                ©RSB 2020  - All rights reserved  
 11.1.3  Minimum areas of reinforcement are given in order to prevent a brittle failure, wide cracks and also to 
resist forces arising from restrained actions . 
11.1.4  This clause g ives methods of analysis and design that will, in general, ensure that for reinforced  
concrete structures, the objectives set out in clause 10 are achieved. Other methods may be used, provided 
that they can be shown to be satisfactory for the type of struc ture or element under consideration.  
11.1.1   Basis of limit states design  
This sub clause follows the limit states principles set out in clause 10. It is assumed that for reinforced 
concrete structures, the critical limit state will be the ultimate limit state. The design methods therefore take 
into account the partial safety factors appropriate to the ultimate limit state, and are followed by 
recommendations to ensure that the serviceability limit states of deflection, cracking or vibration are not 
reached. The serviceability limit states of deflection and cracking will not normally be reached if the 
recommendations given for span/effective depth ratios and reinforcement spacings are followed. The engineer 
may alternatively calculate deflections and crack width t o prove compliance with clause 10.  
11.1.2  Stability  
11.1.2.1  Ultimate horizontal load  
All structures should be capable of resisting an ultimate horizontal load applied at each floor and roof level 
simultaneously, of at least 1 .5 % of the nominal self -weight of the struct ure between mid -height of the storey 
below and either mid -height of the storey above or the roof surface. This force could be shared by the parts of 
the structure, depending on their stiffness and strength.  
11.1.2.2  Safeguarding against vehicular impact  
In order to  obviate the possibility of vehicles running into and damaging or destroying vital load -bearing 
elements in the ground floor of a structure, the provision of elements such as bollards, walls and retaining 
earth banks should be considered.  
11.1.2.3  Provision of ties  
In structures where all load -bearing elements are of concrete, horizontal and vertical ties should be provided.  
11.1.3  Durability and fire resistance  
The durability and the fire resistance of reinforced concrete depend on the amount of concrete cover to 
reinforc ement. Fire test results or other evidence may be used to ascertain the fire resistance of an element.  
11.1.4  Loads  
In this clause, the design load for the ultimate limit state is referred to as the ultimate load or the  maximum 
design load, to avoid confusion wi th the service load, which is the design load for the  serviceability limit states.  
In design, use the values of the ultimate loads given in 10.7, and the values of the service loads given in 10.8.   
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 11.1.5  Strength of materials  
In this clause, the design strengths of materials for the ultimate limit state are expressed (in all the tables and 
equations) in terms of the characteristic strength of the material. Unless specifically stated otherwise, all 
equations and tables include allowances for γ m, the partial safety factor for material strength.  
11.1.5.1  Characteristic strength of concrete  
The values of the 28 d characteristic strength of concrete, fcu, and the required strength of concrete at ages 
exceeding 28 d, for various grades of concrete, are given in Table 12. 
Table 12  — Strength of concrete  
Grade  Characteristic 
strength, fcu  
MPa Required strength at other ages  
MPa 
Age 
Months  
20 20.0 23 24 25 
25 25.0 29 30 31 
30 30.0 34 35 36 
35 35.0 39 40 42 
40 40.0 44 46 48 
45 45.0 49 51 53 
50 50.0 54 56 58 
Design considera tion should be based on the characteristic strength fcu, or, if relevant, on the  appropriate 
strength given in table 12 for the age at loading.  
For reinforced concrete, the lowest grade that should be used is 20 for concrete made with  normal -weight 
aggrega tes and 15 for concrete made with lightweight aggregates.  
11.1.5.2  Characteristic strength of reinforcement  
Base the design on the appropriate characteristic strength of reinforcement given in table 13. (If  necessary, a 
lower design stress may be used to help contr ol deflection or cracking, and possibly a different grade of 
reinforcement may be used.)  
Table 13 — Characteristic strength of reinforcement, fy 
Designation of reinforcement  Nominal size  
mm Characteristic strength fy  
MPa 
Hot rolled mild steel  All sizes  250 
Hot –rolled high -yield steel  All sizes  450 
Cold-work high -yield steel  All sizes  450 
Hard -drawn steel wire  Up to and including 12  850 DRS 142: 2020  
93                ©RSB 2020  - All rights reserved  
  
11.2 Bar spacing  
11.2.1  The spacing of bars shall be such that the concrete can be placed and compacted  satisfactorily fo r 
the development of adequate bond.  
11.2.2  The clear distance (horizontal and vertical) between individual parallel bars or horizontal layers of 
parallel bars should be not less than the maximum of k1 bar diameter, ( dg + k2 mm) or 20 mm where dg is the 
maximum size of aggregate.  
NOTE  The recommended values are of  k1 and k2 are 1 mm and 5 mm respectively.  
11.2.3  Where bars are positioned in separate horizontal layers, the bars in each layer should be located 
vertically above each other. There should be suff icient space between the resulting columns of bars to allow 
access for vibrators and good compaction of the concrete.  
11.2.4  Lapped bars may be allowed to touch one another within the lap length.  
11.3 Permissible mandrel diameters for bent bars  
11.3.1  The mini mum diameter to which a bar is bent shall be such as to avoid bending cracks in  the bar, 
and to avoid failure of the concrete inside the bend of the bar.  
11.3.1  In order to avoid damage to the reinforcement; the diameter to which the bar is bent  (Mandrel 
diameter) should not be less than ϕm, min for bars and wire (See table 14)  
Table14  — Minimum mandrel diameter to avoid damage to reinforcement  
Bar diameter  Minimum mandrel diameter for bends, hooks and 
loops  
ϕ ≤16mm  4ϕ 
ϕ 
 16mm  7ϕ 
11.4 Analysis of  structures and structural frames  
11.4.1  Analysis of complete structures and complete structural frames  
Analysis shall  be in accordance with 10.8  
NOTE In the case of frame structures, ensure that if failure were to occur in critical conditions, it would occur in  the beams 
and not in the columns.   
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 11.4.2  Analysis of structural frames supporting vertical loads only  
11.4.2.1  Simplification into sub frames  
11.4.2.1.1  When a frame supporting vertical loads only is assumed, the moments, loads and shear forces 
to be used in the design o f individual columns and beams may be derived from an elastic analysis of a series 
of sub frames. Each sub frame may be taken to consist of the beams at one level together with the columns 
above and below. The ends of the columns remote from the beams may generally be assumed to be fixed, 
unless the assumption of a pinned end is clearly more reasonable (for example where a foundation detail is 
considered unable to develop moment restraint).  
11.4.2.1.2  It will normally be sufficient to consider the following  critical arrangements of vertical load:  
a) all spans loaded with total ultimate load (1 .4Gk + 1.6Qk); 
b) all spans loaded with ultimate self -weight load (1 .4Gk) and alternate spans loaded with  ultimate 
imposed load (1 .6Qk). 
11.4.2.2  Alternative simplification of sub fra mes (i ndividual beams with associated  columns)  
11.4.2.2.1  The moments and forces in each individual beam may be found by considering a simplified sub 
frame consisting only of that beam, the columns attached to the ends of the beam and the beams on either 
side, if any. The column ends and the beam ends remote from the beam under consideration may generally 
be assumed to be fixed, unless the assumption of pinned ends is clearly more reasonable. The stiffness of the 
beams on either side of the beam under consi deration should be taken as half their actual stiffness values if 
they are taken to be fixed at their outer ends.  
11.4.2.2.2  The critical loading arrangements should be taken as follows:  
a) all spans loaded with total ultimate load (1.4Gk + 1.6Qk); 
b) all spans loaded with ultimate self -weight load (1 .4Gk) and alternate spans loaded with ultimate 
imposed load (1 .6Qk).  
11.4.2.2.3  The moments in an individual column may also be found from this simplified sub frame, provided 
that the sub frame has at its central be am the longer of the two spans framing into the column under 
consideration.  
11.4.2.3  "Continuous beam" simplification  
As a more conservative alternative to the preceding sub frame arrangements, the moments and shear forces 
in the beams at one level may also be obta ined by regarding the beams as a continuous beam over supports 
providing no restraint to rotation.  
11.4.2.4  A symmetrically loaded columns where a beam has been analysed in  accordance with 
11.4.2.3  
In these columns, the ultimate moments may be calculated by simple  moment distribution procedures, on the 
assumption that the columns and beam ends remote from the junction under consideration are fixed and that DRS 142: 2020  
95                ©RSB 2020  - All rights reserved  
 the beams possess half their actual stiffness. The arrangement of the design ultimate imposed load should be 
such as to cause the maximum moment in the column.  
11.4.2.5  Analysis of structural frames supporting vertical and lateral loads  
11.4.2.5.1  When a frame provides lateral stability to the structure as a whole, it will be necessary to  
consider the effect of lateral loa ds. In addition, if the columns are slender, it may be  necessary to consider 
additional moments (e.g. from eccentricity) that may be imposed on beams at beam column junctions.  
11.4.2.5.2  In most cases, the design of individual beams and columns may be base d either on the  
moments, loads and shears obtained by considering vertical loads only or on those  obtained by considering 
both vertical and lateral loads.  
11.4.2.5.3  An elastic analysis of a series of sub frames, each consisting of the beams at one level  together 
with the columns above and below. The ends of the columns remote from the beams may generally be 
assumed to be fixed, unless the assumption of pinned ends is clearly more reasonable.  
11.4.2.5.4  An Lateral loads should be ignored and all beams shou ld be considered to be loaded as in 11.4.3 . 
11.4.2.5. 5 An analysis of the complete frame, assuming points of contra flexure at the centres of all  beams 
and columns, ignoring self -weight and imposed loads and considering only the design wind load on the 
structure. If more realistic, instead of assuming points of contra flexure at the centres of ground floor columns, 
the feet should be considered pinned.  
11.4.3  Redistribution of moments  
Redistribution of the moments obtained by elastic analysis or by the simplified methods given in 11.4.3.  and 
11.4.4 may be carried out, provided the following conditions are satisfied:  
a) condition 1 : equilibrium between internal and external forces is maintained under all appropriate 
combinations of ultimate load.  
b) condition 2 : where the  design ultimate resistance moment of the cross -section subjected to the 
largest moment within each region of hogging or sagging is reduced, the neutral axis depth x should 
not exceed (βb-0.4)d  
where  
d is the effective depth; and  
β is the moment at section after redistribution  
b is the  moment at section before redistribution < 1 from the respective maximum moments  diagrams.  
NOTE  Unless the column axial load is small, condition 2 will  generally rule out reduction in column moment.  
c) condition 3 : the ultimate resistance moment at any section of an element complies with the  
appropriate value obtained from the final envelope of redistributed elastic moments on the element,  
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 and the ultimate resistance moment at any section is at least 75 % or 80 %, as relevant, of the elastic 
moment at that particular section, obtained from elastic maximum moment diagrams covering all 
appropriate combinations of ultimate loads. The value of 75 % is applicable  in the case of uniform 
elements (the cross -section considered does not change along the element). The value of 80 % is 
applicable in the case of non -uniform elements.  
d) condition 4 : in structures exceeding four storeys and in which the structural frame prov ides the lateral 
stability, the redistribution of moments is limited to 10 % and the value given in condition 3 reads 90 
%. 
e) condition 5 : in the case of linear elastic analysis being used, the relative stiffness of the elements is 
not based on the transform ed sections.  
11.4.4  Column and beam construction  
Any structural frame in a building provided with lateral stability by walls or bracing designed to resist all lateral 
forces may be considered to consist of continuous beams and columns.  
11.5 Beams  
11.5.1  General  
11.5.1.1  Design limit ation  
Beams of normal proportions are the subject of this sub clause. In the case of beams of depth  exceeding half 
of their clear span, specialist literature should be consulted.  
11.5.1.2  Effective span of simply supported beams  
The effective span of a simply suppo rted beam is the smaller of:  
a) the distance between the centres of bearings,  
b) the clear distance between supports plus the effective depth.  
11.5.1.3  Effective span of a continuous beam  
The effective span of a continuous beam is the distance between the centres of sup ports. In the case of an 
embedded end, the centre of action of support should be taken to be half the effective depth from the face of 
the support.  
11.5.1.4  Effective length of a cantilever  
The effective length of a cantilever should be taken as its length to the f ace of the support plus half the 
effective depth. If a cantilever forms the end of a continuous beam, the effective span should be taken as its 
clear length plus the distance to the centre of the support.  DRS 142: 2020  
97                ©RSB 2020  - All rights reserved  
 11.5.1.5  Effective width of flanged beam  
In the absence of a  more accurate determination, ensure that the effective flange width  
a) for a T -beam does not exceed the lesser of:  
1) the web width plus L z /5 and  
2) the actual width of the flange, and  
b) for an L -beam does not exceed the lesser of:  
1) the web width plus L z /10 and  
2) the actual width of the flange,  
where L z is the distance between points of zero moment (considering the bending moment envelope on 
spans). For a continuous beam, L z may be taken as 0,7 times the effective span.  
11.5.1.6  Slenderness limits for beams  
To ensure later al stability, the clear distance between lateral restraints should not exceed the following:  
a) for simply -supported and continuous beams, the lesser of 60 bc and 250 b2c /d; and  
b) for cantilevers with lateral restraint provided only at the support, the lesser of  25b c and 100 b2c /d 
where : 
 b  is the width of the compression face of a beam midway between restraints, or width of th e 
compression face of a cantilever; and  
 d is the effective depth.  
For parapet beams, lateral restraint may be assumed to be provided by  slabs attached to the tension zone, 
provided that the slab thickness is at least one -tenth of the effective depth of the parapet beam and the 
parapet beams themselves do not project above the slab by more than ten times their width.  
For the relationship b etween slenderness limits for beams and the strength of concrete to be used, specialist 
literature should be consulted.  
11.5.2  Longitudinal reinforcement of beams  
11.5.2.1  Minimum and maximum reinforcement areas  
11.5.2.1.1  The area of longitudinal tension reinforcement sh ould not be taken as less than As,min  
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 NOTE 1 See also 10.3 for area of longitudinal tension reinforcement to control cracking.  
NOTE 2 The recommended value of  As,min for beams  is given in the following:  
              (11.1)  
but not less than 0,0013b td                                                     
where : 
bt   denotes the mean width of the tension zone; for a T -beam with the flange in compression, only the width 
 of the web is taken into account in calculating the value of bt. 
fctm should be determine d with respect to the relevant strength class according to Table 2.  
Alternatively, for secondary elements, where some risk of brittle failure may be accepted, As,min may be taken 
as 1.2 times the area required in ULS verification.  
11.5.2.1.2  Sections conta ining less reinforcement than As,min should be considered as unreinforced.  
11.5.2.1.3  The cross -sectional area of tension or compression reinforcement should not exceed As,max  
outside lap locations.  
NOTE  The recommended value value of As,max for beams is 0.04Ac. 
11.5.2.1.4  For members prestressed with permanently unbonded tendons or with external prestressing 
cables, it should be verified that the ultimate bending capacity is larger than the flexural cracking moment. A 
capacity of 1 .15 times the cracking m oment is sufficient.  
11.5.2.2  Other detailing arrangements  
11.5.2.2.1  In monolithic construction, even when simple supports have been assumed in design, the 
section at supports should be designed for a bending moment arising from partial fixity of at least β 1 of the 
maximum bending moment in the span.  
NOTE 1 The recommended value  of β 1 for beams is 0 .15. 
NOTE 2 The minimum area of longitudinal reinforcement section defined in 11.5.2.1 .1  applies.  
11.5.2.2.2  At intermediate supports of continuous beams, the total ar ea of tension reinforcement As of a 
flanged cross -section should be spread over the effective width of flange. Part of it may be concentrated over 
the web width (See figure 32).  
 DRS 142: 2020  
99                ©RSB 2020  - All rights reserved  
 
 
Figure 32  — Placing of tension reinforcement in flanged cross -section.  
11.5.2.2.3  Any compression longitudinal reinforcement (diameter ϕ) which is included in the resistance  
calculation should be held by transverse reinforcement with spacing not greater than 15 ϕ. 
11.5.2.3  Curtailment of longitudinal tension reinforcement  
Sufficient reinforcement should be provided at all sections to resist the env elope of the acting tensile force, 
including the effect of inclined cracks in webs and flanges.  
11.5.2.4  Anchorage of bottom reinforcement at an end supports  
The area of bottom reinforcement provided at end supports with little or no end fixity assumed in design, 
should be at least β 2 of the area of steel provided in the span.  
NOTE  The recommended value of β 2 for beams is 0 .25. 
 
 
 
 
 
 
a) Direct support:  
Beam supported wall or column                                                                                                                                                                                                                
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a) Indirect support:  
Beam in tersecting another supporting beam  
 
 
 
 
 
Figure 33  −Anchorage of bottom reinforcement at end supports  
 
11.5.2.5  Anchorage of bottom reinforcement at intermediate supports  
11.5.2.5.1  The area of reinforcement given in 11.5.2.4  applies.  
11.5.2.5.2  The anchorage length should not be less than 10 ϕ (for straight bars) or not less than the 
diameter of the mandrel (for hooks and bends with bar diameters at least equal to 16 mm) or twice the 
diameter of the mandrel (in other cases ) (see Figure 34 (a)).   
11.5.2.5.3  The reinforcement required to resist possible positive mome nts (e.g. settlement of the support, 
explosion, etc.) should be specified in contract documents. This reinforcement should be continuous which 
may be achieved by means of lapped bars (see Figure 34 (b) or (c))  
 
Figure 34  — Anchorage at intermediate suppor ts 
 
11.5.2.6  Continuous beams  
Continuous beams may be analysed in accordance with 11.5.2.7 or 11.5.2.8.  
DRS 142: 2020  
101                ©RSB 2020  - All rights reserved  
 11.5.2.7  Continuous beams: moments and shear forces (general case)  
11.5.2.7.1  The maximum elastic moments and shear forces at any section of a continuous beam may be 
obtained by regarding the beam either as part of a frame in accordance with 11.4.3 , or as continuous over its 
supports and capable of free rotation about them.  
11.5.2.7.2  In the latter case ,make an elastic analysis considering the following arrangements of lo ad: all 
spans loaded with total ultimate load (1 .4Gk + 1.6Qk); all spans loaded with ultimate self -weight load (1 .4Gk) 
and alternate spans loaded with ultimate imposed load (1 .6Qk). 
11.5.2.7.3  For continuous beams over supports, the design hogging moment n eed not be taken as greater 
than the moment at a distance d 12 from the face of the support, i.e. if the support is wide, the moment at the 
centre of the support need not be used.  
11.5.2.8  Continuous beams: moments and shear forces (uniform loading and approximatel y equal 
 spans)  
Provided that the ratio of the characteristic imposed load to the characteristic self -weight load does not exceed 
1.25 for beams that support substantially uniformly distributed loads over three or more spans that do not 
differ by more than  15 % from the longest span, the ultimate bending moments and shear forces used in 
design may be obtained from table 4.  
11.5.2.9  Shear reinforcement  
11.5.2.9.1  The shear reinforcement should form an angle α of between 45° and 90° to the longitudinal axis 
of the structural element.  
11.5.2.9.2  The shear reinforcement may consist of a combination of:  
a) links enclosing the longitudinal tension reinforcement and the com pression zone (see  Figure 35);  
b) bent-up bars;  
c) cages, ladders, etc. which are cast in without enclosing the longitudinal reinforcement bu t are properly 
anchored in the compression and tension zones.  
  
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 Figure 35 — Examples of shear reinforcement  
11.5.2.9.3  Links should be effectively anchored. A lap joint on the leg near the surface of the web is 
permitted provided that the link is not required to resist torsion.  
11.5.2.9.4  At least β 3 of the necessary shear reinforcement should be in the form of links.  
NOTE  The recommended value of β 3  is 0.5. 
11.5.2.9.5  The ratio of shear reinforcement is given by Expression (11.2):  
ρw = Asw / (s . bw . sin α)                                                                                   (11.2)  
where:  
ρw is the shear reinforcement ratio  
ρw should not be less than ρ w,min 
Asw is the area of shear reinforcement within length s 
s  is the spacing of the shear reinforcement measured along the l ongitudinal axis of the  member  
bw  is the breadth of the web of the member  
α  is the angle between shear reinforcement and the longitudinal axis (see 11.5.2.9 .1) 
NOTE  The recommended value of ρ w,min is given Expression (11.3) .  
                                                                          ( 11.3)  
where , 
ρw is the shear reinforcement ratio  
ρw should not be less than ρ w,min 
Asw  is the area of shear reinforcement within length s 
s is the spacing of the shear reinforcement measured along the longi tudinal axis of  the member  
bw is the breadth of the web of the member  
α  is the angle between shear reinforcement and the longitudinal axis (see 11.5.2.9 .1) DRS 142: 2020  
103                ©RSB 2020  - All rights reserved  
 NOTE  The recommended value of ρ w,min  is given in Expression (11.4).  
                                                                             ( 11.4)  
11.5.3  Torsion reinforcement  
11.5.3.1  The torsion links should be closed and be anchored by means of laps or hooked ends, see  Figure 
36, and should form an angle of 90° with the axis of the structural eleme nt. 
 
                            a) recommended shapes                  b) not recommended shape  
Figure 36 — Examples of shapes for torsion links  
NOTE  The second alternative for a2) (lower sketch) should have a full lap length along the top.  
11.5.3.2  The provisions of 11.5.2.9 (5) is generally sufficient to provide the minimum torsion links required . 
11.5.3.3  The longitudinal bars should be so arranged that there is at least one bar at each corner,  the others 
being distributed uniformly around the inner pe riphery of the links, with a spacing not  greater than 350 mm.  
11.5.4  Surface reinforcement  
It may be necessary to provide surface reinforcement either to control cracking or to ensure adequate 
resistance to spalling of the cover.  
11.5.5  Indirect supports  
11.5.5.1  Where a beam is supported by a beam instead of a wall or column, reinforcement should be provided 
and designed to resist the mutual reaction. This reinforcement is in addition to that required for other reasons. 
This rule also applies to a slab not supported at the top of a beam.  
11.5.5.2  The supporting reinforcement between two beams should consist of links surrounding the principal 
reinforcement of the supporting member. Some of these links may be distributed outside the volume of the 
concrete, which is common to the two beams, (see Figure 37).  
  
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 supporting beam with height h1 
  
  supported beam with height h2 (h1 ≥ h2) 
Figure 37  — Placing of supporting reinforcement in the intersection zone of two  beams (plan view)  
Table 15 — Ultimate bending moments* ) and shear forces  
Position  Moment  shear  
At outer support  0 0.45F 
Near middle of end span  
 - 
At first interior support  
 0.6F 
At middle of interior support  
 - 
At interior support  
 0.55F 
*) Do not red istribute the moments obtained from the table.  
NOTE  F is the total ultimate load ( 1,4Gk+ 1,6 Qk) and l is the effective span  
 
11.5.6  Moments of resistance at ultimate limit state for beams  
11.5.6.1  Analysis of beams  
11.5.6.1.1  When a cross -section of a beam is being ana lysed to determine its ultimate moment of 
resistance, the following assumptions should be made:  
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 a. the strain distribution in the concrete in compression and the strains in the reinforcement, 
whether in tension or in compression, are derived from the assumpti on that plane sections 
remain plane;  
b. the simplified stress diagram of concrete in compression is as shown in figure 38.  
11.5.6.1.2  the strain at the outermost compression fibre is taken as 0 .003 5; and  
11.5.6.1.3  where beams are reinforced for tension only , the depth of the concrete in compression is limited 
to half the effective depth of the beam;  
d) the tensile strength of the concrete is ignored;  
e) where the beam is designed to resist flexure only, the lever arm is assumed not to exceed 0 .95 times 
the effecti ve depth. In the analysis of a cross -section of a beam that has to resist a small axial thrust, 
the effect of the ultimate force may be ignored if the force does not exceed the value of 0,1 fcu 
multiplied by the cross -sectional area.  
11.5.6.2  Design possibilities  
In the actual design, in order to find the amount of reinforcement required, either the design formulae given in 
11.5.6.4, or strain compatibility together with the assumption of plane strain (in the case of non -rectangular 
beams) may be used.  
11.5.6.3  Design formula e of moments of resistance for rectangular beams  
NOTE  All formulae given in this sub clause include allo wances for γ m. 
In the case of a rectangular beam, flanged beam, solid slab, ribbed slab or voided slab when the neutral axis 
lies within the flange, use the following equations based on figure 38:  
K/ is 0.156 when redistribution of bending moments does not  exceed 10 % (the neutral axis depth is limited 
to d/2); 
K/ is 0.402 (β b - 0.4) - 0.18 (β b  - 0.4)2 when redistribution exceeds 10 %;   
©RSB 2020  - All rights reserved                  106 
 
 
NOTE  The material factor γ m for concrete differs from γ m for steel.  
Figure 3.1 — Ultimate forces, stresses and strains in reinforced concrete sections at the ultimate limit 
state  
 
If K  ≤ K /, only tension reinforcement is required and  
 
 
x  (d - z)/0,45  
As  M/0,87 fyz; 
If K > K , tension and compression reinforcement are required, and  
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107                ©RSB 2020  - All rights reserved  
 x = (d - z)/0.45 
 
 
In the case o f a flanged beam where the neutral axis lies below the flange, the required steel  area may be 
calculated from the following equation:  
 
provided that the following requirements are met:  
a) hf < 0,45 d; 
b) the design ultimate moment is less than β f fcu bd 2 (βf being as given in Table 5 below);  
c) not more than 10 % of redistribution has been carried out (the neutral axis depth is limited to d/2). 
Table 16  — Values of the factor β f 
b/bw  βf 
d/hf 
 ≤ 2 3 4 5 6 ∞ 
1 0.15 0.15 0.15 0.15 0.15 0.15 
2 0.15 0.14 0.12 0.12 0.11 0.08 
4 0.15 0.13 0.11 0.10 0.09 0.04 
6 0.15 0.13 0.11 0.09 0.08 0.03 
8 0.15 0.13 0.10 0.09 0.08 0.02 
∞ 0.15 0.13 0.10 0.08 0.07 0 
The ultimate design moment of resistance of a flanged beam where the neutral axis lies  below the flange may 
be taken  as the lesser of the values given by the following equations:  
                                                                    (11.5)  
Where it is necessary for the moment of resistance to exceed the value given by equation (11.5).   
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 11.5.7  Shear resistance of beams  
All formulae given in this subclause include allowances for γm. 
11.5.7.1  Shear stress and shear reinforcement in beams  
11.5.7.1.1  The design shear stress v at any cross -section of a beam should in no case exceed a value of 
the lesser of 0.75√fcu or 4.75 MPa, regardless of any shear reinforcement provided.  
 
Where:  
V is the design shear force due to design maximum loads for ultimate limit state;  
b is the width of section (for a flanged beam, should be taken as the rib width); and  
d is the effective depth.  
11.5.7.1.2  Where the shear stress exceeds vc as calculated from equatio n (11.6), provide shear  
reinforcement in the form of links or links combined with bent -up bars  
11.5.7.1.3 Bent-up bars  should not be spaced  at more than 1,5 times the effective depth of the beam.  
Calculate vc from:  
                                               ( 11.6)  
where : 
γm  is the partial safety factor for materials and fcu is the characteristic strength of concrete (but  not exceeding 
40 MPa),   
 
                    should not be taken as greater than 3,  
where : 
As  is the area of properly anchored tension reinforcement (in the case of prestresse d concrete the stressed 
and unstressed reinforcement should be considered), and  
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109                ©RSB 2020  - All rights reserved  
 bv is the width of section (for a flanged beam this should be taken as average width of the rib  below the 
flange),  
d  is the eff ective depth.  
11.5.7.1.4  Table 17 provides values of vc for 25 MPa concrete, for a typical range of steel contents and 
effective depths.  
Table 17 − Maximum design shear stress, vc for grade 25 concrete  
 Maximum design shear stress of concrete, v c 
MPa 
Effective depth, d  
mm 
125 150 175 200 225 250 300 400 500 800 
0.15 0.38 0.36 0.35 0.34 0.33 0.32 0.31 0.28 0.27 0.24 
0.25 0.45 0.43 0.41 0.40 0.39 0.38 0.36 0.34 0.32 0.28 
0.50 0.57 0.54 0.52 0.51 0.49 0.48 0.46 0.43 0.40 0.36 
0.75 0.66 0.62 0.60 0.58 0.56 0.55 0.52 0.49 0.46 0.41 
1.00 0.72 0.68 0.66 0.64 0.62 0.60 0.58 0.54 0.46 0.45 
1.50 0.82 0.78 0.75 0.73 0.71 0.69 0.66 0.61 0.51 0.52 
2.00 0.90 0.86 0.83 0.80 0.78 0.76 0.73 0.67 0.58 0.57 
3.00 1.03 0.99 0.95 0.92 0.89 0.87 0.83 0.77 0.73 0.65 
NOTE  Allowance has been made in these figures for γ m of 1.40 
11.5.7.1.5  When links are used for shear reinforcement, ensure that the spacings of the legs (in the 
direction of the span and at right angles to it) do not exceed 0,75 d and that the following condi tion is satisfied:  
      
fw  is the characteristic strength of link reinforcement (but not exceeding 450 MPa);  
Asv  is the cross -sectional area of two legs of a link; and  
Sv  is the spacing of links along beam.  
11.5.7.1.6  Up to 50 % of the shear reinforce ment may be in the form of bent -up bars, which are  assumed to 
form the tension members of one or more single systems of lattice girders in which the concrete forms the 
compression members. The maximum stress in any bar should be taken as 0 .87f,. 
11.5.7.1.7  The shear resistance in any vertical section is the sum of the vertical components of the tension 
and compression forces cut by the section.   
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 11.5.7.1.8  The shear resistance of a single system of bent -up bars with the bars inclined at 45" or more, 
may be c alculated from the following equation:  
 
where,  
Asb is the cross -sectional area of bent -up bars within the length of that part of a beam traversed  by a shear 
failure plane;  
fw, is the characteristic strength of bent -up bars (but not exceeding 450 MPa);  
α,β  are the angles as in figure 5; and  
Sb  is the spacing of bent -up bars ( see figure 39).  
 
β and α are ≥ 45o 
Figure 39 — Single system of bent -up bars  
11.5.7.2  Shear in sections close to supports  
11.5.7.2.1  Enhanced shear strength of sections close to supports  
11.5.7.2.1.1  Account may be taken of the enhancement in any situation where the section or concentrated 
load under consideration is closer to the face of a support than twice the effective depth d. This  enhancement 
is particularly useful for corbels or pile caps.  
11.5.7.2.1.2  Shear failure at sections of beams and cantilevers without shear reinforcement  will normally 
occur on a plane inclined at an angle of about 300 to the horizontal. If the angle of failure plane is forced to be 
inclined more steeply than this (becau se the section under consideration (x -x in figure 40) is close to a 
support, or for other reasons), the shear force required to produce failure is increased.  
11.5.7.2.1.3  This enhancement of shear strength may be taken into account in the design of section s near a 
support by increasing the design concrete shear stress vc, to vc 2d /av (d is the effective depth and av is as DRS 142: 2020  
111                ©RSB 2020  - All rights reserved  
 
 
shown in figure 40), provided that v at the face of the support remains less than the lesser of and 4 MPa (this 
limit includes a γ m of 1.4). 
 
Figure 40  — Shear failure near supports  
 
11.5.7.2.2  Shear reinforcement for section close to supports  
If shear reinforcement is required, the total area of this is given by      
 
 
where  
av  and dare as in 11.5.7.2.1;  
bv is the width of section (for a flanged beam, this should be taken as average width of the rib  below the 
flange);  
v is the design shear stress at a cross -section;  
vc is the design shear stress of concrete (see 11.5.7.1); and  
fw is the characteristic streng th of the link reinforcement (but not exceeding 450 MPa).   
©RSB 2020  - All rights reserved                  112 
 This reinforcement should be provided within the middle three -quarters of a,. Where a, is less than d, 
horizontal shear reinforcement will be more effective than will vertical, and both should be us ed. 
11.5.7.2.3  Enhanced shear strength near supports  
11.5.7.2.3.1  The procedures given in 11.5.7.2.1 and 11.5.7.2.2 may be used for all beams. However, for 
beams carrying a generally uniform load or where the principal load is located further than 2d from the face o f 
support, the shear stress may be calculated at a section a distance from the face of the support.  
11.5.7.2.3.2  The value of v, is calculated in accordance with 11.5.7.1, and the appropriate shear 
reinforcement assessed. If this amount of shear reinforcem ent is provided at sections closer to the support, no 
further check for shear at such sections is required.  
11.5.7.3  Bottom loaded beams  
Where load is applied through the side face below the neutral axis of a beam or the bottom of a beam, 
sufficient vertical reinfo rcement to carry the load up to the top face of the beam should be provided  in addition 
to any reinforcement required to resist shear.  
11.5.7.4  Shear and axial load  
The design shear stress v/c that can be supported by a section v subjected to shear and to axial  compression 
without shear reinforcement can be calculated from the equation 11.7(a). Both adverse and beneficial load 
combinations should be considered  
                                                                    ( 11.7 (a))  
where  
N is the design a xial force;  
V is the design shear force due to ultimate loads;  
H  is the overall depth;  
Ac is the gross area of concrete section. ( N/A c is intended to be the average stress in the  concrete, acting at 
the centroid of the section); and  
M is the design ultima te moment at the section under consideration.  
The value of Vh/M should be taken as not greater than 1.  DRS 142: 2020  
113                ©RSB 2020  - All rights reserved  
 Where it is considered necessary to avoid shear cracking prior to the ultimate limit state, the shear stress 
should be limited to the value given by equa tion 11.7(b):
                                                                        
( 11.7 (b)) . 
 
11.5.7.5  Torsional shear stress vt 
11.5.7.5.1  11.5.7.5.1  Rectangular sections  
The torsional shear stress vt  at any section should be calculated assuming a plastic stress distr ibution and 
may be calculated from the following equation:  
 
where : 
T   is the torsional moment due to design loads for the ultimate limit state;  
Hmin  is the smaller dimension of rectangular section; and  
Hmax  is the larger dimension of rectangular sectio n. 
11.5.7.5.2  T-, L- or I-sections  
T-, L- or I-sections may be treated by dividing them into their component rectangles; these are chosen in such 
a way as to maximize h3min x hmax, which will generally be achieved if the widest rectangle is made as long as 
possible.  
 
Then 11.5.7.5.1  should be followed, bearing in mind that each of these component rectangles is subjected to 
a torsional moment as follows:  
 
11.5.7.5.3  Reinforcement for torsion  
11.5.7.5.3.1  Where the torsion shear stress vt exceeds the value vt,min in table 17, rei nforcement should be 
provided.   
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 11.5.7.5.3.2  In no case may the sum of the shear stresses resulting from shear force and torsion ( v + vt) 
exceed the value vtu in table 17 nor, in the case of small sections ( y1 < 550 mm), shall the torsion shear stress  
vt exceed vtu y1/550, where y1 is the larger centre -to-centre dimension of a link.  
Table 17 — Minimum and ultimate torsional shear stress in megapascals  
Concrete grade  Minimum torsional shear stress, 
vtmin Ultimate torsional shear stress, v tu 
20* 0.27 3.18 
25 0.30 3.56 
30 0.33 4.00 
≥40 0.36 4.50<v tu<4.75 
*) Grade not recommended  
NOTES  
Allowance has been made in these figures for a γ m of 1.40 
Values of v tu are derived from the equation  
vtu = 
 but not exceeding 4 .75 MPa.  
 
Recommendations for reinforcement for combi nations of shear and torsion are given in table 18.  
Table 18 — Reinforcement for shear and torsion  
 vt ≤ vtmin 
 vt > v tmin 
v≤ v c+0.4 Minimum shear reinforcement; no 
torsion reinforcement  Designed torsion reinforcement but 
not less than the minimum shear 
reinforcement  
v>v c+0.4 Designed shear reinforcement; no 
torsion reinforcement  Designed shear and torsion 
reinforcement  
 
11.5.7.5.4  Area of torsional reinforcement  
Torsional reinforcement should consist of rectangular closed links together with longitudinal  reinforce ment. 
This reinforcement is additional to any requirements for shear and bending and should be such that  
 
 
where  DRS 142: 2020  
115                ©RSB 2020  - All rights reserved  
 Asv is the area of two legs of closed links at a section (in a section reinforced with multiple  links, the area of 
the legs lying closest to the outside of the section should be used);  
As is the area of longitudinal reinforcement;  
Fyv  is the characteristic strength of links (but not exceeding 450 MPa);  
fy  is the characteristic strength of longitudinal reinforcement (but not exceeding 450 MPa) ; 
sv  is the spacing of links;  
x1  is the smaller centre -to-centre dimension of rectangular link; and  
y1  is the larger centre -to-centre dimension of rectangular link.  
11.5.7.5.5  Spacing and type of links  
The spacing of the links sv should not exceed the least of x1, y1/2 and 200 mm.  
11.5.7.5.6   Arrangement of longitudinal torsional reinforcement  
Longitudinal torsional reinforcement should be distributed evenly round the inside perimeter of the links. The 
clear distance between these bars should not exceed 300 mm, and at least f our bars, one in each corner of 
the links, should be used. Additional longitudinal reinforcement required at the level of the tension or 
compression reinforcement may be provided by using larger bars than those required for bending only. The 
torsional rein forcement should extend for a distance at least equal to the largest dimension of the section 
beyond where it theoretically ceases to be required.  
11.5.7.5.7  Arrangement of links in T -, L- or I-sections  
In the component rectangles, the reinforcement cages should be s o detailed that they interlock and tie the 
component rectangles of the section together. Where the torsional shear stress in a minor component 
rectangle is less than vt,min, no torsional reinforcement need be provided in that rectangle.  
11.5.8  Deflection of beams  
11.5.8.1  General  
11.5.8.1.1  Deflection may be calculated and compared with the serviceability requirements given  ,but in all 
normal cases, the deflection of a beam will not be excessive if the ratio of its span to its effective depth does 
not exceed the appropriat e ratio.  
11.5.8.1.2  The deflection of the structure or of any part thereof should not exceed the permissible  value. 
Permissible values of deflection should comply with the requirements of the particular structure, taking the 
efficient functioning of the s tructure, possible damage to adjacent structures or aesthetic considerations into 
account.   
©RSB 2020  - All rights reserved                  116 
 11.5.8.1.3  As a guide, the limits given below can be regarded as reasonable:  
The final deflection (including the effects of temperature, creep and shrinkage), measur ed below the as -cast 
level of the support of floors, roofs and all other horizontal members, should not exceed span/250.  
When appropriate, use the modification factors given in tables 20 and 21 to modify the ratios given in table 19.  
11.5.8.2  Span/effective depth r atio for rectangular beams  
11.5.8.2.1  The basic span/effective depth ratios for rectangular beams are given in table 10. These are 
based on limiting the deflection to span/250 and this should normally prevent damage to finishes and 
partitions for beams of span up to 10 m .For cantilevers, add or subtract, as appropriate, the support rotation 
times the cantilever span.  
11.5.8.2.2  Table 19 may be used for spans exceeding 10 m but only when it is not necessary to limit the 
increase in deflection after the cons truction of partitions and finishes. Otherwise, in order to prevent damage 
to finishes and partitions, the values given in table 19 should be multiplied by 10/span, except for cantilevers, 
where the design should be justified by calculation.  
Table 19 — Basic span/effective depth ratios for rectangular beams  
Support conditions  Ratio  
Truly simply supported beams  16 
Simply supported beams with nominally restrained ends  20 
Beams with one end continuous  24 
Beams with both ends continuous  28 
Cantilevers  7 
 
11.5.8.3  Modification of span/effective depth ratios for reinforcement  
11.5.8.3.1  Tension reinforcement  
11.5.8.3.1.1  Since deflection is influenced by the amount of tension reinforcement and its stresses, it is 
necessary to modify the span/effective depth ratios according  to  the ultimate design moment and the service 
stress at the centre of the span (or at the support in the case of a cantilever). Therefore, values of 
span/effective depth ratio obtained from table 19 should be multiplied by the appropriate factor obtained fro m 
table 20.  
Table 20 — Modification factors for tension reinforcement  
Steel  
Service 
stress   
Modification factors  
M/bd2 
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 
300 1.60 1.33 1.16 1.06 0.98 
 0.93 
 0.89 
 0.85 
 0.82 
 0.80 
 0.78 
 0.76 
 DRS 142: 2020  
117                ©RSB 2020  - All rights reserved  
 290 1.66 1.37 1.20 1.09 1.01 
 0.95 
 0.90 
 0,87 
 0.84 
 0.81 
 0.79 
 0.78 
 
280 1.72 1.41 1.23 1.12 1.03 0.97 0.92 0.89 0.85 0,83 0.81 0.79 
270 1.78 1.46 1.27 1.14 1.06 
 0.99 
 0.94 
 0.90 
 0.87 
 0.84 
 0.82 
 0.80 
 
260 1.84 1.50 1.30 1.17 1.08 
 1.01 
 0.96 
 0.92 
 0.88 
 0.86 
 0.83 
 0,81 
 
250 1.90 1.55 1.34 1.20 1.11 1.04 0.98 0.94 0.90 0.87 0.85 0.82 
240 1.96 1.59 1.37 1.23 1.13 
 1.06 
 1.00 
 0.95 
 0.92 
 0.88 
 0.86 
 0.84 
 
230 2.00 1.63 1.41 1.26 1.16 
 1.08 
 1.02 
 0.97 
 0.93 
 0.90 
 0.87 
 0.85 
 
220 2.00 1.68 1.44 1.29 1.18 1.10 1.04 0.99 0.95 0.91 0.88 0.86 
210 2.00 1.72 1.48 1.32 1.20 
 1.12 
 1.06 
 1.00 
 0.96 
 0.93 
 0.90 
 0.87 
 
200 2.00 1.76 1.51 1.35 1.23 
 1.14 
 1.07 
 1.02 
 0.98 
 0.94 
 0.91 
 0.88 
 
190 2.00 1.81 1.55 1.37 1.25 1.16 1.09 1.04 0.99 0.96 0.92 0.90 
180 2.00 1.85 1.58 1.40 1.28 
 1.18 
 1.11 
 1.06 
 1.01 
 0.97 
 0.94 
 0.91 
 
170 2.00 1.90 1.62 1.143 1.30 
 1.21 
 1.13 
 1.07 
 1.02 
 0.98 
 0.95 
 0.92 
 
160 2.00 1.94 1.65 1.46 1.33 1.23 1.15 1.09 1.04 1.00 0.96 0.93 
150 2.00 1.198 1.169 1.49 1.35 
 1.25 
 1.17 
 1.11 
 1.05 
 1.01 
 0.98 
 0.94 
 
140 2.00 2.00 1.72 1.52 1.38 
 1.27 
 1.19 
 1.12 
 1.07 
 1.03 
 0.99 
 0.96 
 
130 2.00 2.00 1.75 1.55 1.40 
 1.29 
 1.21 
 1.14 
 1.09 
 1.04 
 1.00 
 0.97 
 
120 2.00 2.00 1.79 1.59 1.43 1.31 1.23 1.16 1.10 1.05 1.01 0.98 
NOTES  
1  The values in  the table are based on the formula:  
 
where;  
M   is the design ultimate moment at the centre of the span or, for cantilevers, at the support;  
b   is the width of section;  
d  is the effective depth of section; and  
fs  is the design estima te service stress in tension reinforcement.  
2 For flanged beams, see 11.5.6.5  
3  Span considered is smaller span for 2 -way slabs, larger for flat slabs.  
4 For flat plates (no drops), multiply factor by 0,9.   
©RSB 2020  - All rights reserved                  118 
 11.5.8.3.1.2  The design service stress in the te nsion reinforcement in a beam may be estimated from the 
following equation:  
 
where : 
fs is the estimated service stress in tension reinforcement;  
fy is the characteristic strength of reinforcement;  
γ1 is the self -weight load factor for serviceability limit  states;  
γ2  is the imposed load factor for serviceability limit states;  
γ3  is the self -weight load factor for ultimate limit state;  
γ4   is the imposed load factor for ultimate limit state;  
As,req  is the area of tension reinforcement required at mid -span to resist moment due to ultimate  loads (at 
the support in the case of a cantilever);  
As,prov is the area of tension reinforcement provided at mid -span (at the support in the case of  a cantilever); 
and β b is the ratio of resistance moment at mid -span obt ained from  redistributed maximum moments diagram 
to that obtained from maximum moment  diagram before redistribution.  
11.5.8.3.1.3  If the percentage of redistribution is not known, but the design ultimate moment of mid -span is 
clearly the same or exceeds th e elastic ultimate moment, the stress fs given in table 20 may be calculated 
from the above equation where β b = 1.0. 
11.5.8.3.2  Compression reinforcement  
Because compression reinforcement also influences deflection, the value of the span/effective depth ratio 
modified in accordance with table 20  may be multiplied by a further factor obtained from Table 21. 
Table 21  — Modification factors for compression reinforcement  
 
 Factor*)  
0.15 1.05 
0.25 1.08 
0.35 1.10 
0.50 1.14 DRS 142: 2020  
119                ©RSB 2020  - All rights reserved  
 0.75 1.20 
1.00 1.25 
1.25 1.29 
1.50 1.33 
1.75 1.37 
2.00 1.40 
2.50 1.45 
> 3.00 1.50 
*)Obtain intermediat e values by interpolation.  
The area of compression reinforcement at mid span used in Table 21 may comprise all bars in the 
compression zone, s including those not effectively tied with links.  
11.5.8.4  Deflection due to creep and shrinkage  
Permissible span/effectiv e depth ratios obtained from tables 18 to 20 take account of normal creep and 
shrinkage deflection. If it is expected that creep or shrinkage of the concrete might be particularly high 
(concrete of very poor quality and workmanship, high long -term loadings ), i.e. the free shrinkage stress 
exceeds 0,000 75 or the creep coefficient exceeds 4, the permissible span/effective depth ratio should be 
reduced. A reduction of more than 15 % is unlikely to be required.  
11.5.8.5  Span/effective depth ratio for flanged beams  
11.5.8.5.1  For a flanged beam, the span/effective depth ratio may be determined as in 11.5.8.2  but, when 
the web width is less than 0 .3 times the effective flange width, multiply the final ratio obtained by 0 .8. For 
values of web width to effective flange widt h that exceed 0 .3, this factor may be increased linearly from 0 .8 to 
1.0 as the ratio of web width to effective flange width increases to unity.  
11.5.8.5.2  In the case of inverted flanged beams with the flange in tension, the tension reinforcement within 
the width of the web must be taken into consideration.  
11.5.8.5.3  The compression reinforcement (as in Table 21) should be that within the effective width of the 
flange.  
11.5.8.6  Crack control in beams  
11.5.8.6.1  In general, compliance with the reinforcement spacing  rules given below will be an acceptable 
method of controlling flexural cracking in beams:  
11.5.8.6.2  When the diameter of a bar exceeds the maximum size of coarse aggregate by more than  5 
mm, a spacing smaller than the bar diameter should be avoided. A pa ir of bars in contact or a bundle  of three 
or four bars in contact should be regarded as a single bar of equivalent area when the spacing is being 
assessed.  
11.5.8.6.3  The spacing of bars should be made suitable for the proper compaction of concrete, and  when 
an internal vibrator is likely to be used, adequate spacing should be provided in the  reinforcement to enable  
©RSB 2020  - All rights reserved                  120 
 the vibrator to be inserted. Minimum reinforcement spacing is best determined by experience or proper work 
tests, but in the absence of better  information, the distances given below may be used.  
11.5.8.6.4  In certain cases, particularly where groups of bars are used, advantage may be gained from 
calculating crack widths and comparing them with the recommended values given in limit state design.(  See 
relevant clause).  
11.6 Solid slabs  
11.6.1  Design of solid slabs  
This clause applies to one -way and two -way solid slabs for which b and leff are not less than 5 h. In general, 
the recommendations given in 11.6.2 and the relevant clause of crack control for beams wi ll apply and taken 
into account also to solid slabs  
11.6.2  Moments and forces in solid slabs  
11.6.2.1  General  
In solid slabs, the moments and shear forces resulting from both distributed and concentrated loads may be 
found as for beams.  
11.6.2.2  Resistance moments of solid slabs  
The ultimate moment of resistance of a cross -section in a solid slab may be determined by using the methods 
given in 11.5.6 for beams . 
11.6.2.3  Simplification of load arrangements  
11.6.2.3.1  A continuous slab will be able to withstand the most unfavourable arrangem ents of design loads 
if it is designed to resist the moments and forces arising from the single -load case of maximum design load on 
all spans. The following conditions are to be met:  
a) in a one -way spanning slab, the area of each bay exceeds 30 m2. 
NOTE  In this context, a bay is a strip across the full width of a structure and supported on two sides (see figure 41).  DRS 142: 2020  
121                ©RSB 2020  - All rights reserved  
 
 
Figure 41 — Definition of panels and bays  
b) the ratio of the characteristic imposed load to the characteristic self -weight load does not 
exceed 1.25. 
c) the characteristic imposed load does not exceed 5 kN/m2, excluding partitions.  
11.6.2.3.2  When analysis is carried out for the single -load case of maximum design load on all spans, th en 
resulting support moments, except those at the support of cantile vers, should be reduced by 20 %, with a 
resultant increase in the span moments. When a span is adjacent to a cantilever of length exceeding one -third 
of the span of the slab, the other possibility of loading arrangement should be considered, i.e. the case of slab 
unloaded and the cantilever loaded.  
11.6.2.4  Distribution of concentrated loads on slabs  
11.6.2.4.1  If a slab is simply supported on two opposite edges and carries one or more concentrated loads 
in a line in the direction of the span, the maximum bending mo ments may be assumed to be resisted by an 
effective width of slab (measured parallel to the supports), given below.  
11.6.2.3.2  For solid slabs, the effective width may be taken as the sum of the load width plus  2.4x(1- x/l) 
where x is the distance from the  nearer support to the section under consideration and l is the span. For 
cantilever slabs the equivalent value is 2 .4x. 
11.6.2.3.3  For slabs other than solid slabs, the effective width will depend on the ratio of the transverse  and 
longitudinal flexural r igidities of the slab. The minimum value to be taken, however, is the load width plus 4 x/l 
(1- x/l) metres where x and l are as defined above, such that, for a section at mid -span, the effective width is 
equal to 1 m plus the load width.  
11.6.2.3.4  Where the concentrated load is near an unsupported edge of a slab, the effective width  should 
not exceed the value given in the above paragraphs, as appropriate, nor half that value plus the distance of 
the centre of the load from the unsupported edge (see figur e 42).   
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Figure 42 — Effective width of solid slab carrying a concentrated load near an unsupported edge  
11.6.3  One-way spanning slabs of approximately equal span  
11.6.3.1  Where the length of the longer side of a slab exceeds three times the length of the shorter  side, so 
design the slab as to span one way only.  
11.6.3.2  When the conditions of simplification of load arrangements (see 11.6.2.3) are met, the moments and 
shears in continuous one -way spanning slabs may be calculated using the coefficients given in Table 13. 
Table 22 — Ultimate bending moments and shear forces in one -way spanning slabs  
Position of slab connection  Moment  Shear  
At outer support  0 0.4F 
Near middle of end span  0.086Fl  - 
At first interior support  -0.086Fl  0.6F 
At middle of interior span  0.063Fl  - 
At interior supports  -0. 063Fl  0.5F 
NOTE  F     is the total ultimate load (1 .4G k+1.6Q k) 
              L    is the effective span  
 
11.6.4  Solid slabs spanning in two directions at right angles (uniformly distribute d loads)  
In addition to other methods , the methods given 11.6.4.1 to 11.6.4.3 may be used for the design of slabs 
spanning in two directions at right angles and supporting uniformly distributed loads.  DRS 142: 2020  
123                ©RSB 2020  - All rights reserved  
 11.6.4.1  Simply supported slabs  
11.6.4.1.1  When simply supported rectangular slabs do not have adequa te provision to resist torsion at the  
corners and to prevent the corners from lifting, the maximum moments per unit width are given by the 
following equations:  
 
where : 
Msx, Msy are the maximum bending moments at mid -span on strips of unit width spanning lx and ly 
respectively;  
n  is the total ultimate load per unit area (1,4 gk + 1,6 qk); 
lx  is the length of shorter side;  
ly  is the length of larger side; and  
αsx, αsy are the bending moment coefficients given in table 23.  
11.6.4.1.2  Extend to the supports at least 50 % of the tension reinforcement provided at mid -span. Extend 
the remaining part of the reinforcement to within 0,1 lx or 0,1 ly of the support, as ap propriate.  
Table 22 — Bending moment coefficients for slabs spanning in two directions  at right angles, simply 
supported on four sides  
 αsx αsy 
1.0 0.045 0.045 
1.1 0.061 0.038 
1.2 0.071 0.031 
1.3 0.080 0.027 
1.4 0.087 0.023 
1.5 0.092 0.020 
1.6 0.097 0.017 
1.7 0.100 0.015 
1.8 0.102 0.016 
1.9 0.103 0.016 
2.0 0.104 0.016 
2.5 0.108 0.016  
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 3.0 0.111 0.017 
 
11.6.4.2  Restrained slabs  
Both in continuous and in discontinuous slabs where the corners are prevented from lifting and  provision for 
torsio n is made, the maximum moments per unit width are given by the following  equations:  
                                                                               ( 11.8)  
                                                                                 ( 11.9)  
where  
Msx, Msy are the maximum bending moments at mid -span on strips of unit width spanning lx and Ly 
respectively;  
n is the total ultimate load per unit area (1 .4gk+ 1.6 qk); 
lx  is the length of shorter side;  
ly  is the length of larger side; and  
βsx, βsy   are the bending moment coefficients given in Table 23. 
Table 23 — Bending moment coefficients for rectangular panels supported on four sides with 
provision for torsional reinforcement at the corners  
Ca
se Type of panel and moments 
considered  Short  span coefficients β sx Long 
span 
coeffic
ients, 
βsy Values of ly/lx  
1.0 1.1 1.2 1.3 1.4 1.5 1.75 2.0 
1 Interior panels  
Negative moment at continuous  
edge  0.031 
 0.037 
 0.042 
 0.046 
 0.050 
 0.053 
 0.059 
 0.063 
 .032 
 
Positive moment at mid - span  0.024 0.028 0.032 0.036 0.039 0.041 0.045 0.049 0.024 
2 One short edge discontinuous  
Negative moment at continuous 
edge  0.039 
 0.044 
 0.048 
 0.052 
 0.055 
 0.058 
 0.063 
 0.067 
 0.037 
 
Positive moment at mid -span  0.029 0.033 0.036 0.039 0.041 0.043 0.047 0.050 0.028 
3 One long edge discontinuous  
Negative moment at continuous.  0.039 
 0.049 
 0.056 
 0.062 
 0.068 
 0.073 
 0.082 
 0.089 
 0.037 
 
Positive moment at mid -span  0.030 0.036 0.042 0.047 0.051 0.055 0.062 0.067 0.028 
4 Two adjacent edges  0.047 0.056 0.063 0.069 0.074 0.078 0.087 0.092 0.045 DRS 142: 2020  
125                ©RSB 2020  - All rights reserved  
 discontinuous  
Negative moment at continuous 
edge           
Positive moment at mid -span  0.036 0.042 0.047 0.051 0.055 0.059 0.065 0.070 0.034 
5 Two short edges discontinuous  
Negative moment at continuous  
edge  0.046 
 0.050 
 0.054 
 0.057 
 0.060 
 0.062 
 .067 
 0.070 
 - 
 
Positive moment at mid -span  0.034 0.038 0.040 0.043 0.045 0.045 0.047 0.053 0.034 
6 Two long edges discontinuous  
Negative moment at continuous  
edge  - 
 - 
 - 
 - 
 - 
 - 
 - 
 - 
 0.045 
 
Positive moment at mid-span  0.034 0.046 0.056 0.065 0.072 0.078 0.091 0.100 0.034 
7 Three edges discontinuous (one  
long edge continuous)  
Negative moment at continuous  
edge  0.057 
 0.065 
 0.071 
 0.076 
 0.080 
 0.084 
 0.092 
 0.098 
 - 
 
Positive moment at mid -span  0.043 0.048 0.053 0.057 0.060 0.063 0.069 0.074 0.044 
8 Three edges discontinuous (one  
short edge continuous)  
Negative moment at continuous  
edge  - 
 - 
 - 
 - 
 - 
 - 
 - 
 - 
 0.058 
 
Positive moment at mid -span  0.042 .,054 0.063 0.071 0.078 0.084 0.096 0.105 0.044 
9 Four edges discontinuous  
Positive moment at mid -span  0.055 0.065 0.074 0.081 0.087 0.092 0.103 0.111 0.056 
 
11.6.4.2.1  In the case of continuous slabs  
The nominal self -weight and imposed loads on adjacent slabs should be approximately the same as those on 
the slab under consideration, and the spans of all adjacent slabs should be approximately the same in each of 
the two directions of the lines of the supports.  
11.6.4.2.2  In the case of continuous and discontinuous slabs  
Regard slabs as divided in each direction into middle strips and edge strips as shown in Figure 43, the middle 
strip being three -quarters of the width and each edge strip one -eighth of the width.  
The maximum moments calculated as in 11.6.4.2 apply to the middle strips only and no redistribution is 
permitted.   
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a) For span l x                                                     b) For span l y   
          Figure 43 — Division of slab into middle and edge strips     
a. tension reinforcement at mid -span: extend at least 50 % of the tension reinforcement 
provided at mid -span in the middle strip in the lower part of the slab to within 0,15 l of the 
continuous edge axis, and to within 50 mm of the discontinuous edge axis; extend the 
remaining part of the reinforcement to within 0 .25l of a continuous edge axis, and to within 
0.15l of the discontinuous edge axis;  
b. tension reinforcement over the continuous edges: extend at least 50 % of the tension  
reinforcement provided in the upper part of a middle strip to a distance 0 .3l from the face of 
the support; extend the remaining part of  the reinforcement to a distance of 0 .15l from the 
face of the support;  
c. tension reinforcement over the discontinuous edge: at a discontinuous edge, negative  
moments may arise, depending on the degree of fixity of the edge of the slab; in general, 
tension r einforcement equal to 50 % of that provided at mid -span extending 0 .1l into the span 
(from the face of the support) will be sufficient;  
d. tension reinforcement in an edge strip, parallel to the edge: the reinforcement need not 
exceed the minimum given in the  rules for torsional reinforcement given in (e), (f) and (g) 
below;  
e. torsional reinforcement at any corner where the slab is simply supported on both 
edges meeting at that corner: the reinforcement should comprise top and bottom 
reinforcement, each  with lay ers of bars placed parallel to the sides of the slab and extending 
from the external faces of  the edges a minimum distance of one -fifth of the shorter span; the 
area of reinforcement in each  of these four layers should be three -quarters of the area 
require d for the maximum mid -span  moment in the slab;  
f. torsional reinforcement at any corner contained by edges over only one of which the 
slab is continuous: reinforcement equal to half of that described in (e) above should be 
provided;  
g. torsional reinforcement ne ed not be provided at any corner contained by edges over 
both of which the slab is continuous: where ly /lx exceeds 3, so design slabs as to span 
one way only.  DRS 142: 2020  
127                ©RSB 2020  - All rights reserved  
 11.6.4.2.3   In the case of a restrained slab with unequal conditions at adjacent panels  
11.6.4.2.3.1  If the  support moments for adjacent panels (calculated using Table 23) differ significantly, they 
may be adjusted as follows  
a) calculate the sum of the moments at mid -span and supports (ignoring signs);  
b) treat the values from table 15 as fixed end moments;  
c) distribu te these fixed end moments across the supports according to the relative stiffness of  adjacent 
spans, giving new support moments;  
d) adjust the mid -span moment; this should be such that when it is added to the support moments as in 
(c) above (ignoring signs),  the total should equal that obtained in (a) above;  
11.6.4.2.3.2  If, for a given panel, the resulting support moments now significantly exceed the values given by  
equations (18) and (19).  
The procedure is as follows:  
1) the span moment is taken as parabolic b etween supports; its maximum value is as found in (d) above;  
2) the points of contra flexure of the new support moments (as in (c) above) and the span moment (as in 
(1) above) are determined;  
3) at each end, half the support tension steel is extended to at least  an effective depth or 12 bar  
diameters beyond the nearest point of contra flexure; and  
4) at each end, the full area of the support tension steel is extended to half the distance obtained in (3) 
above.  
11.6.4.3  Loads on supporting beams  
The design loads on beams supp orting solid slabs spanning in two directions at right angles and  supporting 
uniformly distributed loads may be assumed to be in accordance with Figure 10. If the edges of two slabs 
having the same support meet at a corner, the dividing angle is 45°. If a fully restrained edge meets a freely 
supported edge, the dividing angle on the restrained side is 60°. With partial restraint, the angles may be 
assumed to lie between 45° and 60° (see figure 44(b)).    
©RSB 2020  - All rights reserved                  128 
 
                                   
      (a)                                                                                ( b) 
           Figure 44 — Apportionment of load for determining the bearing reactions  
 
11.6.5  11.6.5 Shear resistance of solid slabs  
11.6.5.1  11.6.5.1 Shear stresses in solid slabs  
11.6.5.1.1  The desi gn shear stress v at any cross -section in a solid slab should be compared with the 
allowable shear stress vc and in no case should it exceed the lesser of
  or 4.75MPa,whatever 
reinforcement is provided.  
Calculate v from                                                                                      (11.10)  
where  
v is the design shear stress;  
V is the shear force due to design maximum loads;  
B is the width of slab under consideration (usually 1 000 mm); and  
d is the effective depth; and the allowable stress vc is the maximum design shear stress in concrete without 
shear reinforcement.  
11.6.5.1.2  When the design shear stress v is less than the allowable shear stress vc, no shear 
reinforcement is needed.  
11.6.5.1.3  When v exceeds vc, shear reinforcement should be provided in accordance with the appropriate 
rules for beams.  
DRS 142: 2020  
129                ©RSB 2020  - All rights reserved  
 11.6.5.1.4  It may be assumed that every 10 mm reduction in the slab thickness reduces the links' efficiency 
by 10 %.  The enhancement in design sh ear strength close to supports may also be applied to solid slabs.  
11.6.5.2  Shear stresses in solid slabs under concentrated load  
11.6.5.2.1  The following terms specific to perimeters are used in this sub clause:  
a) perimeter: a boundary of the smallest rectangle (or square) that can be drawn around a loaded area 
and that nowhere comes closer to the edges of the loaded area than some specified distance lp (a 
multiple of 0 .75d) (see figure 45).  
b) failure zone: an area of slab bounded by perimeters 1 .5d apart ;  
c) effective l ength of a perimeter: the length of the perimeter reduced, where appropriate, for the 
effects of openings or external edges;  
d) effective depth d: the average effective depth for all effective reinforcement passing through a 
perimeter; and  
e) effective steel are a: the total area of all tension reinforcement that passes through a zone and that 
extends at least one effective depth (see above) or 12 times the bar size beyond the zone on either 
side.  
NOTE  The reinforcement percentage used to calculate the design ulti mate shear stress vc is given by:  
   
  
where : 
u  is the outer perimeter of zone concerned; and  
d   is the effective depth (as defined above).                                                   
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Figure 45 — Definition of a shear perimeter for typical cases  
11.6.5.2. 2 The maximum design shear stress vmax resulting from the concentrated load and calculated as 
below should not exceed the lesser of 0 ,75
  or 4,75 MPa  
 
where : 
V is the design maximum value of concentrated load;  
uo is the effective leng th of perimeter that touches a loaded area; and  
d is the effective depth of slab.  DRS 142: 2020  
131                ©RSB 2020  - All rights reserved  
 11.6.5.2.3  The shear capacity of punching shear zones is checked first on a perimeter 1 .5 d from the  face 
of the loaded area. If the calculated shear stress does not exceed vc, then no further checks are needed.  
11.6.5.2.4  The spacing of perimeters of reinforcement should not exceed 0 .75d and the spacing of the 
shear reinforcement around any perimeter should not exceed 1 .5d. The shear reinforcement should be 
anchored round at least one layer of tension reinforcement. The shear stress should then be checked on 
successive perimeters at 0 .75d intervals until a perimeter is reached which does not require shear 
reinforcement.  
11.6.5.2.5  The nominal design shear stress v, appropriate  to a particular perimeter, is calculated from:  
 
where  
V, d are as in equation (20); and  
u  is the effective length of the outer perimeter of the zone.  
No shear reinforcement is required when the stress v is less than vc. 
11.6.5.2.6  In the case of zone 1,  As in each direction should include all the tension reinforcement within a 
strip of width bv equal to the width of the loaded area plus three times the effective depth of slab on either side 
of the loaded area.  
11.6.6  Deflection of solid slabs  
11.6.6.1  Deflectio ns may be calculated and compared with the serviceability provisions, but in all normal 
cases, it will be sufficient to restrict the span/effective depth ratio. The appropriate ratio for a solid slab may be 
obtained from table 19, modified by tables 20 and  21. The reinforcement at the middle of the span in the width 
of the slab under consideration should be considered to influence deflection.  
11.6.6.2  In the case of a two -way spanning slab, the ratio should be based on the shorter span and its amount 
of rei nforcement in that direction.  
11.6.7  Crack control in solid slabs  
In general, compliance with the reinforcement spacing rules given relevant clause will be an acceptable 
method of controlling flexural cracking in slabs but, in certain cases, advantage may be gain ed from 
calculating crack widths and comparing them with the recommended values given in limit state design.   
©RSB 2020  - All rights reserved                  132 
 11.6.8  Ribbed slabs (with solid or hollow blocks or with voids)  
11.6.8.1  General  
11.6.8.1.1  Construction  
This sub clause refers to in -situ slabs constructed in one of the fol lowing ways:  
a) where topping is considered to contribute to structural strength:  
i. as a series of concrete ribs cast in situ between blocks that remain part of the completed  structure; the 
tops of the ribs are connected by a topping of concrete of the same str ength as that used in the ribs;  
ii. as a series of concrete ribs with topping cast on forms that may be removed after the concrete has set;  
iii. with a continuous top and bottom face but containing voids of rectangular, oval or other shape.  
b) where topping is not con sidered to contribute to structural strength: as a series of concrete ribs 
cast in -situ between blocks that remain part of the completed structure; the tops of the ribs may be 
connected by a topping of concrete but not necessarily of the same strength as t hat used in the ribs.  
11.6.8.1.2  Thickness of topping  
When a topping is used to contribute to the structural strength, ensure that its thickness, after any necessary 
allowance has been made for wear, is at least  
a) 30 mm for slabs that have permanent blocks and have a c lear distance of not more than 500 mm 
between the ribs;  
b) 25 mm for slabs as in (a) above but with each row of blocks jointed in mortar having a cement -sand 
mixture not weaker than 1:3, or having a cube strength of 11 MPa;  
c) the greater of 40 mm or one -tenth o f the clear distance between the ribs, for all other slabs  containing 
permanent blocks;  
d) the greater of 50 mm or one -tenth of the clear distance between the ribs, for all other slabs without 
permanent blocks.  
11.6.8.2  Size, spacing and position of ribs  
11.6.8.2.1  The minimum width of ribs, whether they are rectangular or tapered, should be at least 65 mm 
and their depth, excluding any topping, should not exceed four times their width.  
11.6.8.2.2  In-situ ribs should be spaced at centres not exceeding 1 .5 m and the edg e rib that bears along 
its length on a beam or wall shall be at least as wide as the bearing, i.e. the block or void shall not be on the 
bearing.  DRS 142: 2020  
133                ©RSB 2020  - All rights reserved  
 11.6.8.3  Hollow blocks and formers  
11.6.8.3.1  Blocks and formers may be of any suitable material but, when required to contribute to the 
structural strength of a slab, they should be made of:  
a) concrete or burnt clay and have a crushing strength of at least 14 MPa measured on the net section when 
axially loaded in the direction of compressive stress in the slab, or  
b) fired bri quettes, clay or shale.  
11.6.8.3.2  When a slab is constructed in accordance with 11.6.8.1.2  (a) but the topping is not used to  
contribute to structural strength, the blocks should comply with 11.6.8.1.4  (a) or (b). In addition, the thickness 
of the block material above its void shall be the greater of at least 20 mm or one -tenth of the clear distance 
between the ribs. The overall thickness of the block and topping (if any) should be not less than one -fifth of the 
clear distance between the ribs.  
11.6.8.3.1  Analysis o f structure  
The moments and forces due to ultimate loads on continuous slabs may be obtained by any of the methods 
given in 11.6.2  for solid slabs. Alternatively, the slabs may be designed as a series of simply supported spans, 
provided that they will not be exposed to weather or corrosive conditions. Wide cracks may develop at the 
supports and the engineer shall satisfy himself that these will not impair finishes or lead to corrosion of the 
reinforcement.  Rules for the arrangement of reinforcement are give n in the clause of arrangement of 
reinforcement.  
11.6.8.3.2  Moments of resistance  
The methods given in 4.3.3 for determining the ultimate moment of resistance of beams may be used.  When 
sections are being analysed, the stresses in burnt clay blocks in the compression  zone may be taken as 0 .25 
times the strength as determined in 11.6.8.1.4 (a). However, when evidence is available to show that not more 
than 5 % of the blocks have a strength below a specified crushing strength, the stress may be taken as 0 .3 
times that st rength.  
11.6.8.3.3  Shear  
 11.8.8.3.3.1  In one -way or two -way spanning slabs, the design shear stress v should be calculated from the  
following equation:  
 
where  
V  is the design shear force due to design ultimate loads on a width of slab equal to t he centre -to-centre  
distance between ribs;  
bv  is the average width of rib; and  
d   is the effective depth.   
©RSB 2020  - All rights reserved                  134 
 11.8.8.3.3.2  In the determination of bv, the following shear contribution cases should be taken into 
consideration:  
a) shear contribution by hollow blocks: bv may be incr eased by the wall thickness of the block, on 
one side of the rib;  
b) shear contribution by solid blocks: when blocks comply with 11.6.8.1.4 , bv may be increased by 
one-half of the rib depth, on each side of the rib;  
c) shear contribution by joints between narrow  precast units: bv may be increased by the width of 
the mortar or concrete joint.  
11.8.8.3.3.3  When v is less than vc, where vc is obtained from 11.6.8.1.4 , no shear reinforcement need be 
provided.  
11.8.8.3.3.4  Where a critical perimeter cuts any ribs, the y should each be designed to resist an equal 
proportion of the applied effective design force. Shear links in the ribs should continue for a distance of at 
least d into the solid area.  
11.6.8.3.4  Deflection  
The provisions given in 11.6.6 in respect of solid slabs may  be applied to the ribs of ribbed slabs. The 
span/effective depth ratios given in 11.5.8.5 for a flanged beam are applicable, but when the final reduction 
factor for web width is calculated, the rib width for hollow block slabs may be assumed to include th e walls of 
the blocks on both sides of the rib. For slabs with voids and slabs constructed of box -section or I -section units, 
calculate an effective rib width by assuming that all material below the upper flange of the unit is concentrated 
in a rectangular  rib having the same cross -sectional are and depth.  
11.6.8.3.5  Arrangement of reinforcement  
11.6.8.3.5.1  The provisions given in the relevant clause in respect of maximum distance between bars apply 
to areas of solid concrete in this form of construction.  
11.6.8.3.5. 2 If a slab has been designed as simply supported but is continuous over supports, the 
reinforcement provided in the top of the slab should be at least one -quarter of that required in the middle of 
adjoining spans. This reinforcement shall extend by at lea st one -tenth of the clear span into adjoining spans.  
11.6.8.3.5.3  A single layer of mesh should be provided in the topping of all ribbed and hollow block slabs.  
The mesh should have a cross -sectional area in each direction of at least 0 .12 % of the topping . The spacing 
of wires should not exceed half the centre -to-centre distance between ribs.  
 
11.6.9  Cover to reinforcement  
The side cover to reinforcement in slabs that have permanent blocks shall be at least 10 mm.  Similarly, for 
slabs that have slip tiles under t he ribs at least 10 mm thick, the cover to the bars shall be at least 10 mm 
above the tiles. In all other cases, provide cover in accordance with the relevant clause of concrete cover to 
reinforcement.  DRS 142: 2020  
135                ©RSB 2020  - All rights reserved  
 11.7 Flat slabs  
11.7.1  General  
11.7.1.1  Construction  
A flat slab is a reinf orced concrete slab with or without drops and supported, generally without beams, by a 
rectangular arrangement of columns with or without flared column heads (see figure 46). A flat slab may be 
solid or may have recesses formed on the soffit such that the soffit comprises a series of ribs in two directions.  
A panel is the area within the lines joining the centres of the columns.  
a) The arrangement of reinforcement in flat slab construction should reflect the behavio ur under working 
conditions. In general this will result in a concentration of reinforcement over the columns.  
b) At internal columns, unless rigorous serviceability calculations are carried out, top  reinforcement of 
area 0 .5 At should be placed in a width equal to the sum of 0 .125 times the panel width  on either side 
of the column. At represents the area of reinforcement required to resist the full negative moment from 
the sum of the two half panels each side of the column.  
c) Bottom reinforcement (≥ 2 bars) in each orthogonal direction should be provided at internal columns 
and this reinforcement should pass through the column.  
           
  
a) Column without column head and slab without drop  
 
  
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 b) Column with column head and slab wit hout drop  
 
c) Column with column head and slab with drop  
Figure  46 — Types of column heads  
NOTE  Any concrete in  areas designated by arrows in a) and b) of the figure 46  is to be ignored in calculations.  
11.7.1.2  Column heads  
Ensure that where column heads are provid ed, the heads of interior columns and such portions of the heads 
of exterior columns as will lie within the structure, meet with the following conditions:  
a) the angle of greatest slope of the head, for the purposes of analysis, does not exceed 45° from the 
vertical; and  
b) the diameter of the column head hc is taken as its diameter measured at a distance of 40 mm  below 
the soffit of the slab (or the soffit of the drop, where provided), as shown in figure 46, but  does not 
exceed 0 .25lm. 
11.7.1.3  Division of panels  
11.7.1. 3.1 Flat slab panels should be assumed to be divided into column strips and middle strips (see 
Figure 47), as follows:  
a) take the width of the column strip as one -half of the width of the panel, except that where drops are 
used, the width may be taken as the  width of the drop; and  
b) take the width of the middle strip as the difference between the width of the panel and that of the 
column strip.  
11.7.1.3.2  Drops should be ignored if their smaller dimension is less than one -third of the shorter span of 
the surrou nding panels. Smaller drops may still be taken into account in assessing the resistance to punching 
shear.  
11.7.1.3.3  In the case of unalike panels: if there is a support common to two panels that are of such 
dimensions  that the strips in one panel do not match those in the other, the division of the panels over the 
region of the common support should be taken as that calculated for the panel giving the wider column strip.  DRS 142: 2020  
137                ©RSB 2020  - All rights reserved  
 11.7.1.4  Thickness of panels  
The thickness of the slab will generally be controlled by conside rations of deflection (see 11.7.3). In no case, 
however, should the thickness of the slab be less than 125 mm.  
The minimum thickness required when shear reinforcement is provided, is 150 mm.  
 
 
L  
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                                                               b) Slab with drop  
                   Figure 47  — Division of flat slab panels into columns and middle strips  
 
NOTE  Drops less than Lx/3 are to be ignored  
11.7.1.5  Openings in panels  
Openings, excluding those that comply with the conditions given in 11.7.1.6. 1 to 11.7.1.6.3 , shall be 
completely framed on all sides by beams that carry the loads to the columns, and an opening shall not 
encroach upon a column head.  
11.7.1.5.1  Openings in the area common to two intersecting middle strips  
The greatest dimension in a directio n parallel to a centre -line of the panel should not exceed 0 .4l, and the total 
positive and negative moments specified in 11.7.5.1 or 11.7.5.2 should be redistributed between the 
remaining principle design sections to meet the changed conditions.  
11.7.1.5.2  Openings in the area common to two column strips  
Aggregate length and aggregate width should not exceed one -tenth of the width of the column strip; the 
reduced sections should be capable of resisting the appropriate moments specified in 11.7.5.1 or 11.7.5.2, 
and th e perimeter for calculating shear stress should be reduced as appropriate (see 11.6.5.2   ). 
11.7.1.5.3  Openings in the area common to one column strip and one middle strip  
Aggregate length and aggregate width should not exceed one -quarter of the width of the column s trip, and the 
reduced sections should be capable of resisting the appropriate moments specified in 11.7.5.1 or 11.7.5.2.  
11.7.2  Shear in flat slabs  
11.7.2.1  General  
Punching shear around the columns is the critical consideration for shear in flat slab structures. The desi gn 
effective shear force should be found in the sub clauses given below and then the procedure given in 11.6.5.2 
should be followed. For flat slabs between 150 mm and 200 mm thick, the allowable stress in the shear 
reinforcement should be reduced from the full value at 200 mm of thickness to zero at 150 mm of thickness, 
with intermediate values being interpolated linearly. Edges of the drop should be considered the consecutive 
perimeter on which the shear stress is to be checked (see figure 48).  
If the rati o of spans exceeds 2, specialist literature should be consulted.  DRS 142: 2020  
139                ©RSB 2020  - All rights reserved  
 
 
Figure 48  — Sections of shear check for flat slabs with drops   
©RSB 2020  - All rights reserved                  140 
 
 
Figure 49  — Shear at slab internal column connection  DRS 142: 2020  
141                ©RSB 2020  - All rights reserved  
 11.7.2.2  Design effective shear force at slab/internal column connection  
11.7.2 .2. 1 In the case of structures in which stability is provided by shear walls or other bracing  designed to 
resist lateral forces, and where the ratio between adjacent spans does not exceed 1 .25, the design effective 
shear force at the perimeter may be calc ulated on the assumption that the maximum design load is applied to 
all panels adjacent to the column under consideration. It will be satisfactory then to take a value of:  
Veff = 1.15Vt 
where : 
Veff  is the design effective shear including allowance for mom ent transfer; and  
Vt   is the design shear transferred to column (see figure 49).  
11.7.2.2.  2 In other cases, i.e. braced frames where the ratio between adjacent spans exceeds 1,25, or  in 
the case of an unbraced frame, the shear force should be calculated as the greater of the following:  
 or                                                            (11.11)  
Veff = 1,15 Vt 
where : 
Veff  is as in 11.7.2.2.1;  
Vt   is the design shear for a particular loading arrangement transferred to column (see Figure 49);  
Mt  is the sum of design moments in column above and below slab for a particular loading  arrangement (see 
11.7.5.1 and 11.7.5.2); and  
x is the length of side of perimeter considered parallel to axis of bending.        
11.7.2.2.  3 Equation (11.11) should be u sed independently for the moments and shear forces about  both 
axes of the column and the design checked for the worst case.  
NOTE  Mt may be reduced by 30 % where the equivalent frame method has been used and analysis has  been based 
on pattern loads.  
11.7.2.3  Design effective shear force at other slab column connections  
11.7.2.3.1  At corner columns and at edge columns that are bent at right angles to the edge, the design 
effective shear force may be calculated from Veff = 1.25 Vt, where Vt is the design shear force tr ansferred to 
the column (see Figure 49). 
11.7.2.3.2  For edge columns that are bent in a direction parallel to the edge and where the structure has  
approximately equal spans, the shear force may be calculated from:   
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 Veff = 1.40 Vt 
where Veff and Vt are as in  11.7.2.2.  
11.7.2.3.3  For other cases of edge columns that are bent in a direction parallel to the edge, the design 
effective shear should be calculated from the following:  
 
where : 
Veff, Vt, Mt and x are as in equation (11.11).  
NOTE  Mt may be reduced by 3 0 % where the equivalent frame method has been used and  analysis has 
been based on pattern loads.  
11.7.2.4  Maximum design shear stress at the column face  
The maximum design shear stress at the column face should not exceed the lesser of 0 .8  
 or 5.0 MPa , 
when assessed by means of equation (11.8) or (11.9), as appropriate, on a perimeter equal to the perimeter of 
the column or column  head (this includes an allowance for γ m of 1.40). 
11.7.2.5  Shear under concentrated loads  
The provisions given in 11.6.5.1 for shear stresses in solid slabs under concentrated load should be followed.  
11.7.3  Deflection of panels  
For slabs with drops of total width in bot h directions equal to at least one -third of the respective spans, follow 
the provisions given in 11.6.6 in other cases, multiply the span/effective depth ratios obtained from 11.5.8.2 by 
0.9. 
11.7.4  Crack control in panels  
In general, compliance with the reinforc ement spacing rules given in the clause of spacing of reinforcement for 
slabs will be an acceptable method of controlling flexural cracking in panels but, in certain cases, advantage 
may be gained from calculating crack widths and comparing them with the r equired values.  
11.7.5  Analysis and design of flat slab structures  
11.7.5.1  Analysis of structure: continuous frame method  
11.7.5.1.1  The structure may be analysed as given below.  
a) the structure may be divided longitudinally and transversely into frames consisting of  colum ns and 
strips of slab. The width of slab used to define the effective stiffness of the slab may, for vertical loads, DRS 142: 2020  
143                ©RSB 2020  - All rights reserved  
 be taken as the distance between the centres of the panels, and for horizontal loads it will be half this 
value.  
b) the torsional flexibility of the connection of the slab to the column may be taken into account.  
c) when the relative stiffness of the slabs and columns is being calculated, the gross cross -section of the 
concrete alone should be considered. In the case of a recessed or coffered slab that is made solid in 
the region of the columns, the stiffening effect may be ignored, provided that the  solid part of the slab 
does not extend more than 0 .15l into the span, measured from the centre -line of the columns.  
11.7.5.1.2  The following arrangemen t of loads should be considered:  
a) all spans loaded with total ultimate load (1 .4Gk+ 1,.6Qk); 
b) all spans loaded with ultimate self -weight load (1 .4Gk) and even spans loaded with ultimate imposed 
load (1 .6Qk); and  
c) all spans loaded with ultimate self -weight loa d (1.4Gk) and odd spans loaded with ultimate imposed 
load (1 .6Qk). 
11.7.5.1.3  The following limitation of negative design moments should be considered:  
a) Negative moments exceeding those at a distance hc /2 from the centre -line of the column may be 
ignored, provided that the sum of the maximum positive design moment and the average of the 
negative design moments in any one span of the slab for the whole panel width is at least:  
 
b) When the above condition is not satisfied, increase the negative moments by the difference between 
the two values under comparison.  
11.7.5.2  Analysis of structure: simplified method  
11.7.5.2.1  In addition to the methods given in 11.7.5.1, the simplified method of determining moments may 
be used for flat slab structures in which lateral stabili ty does not depend on slab/column connections.  
11.7.5.2.2  Table 24 may be used if the following conditions are met:  
a) the design is based on a single -load case of all spans loaded with the maximum design  ultimate load, i.e. 
the conditions as in the clause of  simplification of load arrangement are  satisfied;  
b) there are at least three rows of panels of approximately equal span in the direction under  consideration  
c) the column stiffness EI/l of the columns is not less than the EI / l of the slab, or the detailing  rules in 
11.7.5.4 are followed; and   
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 d) the hogging moments are reduced by 20 % and the sagging moments increased to maintain  equilibrium.  
Table 24 − Bending moments and shear force coefficients for flat slabs  of three or more equal spans  
Position  Moment  Shear  Total column moment  
Outer support  
 
  
Column   
-0.040Fl*  0.045F  0.04F 
 
Wall -0.020Fl 0.40F - 
Near middle of end span  0.083Fl*) - - 
At first interior support  0.063Fl 0.60F 0.022Fl  
At middle of interior 
supports  0.071Fl - - 
At interior supports  -0.055Fl  0.50F 0.022Fl  
*)The design moments in the edge panel may have to be adjusted to  comply with 11.7.5.3.2.  
NOTES  
1.  F   is the total design ultimate load on the strip of slab between  
        adjacent columns (i.e. 1 .4Gk + 1.6Qk). 
2.  l    is the effective span = l1 - 2hc /3. 
3. The limitations of 11.7.5.1.3 need not be checked.  
4. These moments should not be redistributed.  
 
11.7.5.3  Design of flat slabs  
11.7.5.3.1  Internal and edge slabs should be designed for the moments obtained as in 11.7.5.1  (with 
limitations o f negative moments taken into account) or as in 11.7.5.2.  The moments should be divided 
between the column strip and the middle strip in the proportions given in table 25.  
 
Table 25 — Distribution of moments in panels of flat slabs designed as continuous f rames  
Moment  Apportionment between column and middle strips expressed as a 
percentage of the total negative or positive moment*)  
Column strip  Middle strip  
Negative  75 25 
Positive  55 45 
*)Where the column strip is taken as equal to the width of the dro p, and the middle strip is thereby increased in width to a value 
exceeding half the width of the panel, increase the moments to be resisted by the middle strip in proportion to its increased  width. 
The moments to be resisted by the column strip may then be  decreased by an amount such that there is no reduction in either the 
total positive or the total negative moments resisted by the column strip and middle strip together.  
11.7.5.3.2  Design moments transferable between a slab and the edge or corner columns  will only be  able 
to be transferred by a column strip considerably narrower than in the case of an internal column.  
11.7.5.3.3  The breadth of this strip be for various typical cases is shown in figure 50. The value of be 
should never be taken as exceeding  the column strip width appropriate for an internal panel. The maximum 
design moment Mt,max that can be transferred to a column by the appropriate strip may be calculated from the 
following equation:  DRS 142: 2020  
145                ©RSB 2020  - All rights reserved  
 Mt,max = 0.15 be d 2 fcu 
where : 
be is the breadth of str ip; 
d   is the effective depth for the top reinforcement in the column strip; and  
fcu  is the characteristic strength of concrete.  
11.7.5.3.4  The value of Mt,max should exceed half the design moment obtained from an equivalent frame 
analysis or it should e xceed 70 % of the design moment if a grillage or finite element analysis has been used.  
If the value of Mt,max is less than this, the structural arrangements should be changed.  
11.7.5.3.5  Where analysis of the structure indicates a design column moment tha t exceeds Mt,max, the 
design edge moment in the slab should be reduced to a value not exceeding Mt,max and the positive design 
moments in the span should be adjusted accordingly. The normal limitations on redistributions and neutral 
axis depth may be ignor ed in this case. Moments in excess of Mt,max may only be transferred to a column if an 
edge beam or strip of slab along the free edge is so reinforced as to carry the extra moment into the column 
by torsion. In the absence of an edge beam, an appropriate b readth of slab may be assessed using the 
principles illustrated by figure 50.  Alternatively, the method of taking the stiffness of edge columns into 
account may be used.  
 
  
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Figure 50  — Definition of breadth of effective moment transfer strip be for vari ous typical cases  
 
11.7.5.4  Arrangement of reinforcement  
11.7.5.4.1  In general, two -thirds of the amount of reinforcement required to resist the negative design 
moment in the column strip should be placed in a width equal to half that of the column strip and centra l to the 
column.  DRS 142: 2020  
147                ©RSB 2020  - All rights reserved  
 11.7.5.4.2  Half the bottom reinforcement should be extended 20 diameters beyond the centre -line of 
supports.  
11.7.5.4.3  When the simplified method given in 11.7.5.2 is used and the columns are relatively flexible (with 
the stiffness EI/l of smaller order than the stiffness EI/ l of the slab), at least 50 % of the top reinforcement 
shall extend a distance of 0 .3l from the face of supports.  
11.7.5.5  Panels with marginal beams or with walls  
Where the slab is supported by a marginal beam of depth exceed ing 1 .5 times the thickness of the slab, or by 
a wall, ensure that  
a) the total load to be carried by the beam or wall comprises the direct load on the beam or wall plus a 
uniformly distributed load equal to one -quarter of the total load on the panel; and  
b) the moments on the half -column strip adjacent to the beam or wall are one -quarter of the moments 
given in 11.7.5.1 and 11.7.5.2.  
11.8 Columns  
11.8.1  General  
This clause deals with columns for which the larger dimension h is not greater than 4 times the smaller 
dimension b. 
11.8.2  Longitudinal reinforcement  
11.8.2.1  Longitudinal bars should have a diameter of not less than ϕ min. 
NOTE  The recommended value of ϕ min is 12 mm.  
11.8.2.2  The total amount of longitudinal reinforcement should not be less than As,min. 
NOTE  The recommended value of As,min  value is given by Expression (11.12)  
    
  or 0.002 A c whichever is the greater                     ( 11.12)  
 
where:  
fyd is the design yield strength of the reinforcement  
NEd  is the design axial compression force  
 
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 11.8.2.3  The area of longitudinal reinforcement should not exceed As,max. 
NOTE  The recomme nded value of As,max. is 0,04 Ac outside lap locations unless it can be shown that the integrity of 
concrete is not affected, and that the full strength is achieved at ULS. This limit should be increased to 0 .08 Ac at laps.  
11.8.2.4  For columns having a po lygonal cross -section, at least one bar should be placed at each corner. The 
number of longitudinal bars in a circular column should not be less than four.  
11.8.3  Transverse reinforcement  
11.8.3.1  The diameter of the transverse reinforcement (links, loops or heli cal spiral reinforcement) should 
not be less than 6 mm or one quarter of the maximum diameter of the longitudinal bars, whichever is the 
greater. The diameter of the wires of welded mesh fabric for transverse reinforcement should not be less than 
5 mm.  
11.8.3.2  The transverse reinforcement should be anchored adequately.  
11.8.4  Size and reinforcement of columns  
11.8.4.1  The size of a column and the position of the reinforcement in it may be affected by the  requirements 
for durability and fire resistance. Consider t hese, therefore, before commencing with the design.  
11.8.4.2  If a column has a large enough section to withstand the design maximum loads without the  addition 
of reinforcement, it may be designed in the same way as a plain concrete.  
11.8.5  Braced and unbraced col umns  
A column may be considered braced in a given plane if lateral stability to the structure as a whole is provided 
by walls, bracing or buttressing designed to resist all lateral forces in that plane. It should otherwise be 
considered unbraced.  
11.8.6  Short an d slender columns  
A column may be considered slender in a particular plane if its slenderness ratio in that plane ( lex/h or ley/b) 
exceeds 10 for unbraced columns and 17 -7M1/M2 for braced columns. It should otherwise be  considered 
short. It is therefore po ssible that a column may be slender in one plane and short in the other plane and it 
should be treated accordingly.  
11.8.7  Slenderness limits for columns  
Generally, the clear height lo should satisfy the following:  
a) lo < 60 b and b > 0.25h. 
If, in any given plane, one end of an unbraced column is unrestrained (e.g. a cantilever column), its clear 
height lo should satisfy the following:  
b) lo < 25b and b > 0.25h. DRS 142: 2020  
149                ©RSB 2020  - All rights reserved  
 For unbraced columns, the considerations of deflection may introduce further limitations.  
11.8.8  Effective height o f a column  
11.8.8.1  Effective height of a column: general method  
11.8.8.1.1  The effective height le of a column in a given plane may be obtained from the following equation:  
le = βlo 
11.8.8.1.2  Values of β are given in tables 26 and 27 (for braced and unbraced col umns, respectively) as a  
function of the end conditions of the column. Figure 28 may be used to obtain an approximate  assessment of 
the effective height, if desired. It should be noted that the effective height of a column in the two plane 
directions may b e different.  
11.8.8.1.3  In tables 26 and 27, the end conditions are defined in terms of a scale of 1 to 4. An increase in 
this scale corresponds to a decrease in end fixity. An appropriate value can be assessed from the following 
four end conditions:  
a) end c ondition 1: the end of the column is connected monolithically to beams on either side that are 
at least as deep as the overall dimension of the column in the plane under consideration. Where the 
column is connected to a foundation structure, this should be  of a form specifically designed to carry 
moment.  
b) end condition 2: the end of the column is connected monolithically to beams or slabs on either side 
that are shallower than the overall dimensions of the column in the plane under consideration.  
c) end conditi on 3: the end of the column is connected to members that, while not specifically  designed 
to provide restraint to rotation of the column, will nevertheless provide some nominal  restraint.  
d) end condition 4: the end of the column is unrestrained against both lateral movement and rotation 
(e.g. the free end of a cantilever column in an unbraced structure).  
Table 26  — Values of β for braced columns  
End condition at top  β 
End condition at bottom  
1 2 3 
End condition 1  0.75 0.80 0.90 
End condition 2  0.80 0.85 0.95 
End condition 3  0.90 0.95 1.00 
 
Table 27  — values of β for unbraced columns  
End condition at top  β 
End condition at bottom   
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 1 2 3 
End condition 1  1.2 1.3 1.6 
End condition  1.3 1.5 1.8 
End condition 3  1.6 1.8 - 
End condition  2.2 - - 
 
11.8.8.2  Effective height of a column: more rigorous method  
11.8.8.2.1  For a framed structure, effective height may be obtain ed from the following equations:  
a) for a braced column, the lesser of  
le = lo [0.7 + 0 .05 (α c1 + α c2)] < lo and 
le = lo (0.85 + 0 .05 α c,min) < lo 
b) for an unbraced column, the lesser of  
le = lo [1.0 + 0 .15 (α c1 + α c2)] and  
le = lo (2.0 + 0 .3 α c,min) 
where  
lo  is the clear height between end restraints;  
αc1 is the ratio of sum of column stiffne sses to sum of beam stiffnesses at one end of column;  
αc2  is the ratio of sum of column stiffnesses to sum of beam stiffnesses at other end of  column; and αc,min is 
the lesser of α c1 and α c2. 
11.8.8.2.2  The stiffness of a member should be obtained by divi ding the second moment of area of its  
concrete section by its actual length, which is the distance centre -to-centre of restraints.  
11.8.8.2.3  When α c   is being calculated, only elements properly framed into the end of the column in the 
appropriate plane of bending should be considered. In cases of relative stiffness, the following simplifying 
assumptions may be made:  
(i) flat slab construction: the stiffness of an equivalent beam that has the width and thickness of the 
slab forming the column strip should be assumed; (For edge columns, see 11.7.5.3.2.)  
(ii) simply supported beams framing into a column: α c may be taken as 10;  
(iii) connection between column and base design to resist nominal moment only: α c may be taken as 10;  DRS 142: 2020  
151                ©RSB 2020  - All rights reserved  
 (iv) connection between column and base design to resist column moment: α c may be taken as 1,0.  
11.9 Walls  
11.9.1  General  
11.9.1.1  This clause refers to reinforced concrete walls with a length to thickness ratio of 4 or more and in 
which the reinforcement is taken into account in the strength analysis.  
11.9.1.2  These elements of construction provide lateral sta bility to the structure as a whole and need not be 
designed to support the forces transmitted by lateral supports in addition to the other  design loads and forces.  
11.9.1.3  The overall stability of a multistorey building should not, in any direction, depen d on unbraced walls 
alone.  
11.9.2  Forces in lateral supports  
11.9.2.1  A lateral support is an element (a prop, a buttress, a floor, cross -wall or other vertical or  horizontal 
element) able to transmit lateral forces from a braced wall to the principal structural bracing or to the 
foundations.  
11.9.2.2  The forces that lateral supports should be able to transmit are assumed to be equal in  magnitude to 
the sum of the following:  
a) the simple static reactions to the sum of the applied maximum design horizontal forces at the point of 
lateral support; and  
b) 2.5 % of the total maximum design vertical load that the wall or column is designed to carry at the 
point of lateral support.  
11.9.3  Resistance of lateral supports to rotation  
Resistance of lateral supports to rotation should onl y be considered to exist in the following cases:  
a) where both the lateral support and the braced wall are concrete walls that are adequately detailed to 
provide bending restraint; or  
b) where precast or in -situ concrete floors (irrespective of the direction of span) have a bearing on at 
least two -thirds of the thickness of the wall, or where there is a connection that provides adequate 
bending restraint.  
11.9.4  Vertical reinforcement  
11.9.4.1  The area of the vertical reinforcement should lie between As,vmin  and As,vma x. 
NOTE 1 The recommended value of As,vmin  is 0,002 Ac.   
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 NOTE 2 The recommended value of As,vmax    is 0,04 Ac outside lap locations unless it can be shown that the 
concrete integrity is not affected and that the full strength is achieved at ULS. This limi t may be doubled at laps.  
11.9.4.2  Where the minimum area of reinforcement, As,vmin, controls in design, half of this area should be 
located at each face.  
11.9.4.3  The distance between two adjacent vertical bars shall not exceed 3 times the wall thickness or 400 
mm whichever is the l . 
11.9.5  Horizontal reinforcement  
11.9.5.1  Horizontal reinforcement running parallel to the faces of the wall (and to the free edges) should be 
provided at each surface. It should not be less than As,hmin. 
NOTE  The recommended of As,hm in is either 25  % of the vertical reinforcement or 0 .001 Ac, whichever is greater.  
11.9.5.2  The spacing between two adjacent horizontal bars should not be greater than 400 mm.  
11.9.6  Transverse reinforcement  
11.9.6.1  In any part of a wall where the total area of the vertical reinforcement in the two faces exceeds 0 .02 
Ac, transverse reinforcement in the form of links should be provided in accordance with the requirements for 
columns.  
11.9.6.2  Where the main reinforcement is placed nearest to the wall faces, transv erse reinforcement should 
also be provided in the form of links with at least of 4 per m2 of wall area.  
NOTE  Transverse reinforcement need not be provided where welded wire mesh and bars of diameter  ϕ ≤ 16 mm are 
used with concrete cover larger than 2  ϕ , 
11.9.7  Forces and moments in reinforced concrete walls  
11.9.7.1  Axial forces  
The axial force in a reinforced wall may be calculated on the assumption that the beams and slabs that 
transmit force into the wall are simply supported.  
11.9.7.2  Design transverse  moments  
11.9.7.2.1  Design transverse moments, where derived from beams or other constructions designed to  
frame monolithically at right angles into the wall, should be calculated using elastic analysis.  
11.9.7.2.2  When a construction is designed to be simply supported by a wall,  the eccentricity may be  
assessed as for plain walls and the resultant moment calculated. Except for short -braced  walls that are loaded 
almost symmetrically, the moment per unit length in the  direction at right angles to a wall should be taken as 
the great er of 0 .05nw x h, or nw x 15 mm,  
where:  DRS 142: 2020  
153                ©RSB 2020  - All rights reserved  
 nw is the axial load per unit length and h is the thickness of the wall.  
11.9.7.2.3  In a slender wall, significant additional moments may be induced by lateral deflections of  the wall 
under load. To make appropriate allowance for this, such a wall may be considered a slender column bent 
about the minor axis except that where a wall is reinforced with only one central layer of reinforcement, the 
additional moments should be doub led. 
11.9.7.3  Design in -plane moments  
Moments in the plane of a single wall, due to horizontal forces, can be calculated from statics. When a 
horizontal force is resisted by several walls, the proportion allocated to each wall should be proportional to its 
stiffnes s. When a shear connection is assumed between vertical edges of adjacent walls, an appropriate 
elastic analysis may be used, provided the shear connection is designed to withstand the design force.  
11.9.8  Short reinforced walls  
11.9.8.1  Short braced axially loaded reinfor ced walls  
Short braced axially loaded reinforced walls that by the nature of the structure cannot be subjected to 
significant moments, may be designed in the presence of the nominal eccentricity moment by the following 
equation:  
N < 0.40 fcuAc + 0.67Ascfy 
NOTE  This includes an allowance for γ m. 
where:  
N is the total design axial load on the wall due to maximum design loads;  
Fcu  is the characteristic strength of concrete;  
Ac is the net cross -sectional area of concrete in wall;  
Asc is the area of vertical re inforcement; and  
fy is the characteristic strength of compression reinforcement.  
11.9.8.2  Walls subjected to transverse moments and to uniformly distributed axial forces  
When the only eccentricity of force derives from the transverse moments, the design axial load may be 
assumed to be distributed uniformly along the length of the wall. The cross -section of the wall should be 
designed to resist the appropriate design ultimate axial load and transverse moment. The assumptions made 
in the analysis of beam sections appl y.  
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 11.9.8.3  Walls subjected to in -plane moments and to axial forces  
The cross -section of the wall should be designed by application of the assumptions given in the clause of 
moments of resistance at ultimate limit state for beams.  
11.9.8.4  Walls subjected to axial forces an d to sign ificant transverse and in -plane moments  
11.9.8.4.1  The assessment of the effects should comprise three stages, as follows:  
a) in-plane moments and axial forces: the distribution of force along the wall is calculated by elastic 
analysis, assuming no t ension in the concrete;  
b) transverse moments: the tr ansverse moments are calculated . 
11.9.8.4.2  At various points along the wall, effects (a) and (b) above are combined and checked, using the  
assumptions given in the clause of moments of resistance at ultima te limit state for beams.  
11.9.9  Slender reinforced walls  
11.9.9.1  Design procedure  
11.9.9.1.1  The assessment of the effects should comprise three stages, as follows:  
a) in-plane moments and axial forces: the distribution of force along the wall is calculated by elastic 
analysis, assuming no tension in the concrete ;  
b) transverse moments: the transverse moments are calculated  
11.9.9.1.2  At various points along the wall, effects (a) and (b) above are combined and checked, using the  
assumptions given in the clause of design of c olumn section for ULS . 
11.9.9.2  Limits of slenderness  
The slenderness ratio is the ratio of the effective height of the wall le to its thickness h. The following 
limitations of the slenderness ratio shall be observed:  
a) in the case of a braced wall reinforced as in t he clause of area of reinforcement in elements, but less 
than 1 %, the ratio le/h shall not exceed 40;  
b) in the case of a braced wall reinforced as in the clause of area of reinforcement in elements but 
exceeding 1 %, the ratio le/h shall not exceed 45;  
c) in the case of an unbraced wall reinforced as in the clause of area of reinforcement in elements, the 
ratio le/h shall not exceed 30.  DRS 142: 2020  
155                ©RSB 2020  - All rights reserved  
 11.9.9.3  Deflection of reinforced walls  
The deflection of a reinforced concrete wall will be within reasonable limits if the preceding provisions are 
followed and if, in the case of a cantilever shear wall, the total height of the wall does not exceed 12 times its 
length.  
11.9.9.4  Crack control in reinforced walls  
Cracks in a reinforced concrete wall will be within reasonable limits if the reinfor cement is arranged in two 
layers and each layer complies with the bar spacing rules given in the appropriate clause.  
11.10  Staircases  
11.10.1  General  
11.10.1.1  Distribution of loading  
11.10.1.1.1  Assume the ultimate load to be uniformly distributed over the plan area of the stair case.  
11.10.1.1.2  When, however, staircases surrounding open wells include two spans that intersect at right 
angles, the load on the areas common to both spans may be assumed to be divided equally between the two 
spans.  
11.10.1.1.3  When staircases or landi ngs that span in the direction of the flight are built at least 110 mm  into 
walls along part or all of their length, a 150-mm strip adjacent to the wall may be deducted from the loaded 
area.  
 
11.10.1.2  Effective width of staircases  
11.10.1.2.1  Take the effective wid th of a staircase without stringer beams as the actual width of the 
staircase.  
11.10.1.2.2  When a staircase is built into a wall along part or all of its span, include two -thirds of the 
embedded width up to a maximum of 80 mm, in the effective width.  
11.10.1.3  Effec tive span of staircases  
11.10.1.3.1  When a staircase without stringer beams is built monolithically at its ends into structural  
elements spanning at right angles to the span of the staircase, take the effective span as the sum of the clear 
horizontal dista nce between the supporting elements plus half the widths of the supporting elements, subject 
to maximum additions of 900 mm at both ends.  
11.10.1.3.2  When a staircase without stringer beams is simply supported, take the effective span as the 
horizontal dis tance between the centre -lines of the supports.  
11.10.1.3.3  For the purposes of this sub clause, a staircase may be taken to include a section of landing  
spanning in the same direction and continuous with the stair flight.   
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 11.10.1.4  Depth of section  
Take the depth o f the section as the minimum thickness perpendicular to the soffit of the staircase.  
11.10.2  Design of staircases  
11.10.2.1  Loading  
Staircases should be designed to support the ultimate design load in accordance with the load  arrangements 
given in the appropriate clause.  
11.10.2.2  Strength, deflection and crack control  
The provisions given in the clause of beams and solid slabs and for beams and slabs may be used except for 
the span/effective depth ratio of a staircase without stringer beams, where 11.10.2.3 applies.  
11.10.2.3  Permissible span/ effective depth ratio for staircases without stringer beams  
Provided the stair flight occupies at least 60 % of the span, the ratio calculated in accordance with the clause 
of Span/effective depth ratio for rectangular beams  may be increased by 15 %.  
11.11  Found ations  
11.11.1  General  
This sub clause covers the design of pad footings and pile caps.  
11.11.2  Moments and forces in foundations  
11.11.2.1  Except where the reactions to the applied design ultimate loads and moments are derived by 
more accurate methods, e.g. an elastic an alysis of a pile group or the application of established principles of 
soil mechanics, make the following assumptions:  
a) when the base is axially loaded, assume the reactions to ultimate design loads to be uniformly 
distributed per unit area or per pile;  
b) when the base is eccentrically loaded, assume the reactions to vary linearly across the base or 
across the pile system.  
11.11.2.2  The critical section for bending moment in the design of an isolated base may be taken at  the 
face of the column or wall.  
11.11. 2.3 The design moment on a vertical section passing completely across a base should be taken  as 
the moment due to reactions to all design ultimate loads on one side of this section. No  redistribution of 
moments should be made.  DRS 142: 2020  
157                ©RSB 2020  - All rights reserved  
 11.11.2.4  When the flexural a nd shear strengths of sections are being calculated, account should be  taken 
of pockets for precast members unless they are to be subsequently grouted with a cement mortar of 
compressive strength at least equal to that of the concrete in the base.  
11.11.2. 5 When the resistance to bending is being calculated, bases may be regarded as beams or  solid 
slabs, as appropriate.  
11.11.3  Design of pad footings  
11.11.3.1  Design moments and forces  
Shall refer to clause  11.11.2.  
11.11.4  Distribution of reinforcement  
11.11.4.1  The reinforcement considered in this sub clause is that at right angles to the concrete section. 
The reinforcement required in the shorter cross -section of a rectangular base should be placed evenly across 
the section. If any reinforcement is required in the longer section of a rectangular base in order to resist the 
bending moment, it should be distributed as follows:  
a) the amount equal to A s   
     of reinforcement should be spread over a band centred on the column 
or support and of width equal to the dimension o f the short side of the base;  
where,  
 As is the total area of reinforcement required and β1 is the ratio of the longer to the shorter side.  
b) the remaining reinforcement should be spread evenly over the outer parts of the section.  
11.11.4.2  Where there are two or more columns and lc is the greater of half the spacing between them or 
the distance  to the edge of the pad, then the following should be considered:  
11.11.4.3  When lc exceeds (3 c/4 + 9 d/4), where c is the column width and d is the effective depth of a pad  
footing, two -thirds of the required reinforcement should be concentrated within a z one from the  centre -line of 
the column to a distance 1 .5d from the face of the column; otherwise the reinforcement should be uniformly 
distributed over lc. 
 
11.11.4.1  Shear  
11.11.4.1.1  The design shear force is the algebraic sum of all the ultimate vertical loads an d reactions  acting 
on one side or outside the periphery of the critical section.  
11.11.4.1.2  The shear strength of bases in the vicinity of concentrated loads or reactions is governed  by the 
more severe of the following two conditions:   
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 a) shear along a vertic al section that extends across the full width of the base (for pad footings, this 
section may be considered at 1 .5 times the effective depth from the face of the loaded area and the 
provisions given in the clause of shear stress and shear reinforcement in beams  will apply); and  
b) punching shear around the loaded area, where the provisions given in the clause of shear stresses in 
solid slabs under concentrated load  will apply.  
11.11.4.2  Bond and anchorage  
The provisions given in relevant clause for  bond, anchorage, bear ing, laps, joints, and bends  in bars  apply to 
reinforcement in bases.  
The critical sections for local bond stress are:  
a) the critical sections described in the relevant clause of bond, anchorage, bearing, laps, joints, and 
bends in bars ; and  
b) sections at whic h the depth changes or any reinforcement ends.  
11.11.4.3  Limit state of deflection  
This limit state may be ignored for bases.  
11.11.4.4  Crack control in bases  
The provisions given in the relevant clause of maximum distances between bars in tension  concerning the 
maximum dista nce between bars in tension apply to bases, but reinforcement need not be provided in the side 
of bases to control cracking.  
11.11.5  Design of pile caps  
11.11.5.1  General  
11.11.5.1.1  Pile caps are designed either by the bending theory or by truss analogy; if the latter is u sed, the 
truss should be of triangulated form, with a node at the centre of the loaded area.  
11.11.5.1.2  The lower nodes of the truss lie at the intersections of the centre -lines of the piles with the 
tensile reinforcement.  
11.11.5.2  Shear forces  
11.11.5.2.1  The des ign shear strength of a pile cap is normally determined by the shear along a vertical  
cross -section of the full width of the cap. Critical sections for the shear should be assumed to be  located at 20 
% of the diameter of the pile inside the face of the pil e.  
11.11.5.2.2  The whole of the force from the piles with centres lying outside this line should be considered to 
be applied outside this line.  DRS 142: 2020  
159                ©RSB 2020  - All rights reserved  
 11.11.5.3  Design shear resistance  
11.11.5.3.1  The design shear resistance of pile caps may be determined in accordance wi th the clause of  
shear resistance of solid slabs , subject to the  limitations given below.  
11.11.5.3.2  Where the spacing of the piles is less than or equal to 3 pile diameters, the enhancement  of the 
shear strength may be applied over the whole of the crit ical section.  
11.11.5.3.3  Where the spacing is greater, the enhancement may only be applied to strips of width equal to 3 
pile diameters, centred on each pile. Minimum stirrups are not required in pile caps where v < vc (enhanced if 
appropriate).  
11.12  Considera tions affecting design details  
11.12.1  Constructional deviations  
11.12.1.1  Sizes of elements  
When deciding on the nominal overall size of a reinforced concrete element, take account of the  principles of 
dimensional co -ordination. Bear in mind that absolute accuracy exists o nly in theory and that tolerable 
degrees of inaccuracy have to be accepted in practice. Specify as large a degree of tolerance as possible, 
without rendering the finished structure or any part thereof unacceptable for the purpose for which it is 
intended.  
11.12.1.2  Dimensional tolerance  
The partial safety factor for loads will, on a design based on nominal dimensions, provide for all normal 
tolerances. However, when large tolerances are being specified for small highly stressed elements, it may, in 
exceptional cases,  be necessary to base the design on net dimensions after making allowance for the 
maximum specified tolerance.  
11.12.1.3  Tolerance on position of reinforcement  
11.12.1.3.1  In all normal cases, the design may be based on the assumption that the reinforcement is  in its 
nominal position. However, when reinforcement is located in relation to more than one face of an element 
(e.g. a link in a beam in which the nominal cover for all sides is given), the actual concrete cover on one side 
may be greater and can be derived fr om consideration of certain other tolerances appropriate to:  
a) dimensions and spacing of cover blocks, spacers or chairs or both (including the compressibility of 
these items and the surfaces they bear on);  
b) stiffness, straightness, and accuracy of cutting, b ending and fixing of bars or reinforcement cage;  
c) accuracy of formwork in both dimension and plan (this includes permanent forms such as blinding or 
brickwork); and  
d) the size of the structural part and the relative size of the bars or reinforcement cage.   
©RSB 2020  - All rights reserved                  160 
 11.12.1.3.2  In certain cases where bars or reinforcement cages are positioned accurately on one face  of a 
structural element, this may lead to an accumulation of tolerances affecting the position of highly stressed 
reinforcement at the opposite face of the el ement. The consequent  possible reduction in effective depth to this 
reinforcement may exceed the percentage  allowed for in the normal value of the partial safety factor for loads. 
In the design of a particularly critical element, therefore, appropriate adj ustment to the effective depth 
assumed may be necessary.  
11.12.1.4  Construction and movement joints  
11.12.1.4.1  Construction joints  
11.12.1.4.1.1  The number of construction joints should be kept to the necessary minimum. Their exact location 
should be indicated on a drawing or agreed on with the contractor. Generally, construction joints should be at 
right angles to the direction of the element.  
11.12.1.4.1.2  The concrete at the joint should be bonded with the concrete subsequently placed against it to 
such degree that the load -bearing capacity of the concrete in the area of the joint is not impaired. If it is 
necessary for a joint to transfer tensile or shear stresses, the surface of the first pour should be roughened to 
increase the bond strength and to provide aggregate interl ock.  
11.12.1.4.2  Movement joints  
11.12.1.4.2.1  Movement joints are those specifically designed and provided to allow relative movement of 
adjacent parts of an element or structure to occur without impairment of the functional integrity of the element 
or structure. Th ey may also act as connection joints between several parts of an element or structure, or they 
may be provided solely to permit translocation or rotation or both.  
11.12.1.4.2.2  Careful consideration should be given to the location of movement joints and th eir position 
should be clearly indicated on the drawings, both for the individual elements and for the structure as a whole.  
11.12.1.4.2.3  In general, movement joints in the structure should pass through the whole structure in one 
plane. If special prepara tion of the joint faces is required, this should be specified.  
11.12.2  Concrete cover to reinforcement  
11.12.2.1  Nominal cover is that dimension used in design and indicated on the drawings.  Determine the 
concrete cover to reinforcement by consideration of fire re sistance and  durability under the envisaged 
conditions of exposure.  
11.12.2.2  Cover is not required to the end of a straight bar in a floor or roof unit when the end of the  unit is 
not exposed to the weather. However, the ends of simply supported beams not  directly exposed to the 
weather may be liable to condensation with the consequent need to protect the reinforcement against 
corrosion. Regard the following as subject to moderate exposure: roofs, balconies, washed down floors, car 
parks, or any other cons truction that, although nominally protected from water, might become moist as a result 
of deterioration of finishes or for other reasons.  
11.12.2.3  Always make the nominal cover at least equal to the diameter of the bar and, in the case of 
bundles of three  or more bars, equal to the diameter of a single bar of equivalent area.  DRS 142: 2020  
161                ©RSB 2020  - All rights reserved  
 11.12.2.4  Concrete cover to all reinforcement, including links, should be at least equal to the maximum  
nominal size of the aggregate.  
11.12.2.5  Where a surface treatment (such as bus h hammering) cuts into the face of the concrete, add  the 
expected depth of treatment to the nominal cover.  
11.12.2.6  Where, owing to its particular situation, an element is required to resist the action of fire for  a 
specified period, the nominal cover may  need to be increased or, alternatively, the concrete cover to the main 
bars may need to be reinforced to prevent premature spalling.  
11.12.2.7  Take special care in conditions of extreme exposure or where low density or porous  aggregates 
are used.  And t ake account of possible deviations in reinforcement fitting between two concrete faces  
11.12.3   Reinforcement (general considerations)  
11.12.3.1  Groups of bars  
11.12.3.1.1  Bars may be arranged in pairs in contact or in groups of three -bar or four -bar bundles in contact. 
Each p air or bundle should be treated as a single bar of equivalent area.  
11.12.3.1.2  Terminate bars in a bundle at different points spaced at least 40 times the bar size apart except 
for bundles that stop at a support. Laps may be made to one bar in a bundle at  a time. Never, even at laps, 
should more than four bars be arranged in contact.  
11.12.3.1.3  The designer should not use  bundles in an element without links.  
11.12.4  Minimum areas of reinforcement in elements  
11.12.4.1  Minimum area of main reinforcement  
11.12.4.1.1  The mini mum percentages of main reinforcement appropriate for various conditions of  loading 
and types of member are given in Table 28. 
11.12.4.1. 2 Should e nsure that the minimum number of longitudinal bars provided in a column is four in  
rectangular columns and si x in circular columns and that the diameter of the bars is at least 12 mm.  
11.12.4.1.3  Should ensure that the total cross -sectional area of these bars will be at least 0 .4 % of the cross -
sectional area of the column.  
11.12.4.1.4  A wall should not  be regard ed as a reinforced concrete wall unless the percentage of vertical  
reinforcement provided is at least 0 .4 % of the gross cross -sectional area. This vertical reinforcement may be 
in one or two layers.  
11.12.4.1.5  For purposes of fire resistance, a wall cont aining less than 1 .0 % of vertical reinforcement  is 
classed as a plain concrete wall.   
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 11.12.4.2   Minimum area of secondary reinforcement  
11.12.4.2.1  For a solid concrete suspended slab, the amount of reinforcement provided at right angles  to the 
main reinforcement i s given in table 28. The distance between bars of the secondary  reinforcement shall not 
exceed five times the effective depth of the slab.  
11.12.4.1.2  Where the main vertical reinforcement in a wall is used to resist compression or to provide  
horizontal re inforcement, the amount of reinforcement provided, expressed as a percentage of the gross 
cross -section, shall be at least 0 .25 % in the case of high -yield steel or 0 .3 % in the case of mild steel. The 
reinforcement shall be of diameter at least 6 mm or at  least one -quarter of the diameter of the vertical bars. It 
may also be necessary to provide lin ks in the thickness of the wall.  
11.12.4.3  Minimum size of bars near side faces of beams of overall depth exceeding 750 mm  
In order to control cracking, bars provided nea r side faces of beams should be of diameter at least, where sb is 
the bar spacing and b the width of the section at s the point considered (or 500 mm, b b/fy whichever is the 
smaller). The bars should be distributed at a spacing not exceeding 250 mm near th e side faces of the beam 
and the distribution should be done over a distance of two -thirds of the overall depth of the beam, measured 
from its tension face.  
11.12.4.4  Minimum area of links  
11.12.4.4.1  In a beam or column, where part or all of the main reinforcement  is required to resist  
compression, provide links or ties of diameter at least one -quarter of the diameter of the largest  compression 
bar at a maximum spacing of twelve times the diameter of the smallest compression bar.  
11.12.4.4.2  So arrange links that e very corner bar and alternate bar or group in an outer layer of 
reinforcement is supported by a link passing round the bar and having an included angle of not more than 
135o. Ensure that all other bars or groups within a compression zone are within 150 mm of a restrained bar.  
11.12.4.4.3  In the case of circular columns, where the longitudinal reinforcement is located round the 
periphery of a circle, provide adequate lateral support by using a circular tie that passes round the bars or 
groups.  
11.12.4.4.4  In a wall, where the percentage of vertical reinforcement used to resist compression  exceeds 2 
%, provide links of diameter at least 6 mm (or at least one -quarter of the diameter of the largest compression 
bar) throughout the thickness of the wall. Ensure th at the spacing of these links does not exceed twice the wall  
thickness in either the horizontal or the vertical direction and, in the vertical direction, does not exceed 16 
times the bar diameter.  
11.12.4.4.5  The Designer should e nsure that any vertical co mpression bar not enclosed by a link is within 
200 mm of a restrained bar.  
Table 28  — Minimum percentage of reinforcement  
Situation  Definition of percentage  Minimum percentage  
fy = 250 MPa  fy = 450 MPa  
Tension reinforcement  
Sections subjected mainly 
to tension  100 As/ Ac  0.8 0.45 DRS 142: 2020  
163                ©RSB 2020  - All rights reserved  
 Section subjected to 
flexure  
 
a)Flanged beams, web in 
tension:  
 
− bw / b < 0 .4 
  
bw ≥ 0 .4 
 
b)flanged beams, flange in 
tension over a continuous 
support:  
 
− T-beam  
 
− L-beam  
 
c)rectangular section(in 
solid slabs, this minimum 
should be provided in both 
directions)   
 
 
 
 
 
100As/ bwh  
 
100As/ bwh  
 
 
 
 
 
100As/ bwh  
 
100As/ bwh  
 
 
 
100As/Ac  
  
 
 
 
 
 
0.32 
 
0.24 
 
 
 
 
 
0.48 
 
0.36 
 
 
 
0.24  
 
 
 
 
 
0.18 
 
0.13 
 
 
 
 
 
0.26 
 
0.20 
 
 
 
0.13 
Compression 
reinforcement  
(Where such reinforcement 
is required for the ultimate 
limit state)  
 
General rule  
 
 
Simplified rules for 
particular cases:  
 
Rectangu lar column or wall  
 
Flanged beam:  
 
− flange in compression  
 
− web in compression  
 
c) rectangular beam   
 
 
 
 
 
 
100Asc/Acc  
 
 
 
 
 
 
100Asc/Ac  
 
 
 
100Asc/bht  
 
 
100Asc/bwh  
 
100Asc/Ac   
 
 
 
 
 
 
0.4 
 
 
 
 
 
 
0.4 
 
 
 
0,4 
 
 
0.2 
 
0.2  
 
 
 
 
 
 
0.4 
 
 
 
 
 
 
0.4 
 
 
 
0,4 
 
 
0.2 
 
0.2 
Transverse reinforcement 
in flanges of  flanged     
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 beams(provided over full 
effective flange width near 
top surface to resist 
horizontal shear)   
 
100Ast/ht   
 
0.15  
 
0.15 
11.12.4.4. 6 In all beams except those of minor structural importance (e.g. lintels) or where the maximum 
shear stress, calcu lated in accordance with the clause of Shear resistance of beams , is less than half the 
recommended value, provide nominal links throughout the span such that for high -yield steel links,  
 
For mild steel links,  
 
where:  
Asv is the cross -sectional area of t he two legs of a link;  
bt  is the width of the beam at the level of the tension reinforcement; and  
sv is the spacing of links.  
11.12.4.4.7  The spacing of links shall not exceed 0 .75 times the effective depth of the beam, and the  lateral 
spacing of the indi vidual legs of the links shall not exceed this value. Links shall enclose all tension 
reinforcement.  
11.12.5  Maximum areas of reinforcement in element  
11.12.5.1  Beams  
Neither the area of tension reinforcement nor the area of compression reinforcement should exceed 4 % of 
the gross cross -sectional area of the concrete.  
11.12.5.2  Columns  
The amount of longitudinal reinforcement should not exceed 6 % of the gross cross -sectional area of the 
column in vertically cast columns or 8 % in horizontally cast columns, except that it may be 10 % at laps in 
both types of column.  
11.12.5.3  Walls  
The area of vertical reinforcement should not exceed 4 % (including laps) of the gross cross -sectional area of 
the concrete.  DRS 142: 2020  
165                ©RSB 2020  - All rights reserved  
 11.12.6  Spacing of reinforcement  
11.12.6.1  Minimum distances between bars  
11.12.6.1.1  When the diameter of a b ar exceeds the maximum size of coarse aggregate by more than  5 
mm, a spacing smaller than the bar diameter should be avoided. A pair of bars in contact or a bundle of three 
or four bars in contact should be regarded as a single bar of equivalent area when the spacing is being 
assessed.  
11.12.6.1.2  The spacing of bars should be made suitable for the proper compaction of concrete, and when 
an internal vibrator is likely to be used, adequate spacing should be provided in the  reinforcement to enable 
the vibrato r to be inserted. Minimum reinforcement spacing is best determined by experience or proper work 
tests, but in the absence of better information, the distances given below may be used.  
11.12.6.1.1  Individual bars  
Except where bars form part of a pair or bundle,  the hor izontal distance between bars should be at least ( hagg 
+ 5) mm, where hagg is the maximum size of the coarse aggregate. Where there are two or more rows:  
a) the gaps between corresponding bars in each row should be vertically in line; and  
b) the vertical distanc e between bars should be at least 2/3 hagg. 
11.12.6.1.2  Pairs of bars  
Bars may be arranged in pairs either touching or closer than in 11.12. 6.1.1  in which case:  
a) the gaps between corresponding pairs in each row should be vertically in line and of width at least 
(hagg + 5) mm;  
 
b) when the bars forming the pair are one above the other, the vertical distance between pairs should be 
at least 2/3 hagg;  
c) when the bars forming the pair are side by side, the vertical distance between pairs should be at least 
(hagg + 5) mm.  
11.12.6.1.3  Bundled bars  
Horizontal and vertical distances between bundles should be at least ( hagg + 15) mm and the gaps between 
the rows or bundles should be vertically in line.   
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 11.12.6.2  Maximum distances between  bars in tension  
11.12.6.2.1  Beams  
11.12.6.2.1.1  The rules given below for beams ma y apply in normal internal or external conditions of  exposure 
where a crack width limited to 0 .3 mm is appropriate, unless the calculations of crack width show that greater 
spacing is acceptable.  
11.12.6.2.1.2  In the application of these rules in the case of bars of mixed sizes, any bar of diameter  less than 
0.45 times the diameter of the maximum bar in the section should be ignored, except when those near the 
side faces of beams are being considered.  
11.12.6.2.2  Slabs  
11.12.6.2.2.1  The clear spacing between main bars should not exceed the lesser of three times the effective 
depth or 750 mm. In normal internal or external conditions, unless crack widths are checked by direct 
calculations, the additional rules given below ensure adequate control of cracking.  
11.12.6.2.2. 2 No additional check is required on bar spacing if:  
a) grade 250 steel is used and the slab depth does not exceed 250 mm;  
b) grade 450 steel is used and the slab depth does not exceed 200 mm; or  
c) the amount of tension reinforcement in a slab, expressed as a perc entage of the cross -sectional area 
(the width of section times the effec tive depth), is less than 0 .3 %. 
12 Design and detailing of Precast, composite and plain concrete constructions  
12.1 General  
12.1.1  Design objectives  
This section is concerned with the additional co nsiderations that arise in design and detailing when precast 
units, including large panels, are incorporated into a structure, or when a structure in its entirety is of precast 
concrete construction. It also covers the use of plain concrete for walls or wh ere the reinforcement provided is 
less than the minimum required for reinforced concrete.  
This section provides additional rules for plain concrete structures  
12.1.2  Limit states design  
12.1.2.1  Basis of design  
…..Shall comply with provisions given in RS 112.  DRS 142: 2020  
167                ©RSB 2020  - All rights reserved  
 12.1.2.2  Handling st ress 
12.1.2.2.1  Precast units should be designed to resist, without permanent damage, all stresses induced by  
handling, storage, transport and erection.  
12.1.2.2.2  When necessary, specify the positions of lifting and supporting points. Consultation at the  design 
stage with those responsible for handling is an advantage. Ensure that the design takes into account the 
effects of both snatch lifting from and placing onto supports.  
12.1.2.3  Connections  and joints  
12.1.2.3.1  The design of connections is of fundamental im portance in precast construction and should  be 
carefully considered.  The engineer responsible for the overall stability of the structure should ensure the 
compatibility of the design and details of components. The responsibility for overall stability shall  be clearly 
assigned when some or all of the design and details are not worked out by the engineer.  
12.1.2.3.2  Joints to allow for movement due to shrinkage, thermal effects and possible differential  
settlement of foundations are of as great importance in precast as in in -situ construction. Determine the 
number and spacing of such joints at an early stage in the design. In the design of beam and slab ends on 
corbels and nibs, take particular care to provide overlap and anchorage of all reinforcement adjacen t to the 
contact faces, taking constructional tolerances into consideration.  
12.1.2.4  Stability  
12.1.2.4.1  The provisions regarding stability for other concrete elements apply also to precast, composite 
and plain concrete construction except that, in structures of five storeys or more, supported by plain concrete 
walls, it will be necessary to ensure that the area of effective vertical ties from foundation to roof level is at 
least 0 .2 % of the cross -sectional area of the walls.  
12.1.2.4.2  The minimum dimension of a ny in -situ concrete section in which tie bars are provided should  be 
not less than the sum of the bar size (or twice the bar size at laps) plus twice the maximum  aggregate size 
plus 10 mm.  
12.1.2.4.3  The tie should be able to transmit the forces from the r einforcement in the precast units and  to 
develop the required strength at all lapped joints. If enclosing links are used, the ultimate tensile resistance of 
the links should be not less than the ultimate tension in the tie.  
12.1.2.4.4  Ensure that column an d wall ties do not, for their anchorage at either end, rely solely on the  
bond of a straight plain bar. So bend or so hook plain bars as to provide the required anchorage in bearing on 
sound concrete unless they are welded or mechanically anchored to the m ain reinforcement in a precast unit.  
12.1.2.4.5  As an alternative to providing the vertical ties recommended above for structures of five  storeys 
or more, such structures may be designed in accordance with the provisions given below.  
12.1.2.4.6  Any vertica l load -bearing element that cannot be allowed to become ineffective, together  with its 
connections, shall be so designed as to withstand a load of 34 kN/m2 applied to it from any direction. Any 
horizontal element (or any part thereof) that provides lateral  support vital to the stability of that vertical load -
bearing element shall be so designed, together with its connections, as to withstand a load of 34 kN/m2 
applied to it from any direction. Any element or lateral support so designed should also be capabl e of 
supporting the reaction from any attached building components also subject to a loading of 34 kN/m2 or such  
©RSB 2020  - All rights reserved                  168 
 reaction as might reasonably be transmitted, having regard to the strength of the attached component and the 
strength of its connection.  
12.2 Precas t concrete construction  
12.2.1  Framed structures and continuous beams  
When the continuity of reinforcement or tendons through the connections or the interaction between units (or 
both) is such that the structure will behave as a frame or as a continuous beam, the  analysis, redistribution of 
moments, and the design and detailing of individual units may all be in accordance with clause of reinforced 
concrete or prestressed concrete as appropriate.  
12.2.2  Slabs  
12.2.2.1  When assessing the effect of concentrated loads (inclu ding partitions in the direction of span),  ensure 
that the width of slab assumed to contribute to the support of the load does not exceed the width of the loaded 
area together with the width of three precast units and joints (when there is no topping) or t he width of four 
precast units and joints (where the topping is at least 30 mm thick), unless test results substantiate the use of 
a wider area. In no case take the width as extending more than 0 .25l on either side of the loaded area, where l 
is the span.  
12.2.2.2  Design precast units intended for use in composite constructions as such, but also check or design 
for the conditions arising during handling, transportation and erection. In a floor or roof construction of hollow 
blocks supported by precast concr ete ribs, pay particular attention to the bearing of blocks on the ribs when no 
topping is provided.  
 
12.2.3  Continuous concrete nibs  
12.2.3.1  Where a continuous nib less than 300 mm deep provides a bearing, as on a boot lintel, design the 
nib as a short cantilev er slab in accordance with the provisions given below . 
12.2.3.2  Ensure that the projection of the nib is sufficient to provide an adequate bearing width for the type of 
unit to be supported. Give the reinforcement in the nib and any reinforcement  in the su pported unit a minimum 
nominal overlap in plan of 60 mm.  
12.2.3.3  Assume the line of action of the design load to occur at the outer edge of the loaded area, i.e. at the 
front edge of the nib, or at the beginning of the chamfered edge, or at the outer edge  of the bearing pad, as 
appropriate.  
12.2.3.4  Take the maximum design bending moment as the distance from the line of action of the  load to the 
nearest vertical leg of the links in the beam element from which the nib projects, times the load.  
12.2.3.5  Provide links in the element from which the nib projects. The links should be capable of  transmitting 
(in addition to any other forces they resist) the load from the nib to the compression zone of the element.  
12.2.4  Allowance for construction inaccuracies  
The allow ance for construction inaccuracies should cover deviations that can occur during the  assembling of 
components, site construction, manufacture and erection, and may be assessed from a statistical analysis of DRS 142: 2020  
169                ©RSB 2020  - All rights reserved  
 measured or predicted deviation. Alternatively, f or supported members of span up to  15 m and with average 
standards of accuracy, the allowance may be taken as the greatest of:  
a) 15 mm, or 3 mm per metre of distance between the faces of steel or precast concrete  supports  
b) 20 mm, or 4 mm per metre of distance  between the faces of masonry supports; and  
c) 25 mm, or 5 mm per metre of distance between the faces of in -situ concrete supports.  
12.2.5  Horizontal forces or rotation at a bearing  
12.2.5.1  The presence of horizontal forces at a bearing can reduce the load -carrying  capacity of the 
supporting unit considerably by causing premature splitting or shearing. These forces may be due to creep, 
shrinkage, and temperature effects, or may result from misalignment, lack of plumb or other causes.  
12.2.5.2  When they are likely to  be significant, consider these forces in designing and detailing the joints by 
providing:  
a) either sliding bearings or suitable lateral reinforcement in the top of the supporting unit, and  
b) continuity reinforcement to tie together the ends of the supported u nits. 
12.2.5.3  Where, owing to large spans or other reasons, large rotations are likely to occur at the end supports 
of flexural units, use bearings that are capable of accommodating these rotations.  
12.2.6  Joints between precast units  
12.2.6.1  General  
12.2.6.1.1  Design t he critical sections of precast units close to joints to resist the worst combinations  of 
shear, axial force and bending caused by the ultimate vertical and horizontal forces. When the design of the 
units is based on the assumption that the joint between t hem is not capable of  transmitting moment, either 
design the joint to ensure that this is or take suitable precautions to ensure that if any cracking develops, it will 
not be unsightly and will not excessively reduce the unit's resistance to shear or axial  force.  
12.2.6.1.2  Where a space is left between two or more precast units, which is to be filled later with in -situ 
concrete or mortar, make the space large enough for the filling material to be placed easily and  compacted 
sufficiently to fill the gap wit hout abnormally high standards of workmanship or  supervision. The assembly 
instructions shall specify clearly at what stage during construction the gap should be filled.  
12.2.6.1.3  As the majority of joints will incorporate a structural connection, give co nsideration to this aspect 
in the design of the joint.  
12.2.6.2  Joints transmitting mainly compression  
12.2.6.2.1  A joint that transmits mainly compression is most commonly used for horizontal joints  between 
load-bearing walls or columns. Design the joint to resist  all the forces and moments implicit in the assumptions 
made in analysing the structure as a whole and in designing the individual units to be joined. In the absence of  
©RSB 2020  - All rights reserved                  170 
 more accurate information derived from a comprehensive programme of suitable tests, the  area of concrete to 
be considered when the strength of the joint in a wall or column is being calculated, should be the greater of:  
a) the area of the in -situ concrete, ignoring the area of any intruding floor or beam units (but not more 
than 90 % of the wal l or column area);  
b) 75 % of the area of contact between wall or column and joint.  
12.2.6.2.2  Consider only those parts of the floor units that are solid over the bearing, and bed the units 
properly on concrete or mortar of adequate quality.  
12.2.6.2.3  Pay p articular attention to detailing the joint and joint reinforcement to prevent premature  
splitting or spalling of the concrete in the ends of the precast units.  
12.2.6.2.4  Where a wall or a column is subjected to lateral loads, design the horizontal joints for shear  
12.2.6.3  Joints transmitting shear in slabs  
12.2.6.3.1  A joint may be assumed to transmit a shear force between panels when, for example, a wall acts 
as a wind -bracing wall or a floor acts as a wind girder, provided that one of the provisions given below is 
complied with.  
12.2.6.3.2  Floor units transmitting shear in a horizontal plane should be restrained to prevent their  moving 
apart horizontally, and the joints between them should be formed by grouting with a suitable concrete or 
mortar mix. When the cal culated shear stress in the joint under ultimate loads does not exceed 0 .23 MPa, no 
reinforcement need be provided in or across the joint, and the sides of the unit forming the joint may have the 
normal finish.  
12.2.6.3.3  When the sides or ends of the pane ls or units forming the joints have a finish "as -extruded"  and 
when the shear stress due to ultimate loads does not exceed 0 .45 MPa, no reinforcement need be provided in 
joints that are under compression in all loading conditions.  
12.2.6.3.4  The shear stre ss due to design ultimate loads, calculated on the minimum root area of a  
castellated joint, should be less than 1 .3 MPa. Separation of the units normal to the joint should be prevented 
either by the provision of steel ties across the ends of the joint or by the provision of a compressive force 
normal to the joint under all loading conditions. A taper should usually be provided to the projecting keys of a 
castellated joint to ease the removal of formwork; to limit movements in the joint, ensure that this ta per is not 
excessive.  
12.2.6.3.5  When reinforcement is provided to resist the entire shear force due to design ultimate loads, the 
shear force V should comply with the following equation:  
V = 0.6 Fb tan α f 
where : 
Fb is the lesser of 0 .87fy  As or the anchorage value of the reinforcement;  
As is the minimum area of reinforcement;  DRS 142: 2020  
171                ©RSB 2020  - All rights reserved  
 Fy is the characteristic strength of reinforcement; and  
αf  is the angle of internal friction between faces of joint.  
12.2.6 .3.6 Tan α f can vary between 0 .7 and 1 .7 and is best determined by tests. However, for  concrete -to-
concrete connections, the following values may be assumed:  
a) tan α f = 0.7 for a smooth interface, as in untreated concrete;  
b) tan α f = 1.4 for a roughened or cas tellated joint without continuous in -situ strips across the ends of 
joints; and  
c) tan α f = 1.7 for a roughened or castellated joint with continuous in -situ strips across the ends of joints.  
It should be able to be demonstrated that resistance to sliding of t he joint is provided by  other means.  
12.3 Structural connections between units  
12.3.1  General  
12.3.1.1  Structural requirements for connections  
12.3.1.1.1  When designing and detailing the connections across joints between precast units, consider the 
overall stability of the st ructure, including its stability during construction or after accidental local damage.  
12.3.1.1.2  Take the provisions given in 12.1.2.4 into account and, in addition, consider the severe forces 
and stresses that may be applied to units during the various s tages of handling, transportation and erection.  
12.3.1.1.3  Tie all units together adequately as soon as they have been placed in their final positions. When  
prestressed elements are built into supports, restrained creep effects should be considered.  
12.3.1.2  Design  method  
12.3.1.2.1  Design connections in accordance with the generally accepted methods applicable to reinforced  
Concrete, prestressed concrete or structural steel. Where, by the nature of the construction or material used, 
such methods are not applicable,  prove the efficiency of the connection by appropriate tests in accordance 
with the following: ????  
12.3.1.2.2  Deem a design to be satisfactory on the basis of satisfactory results from an appropriate model 
test coupled with the use of model analysis to pre dict the behaviour of the actual structure, provided the work 
has been carried out by engineers with the relevant experience and using suitable equipment.  
12.3.1.3  Considerations affecting design details  
In addition to ultimate strength requirements and the provisi ons given in 12.1.2.4 regarding minimum tying 
together of the structure, consider the provisions given below.   
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 12.3.1.3.1  Protection  
So design connections that the standard of protection against weather, fire and corrosion that is  required for 
the remainder of the str ucture is maintained.  
12.3.1.3.2  Appearance  
Where connections are to be exposed, so design them that the quality of appearance required for the 
remainder of the structure can be readily achieved. This may often be better done by emphasizing the 
connections rather tha n by attempting to conceal them.  
12.3.1.3.3  Manufacture, assembly and erection  
During design, consider methods of manufacture, assembly and erection, and give particular attention to the 
following points:  
a) where projecting bars or sections are required, keep them to a  minimum and make them as simple as 
possible; make such projections no longer than is necessary for security;  
b) avoid fragile fins and nibs;  
c) locate fixing devices of adequate strength in concrete sections;  
d) consider the practicability of both casting and asse mbly;  
e) most connections require the introduction of suitable jointing material; in the design, allow  sufficient 
space for such material to ensure that the proper filling of the joint is practicable;  
f) it may be desirable to slacken, release or remove levellin g devices such as nuts, wedges,  etc., that 
have no load -bearing function in the completed structure; where this is necessary,  ensure that the 
details are such that inspection (to make certain that this has been done)  can be carried out without 
undue diffic ulty. 
12.3.1.4  Site instructions  
12.3.1.4.1  General  
The strength and stiffness of any connection can be significantly affected by workmanship  on site. The 
diversity of types of joints and their critical role in the strength and stability of the structure place a p articular 
responsibility on the designer to make clear to those responsible for manufacture and erection, those details 
that are essential to the correct operation of the joint.  
12.3.1.4.2  Consider the following points and, where necessary, pass specific i nstructions to the site:  
a) the sequence of forming the joint;  
b) critical dimensions, allowing for permitted deviations, e.g. minimum permissible bearing;  DRS 142: 2020  
173                ©RSB 2020  - All rights reserved  
 c) critical details, e.g. accurate location of a particular reinforcing bar;  
d) the method of correcting possibl e lack of fit in the joint;  
e) the description of the general stability of the structure, with details of any temporary bracing 
necessary;  
f) the extent to which the uncompleted structure may proceed above the completed and matured 
section;  
g) full details of speci al materials; and  
h) the weld sizes, fully specified (where weld symbols are used, ascertain that these are  understood on 
site).  
12.3.2  Continuity of reinforcement  
12.3.2.1  General requirements  
Where continuity of reinforcement is required through the connection, use a joint ing method such that the 
assumptions made in analysing the structure and critical sections are realized. The following methods may be 
used to achieve continuity of reinforcement:  
a) lapping of bars;  
b) sleeving;  
c) threading of bars;  
d) welding; and  
e) any other method p roven by tests.  
12.3.2.2  Lapping of bars  
Where straight bars passing through the joint are lapped, the provisions given in the appropriate clause of laps 
and joints apply. When reinforcement is grouted into a pocket or recess, provide an adequate shear key on 
the inside of the pocket.  
12.3.2.3  Sleeving  
12.3.2.3.1  Three principal types of sleeve jointing may be used, provided that the strength and  deformation 
characteristics have been determined by tests in accordance with the second paragraph of 12.3.1.2 . The three 
types ar e: 
a) grout -filled or resin -filled sleeves capable of transmitting both tensile and compressive forces;   
©RSB 2020  - All rights reserved                  174 
 b) sleeves that mechanically align the square -sawn ends of two bars to allow the transmission  of 
compressive forces only; and  
c) swaged connectors.  
12.3.2.3.2  Ensure that the detailed design of the sleeve and the method of manufacture and assembly  are 
such that the ends of the two bars will be accurately aligned into the sleeve. Ensure that the  concrete cover 
provided for the sleeve is at least that specified for normal reinforcement.  
12.3.2.4  Threading  
12.3.2.4.1  The following methods may be used for jointing threaded bars:  
a) the threaded ends of bars may be joined by a coupler having left -hand and right -hand  threads; this 
type of threaded connection requires a high degree o f accuracy in manufacture  in view of the difficulty 
of ensuring alignment;  
b) one set of bars may be welded to a steel plate, which is drilled to receive the threaded ends  of the 
second set of bars; the second set of bars is fixed to the plate by means of nut s; and  
c) threaded anchors may be cast into a precast unit to receive the threaded ends of  reinforcement.  
12.3.2.4.2  When there is a risk of the threaded connection working loose, e.g. during vibration while in -situ 
concrete is being cast, use a locking devi ce. 
12.3.2.4.3  Restrict the threading of reinforcement to plain round mild steel bars. Where there is difficulty in 
producing a clean thread at the end of a bar, use steel that is normally specified for black bolts and that has a 
characteristic strength of  430 MPa.  
12.3.2.4.4  Base the structural design of special threaded connections on tests in accordance with 12.3.1.2 . 
12.3.2.4.5  Where tests have shown the threaded connection to be at least as strong as the parent bar, the  
strength of the joint may be bas ed on 80 % of the specified characteristic strength of the joined bars in tension 
and on 100 % of that of bars in compression, divided in each case by the appropriate γ m factor.  
12.3.2.5  Welding of bars  
12.3.2.5.1  The design of welded connections may be done by ensuring that welded joints do not occur at 
bends in reinforcement. Where possible, stagger joints in para llel bars of the principal tensile reinforcement in 
the longitudinal direction.  
NOTE  Joints may be considered staggered if the distance between them is not less than the end anchorage length 
for the bar.  
12.3.2.5.2  Joints with structural steel inserts gene rally consist of a steel plate or rolled steel section 
projecting from the face of a column to support the end of a beam. Design the reinforcement in the ends of the 
supported beam in accordance with clause of the design of reinforced concrete.  DRS 142: 2020  
175                ©RSB 2020  - All rights reserved  
 12.3.2.5.3  Except where the design ensures that the reaction does not act at the end of the steel section, 
base the design of the supported unit on a span equal to its overall length, including any projecting steel 
sections. For the design of the supporting unit and its projecting steel section, assume that the reaction is 
applied at the end of the projecting steel section.  
12.3.3  Connections with structural steel inserts  
In the design, consider the possibility of vertical splitting under the steel section due to shrinkage e ffects and 
localized bearing stresses, e.g. under a narrow steel plate.  
12.3.4  Other types of connection  
12.3.4.1  Any other type of connection that can be shown to be capable of carrying the ultimate loads acting on 
it may be used. Amongst those suitable for resi sting shear and flexure are those made by prestressing across 
the joint.  
12.3.4.2  Resin adhesives may be used to form joints subjected to compression but may not be used to resist 
tension or shear. Use them only where they are adequately protected from the  effects of fire . 
12.4 Composite concrete construction  
12.4.1  General  
12.4.1.1  The provisions of this sub clause apply to flexural composite elements consisting of precast  concrete 
units acting in conjunction with added concrete where provision has been made for the  transfer of horizontal 
shear at the contact surface. The precast units may be of either reinforced or prestressed concrete. Analyse 
and design composite concrete structures and elements in accordance with appropriate clauses for the design 
of reinforced and  prestressed concrete.  
12.4.1.2  Pay particular attention, in the design of both the components and the composite section, to the 
effect of the method of construction, on stresses and deflections, and to whether or not propping is to be used.  
12.4.1.3  Base the relative stiffnesses of elements on the properties of the concrete, gross or  transformed 
sections, as described in the appropriate clause of analysis of structures .  
12.4.1.4  If the concrete strength in the two components of a composite element differs  by more than 10 MPa, 
make allowance for this when stiffness is being assessed.  
12.4.1.5  Differential shrinkage of the added concrete and precast concrete units may require  consideration in 
analysing composite elements for the serviceability limit states; differential shrinkage need not be considered 
for the ultimate limit state.  
12.4.1.6  When precast prestressed units, having pre -tensioned tendons, are designed as continuous  
elements and continuity is obtained with reinforced concrete cast in -situ over the  supports, the  compressive 
stresses due to prestress in the ends of the units may be ignored over the transmission length of the tendons 
when the strength of sections is being assessed.   
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 12.4.2  Shear  
12.4.2.1  Carry out the analysis of the resistance of composite s ections to vertical shear due to design  ultimate 
loads in accordance with the appropriate clause of Shear resistance of beams  for reinforced concrete and for 
prestressed concrete.  
12.4.2.2  However, when in -situ concrete is placed between precast prestresse d units and the composite  
concrete section is used in design, ensure that the principal tensile stress does not exceed 0 .24 fcu anywhere 
in the prestressed units; calculate this stress by making due allowance for the construction sequence and by 
taking int o account only 0 .8 of the compressive stress due to prestress at the section under consideration.  
12.4.2.3  Calculations for horizontal shear between the two components of a composite section are  governed 
by the ultimate limit state.  
12.4.3  Serviceability limit s tates  
12.4.3.1  General  
In addition to the provisions given in the appropriate clauses concerning deflection and control of cracking, the 
design of composite construction will be affected by the provisions of the following subclauses.  
12.4.3.2  Compression in the concrete in the case of prestressed precast units  
For composite elements comprising prestressed precast units and in -situ concrete, the methods of analysis 
may be as given in the clause of Ultimate limit state for beams in flexure . However, the compressive stresses 
in the precast unit at the interface may be increased by not more than 50 % above the value given in Table 
29, provided that the ultimate failure of the composite element is due to excessive elongation of the steel.  
Table 29 — Compressive stresses fcu in con crete for serviceability limit states  
Nature of loading  Allowable compressive stresses  
Design load in bending  0.33 fcu 
In continuous beams and other statically  
indeterminate structures, this may be increased to 0 .4 fcu 
within the range of support moments  
Design load in direct  
compression  0.25 fcu 
 
12.5 Plain concrete walls  
12.5.1  General  
12.5.1.1  A plain concrete wall is a vertical load -bearing concrete element whose greatest lateral  dimension 
exceeds four times its least lateral dimension, and one that is assumed t o be without  reinforcement when its 
strength is being considered.  DRS 142: 2020  
177                ©RSB 2020  - All rights reserved  
 12.4.2.2  Where the greatest lateral dimension is less than four times the thickness, the provisions of this 
clause may still be applied.  
12.4.2.3  The definitions for short, slender, braced o r unbraced reinforced concrete walls given in the 
appropriate clause of reinforced concrete walls also apply to a plain concrete wall.  
12.5.2  Structural stability  
Refer to  12.5.3 and other sub clauses related to reinforced concrete walls may be applied.  
12.5.3  Design of  plain concrete walls  
12.5.3.1  Axial force  
The design ultimate axial force in a plain concrete wall may be calculated on the assumption that the beams 
and slabs transmitting forces into it are simply supported.  
12.5.3.2  Effective height of unbraced plain concrete walls  
The effective height le of an unbraced plain concrete wall should be taken as follows:  
a) in the case of a wall supporting at its top a roof or floor slab spanning at right angles:  
        le = 1.5 lo 
b) in the case of other walls: le = 2 lo 
where , 
lo is the clear h eight of the wall between lateral supports; for gable walls, lo may be measured midway 
between eaves and ridge.  
12.5.3.3  Effective height of braced plain concrete walls  
The effective height of braced plain concrete walls should be taken as follows:  
a) where the latera l supports provide resistance both to lateral movement and to rotation, le equals three -
quarters of the clear distance between lateral supports or twice the distance  between a support and a 
free edge, as appropriate;  
 NOTE  This distance is measured vertica lly if the lateral supports are horizontal (e.g. floors) or horizontally if 
the lateral supports are vertical (e.g. other walls).  
b) where the lateral supports provide resistance to lateral movement only, le equals the distance  
between centres of supports, or  two and a half times the distance between a support and a free edge, 
as appropriate.   
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 12.5.3.4  Limits of slenderness  
The slenderness ratio le/h should not exceed 30, whether the wall be braced or unbraced.  
 
12.5.3.5  Minimum transverse eccentricity of forces  
Whatever the arr angements of vertical or horizontal forces, the resultant force in every plain concrete wall 
should be assumed to have a transverse eccentricity of the greater of at least h/20 or 20 mm. In the case of a 
slender wall, additional eccentricity can arise as a  result of deflection under load.  
12.5.3.6  Eccentricity in the plane of the wall  
12.5.3.6.1  In the case of a single wall in -plane  
Eccentricity due to forces may be calculated by statics alone.  
12.5.3.6.2  In a case where a horizontal force is resisted by two or more parallel walls  
12.5.3 .6.2.1  The force should be assumed to be shared between the walls in proportion to their relative 
stiffnesses, provided the resultant eccentricity in any individual wall does not exceed one -third of the length of 
that wall.  
12.5.3.6.2.2  Where the eccentric ity in any individual wall is found to exceed this, the wall stiffness should be  
as zero and an adjustment made to the forces that are assumed to be carried by the  remaining wall(s).  
12.5.3.6.3  In the case of a shear connection being assumed between vertical edges of  adjacent walls  
An appropriate elastic analysis may be made, provided the shear connection is designed to resist the design 
ultimate forces.  
12.5.3.7  Eccentricity at right angles to the wall  
12.5.3.7.1  The load transmitted to a wall by a concrete floor or roof may be assumed to act at one -third of 
the depth of the bearing area from the loaded face. Where there is an in -situ concrete floor on either side of 
the wall, the common bearing area may be assumed to be shared equally by each floor.  
12.5.3.7.2  Loads may be ap plied to walls at eccentricities exceeding half the thickness of the wall by  
means of special fittings (e.g. joist hangers), provided that the adequacy of such fittings against local failure is 
proved by testing or other means.  
12.5.3.7.3  The resultant ecc entricity of the total load on a braced wall at any level may be calculated  on the 
assumption that, immediately above a lateral support, the resultant eccentricity of all the vertical loads above 
that level is zero.  DRS 142: 2020  
179                ©RSB 2020  - All rights reserved  
 12.5.3.8  In-plane and transverse eccentricity of resultant force on an unbraced wall  
At any level, full allowance should be made for the eccentricity of all vertical loads and the overturning 
moments produced by any lateral forces above that level.  
12.5.3.9   Concentrated loads  
When loads are purely local (as at b eam bearings), they may be assumed to be immediately  dispersed, 
provided that the local design stress under the load does not exceed 0 .6fcu for concrete of grade 25 or higher, 
or 0.5fcu for concrete of a lower grade.  
12.5.3.10  Calculation of design load per unit len gth 
The design load per unit length nw should be assessed on the basis of a linear distribution of load along the 
length of the wall, with no allowance for any tensile strength.  
12.5.3.11  Maximum unit axial load for short braced plain walls  
The maximum design ultima te axial load per unit length of wall due to ultimate loads, nw, should satisfy the 
following equation:  
nw < 0.3 (h - 2ex) fcu                                                                                                     (12.1)  
where , 
nw is the maxim um design axial load per unit length of wall due to design ultimate loads;  
h is the thickness of wall;  
ex is the resultant eccentricity of load at right angles to plane of wall  
fcu   is the characteristic strength of concrete.  
12.5.3.12  Maximum unit axial load for slender braced plain walls  
At every section of a slender braced wall, the maximum design axial load nw should satisfy  equation (12.1) 
and, additionally, the following:  
nw < 0.3 (h - 1.2ex - 2ea) fcu                                                                                        (12.12)  
where , 
nw, h, ex and fcu are as in 12.5.3.11 ; and  
ea is the additional eccentricity due to deflections, which may be taken as le 2/2 500 where le is the 
effective  height of the wall.   
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 12.5.3.13  Maximum unit axial load for unbrac ed plain walls  
The maximum unit axial load at every section of an unbraced plain wall should satisfy the following two 
conditions:  
a) nw < 0.3 (h - 2ex1) fcu 
b) nw < 0.3 [h - 2(ex2 + ea)] fcu 
where , 
nw, h, ea, and fcu   are as in 12.5.3.11 and 12.5.3.12 ; 
ex1 is the resultant eccentricity calculated at top of wall ; and  
ex2 is the resultant eccentricity calculated at bottom of wall.  
12.5.3.14  Shear strength  
The design shear resistance of plain walls need not be checked if one of the following conditions is satisfied:  
a) the ho rizontal design shear force is less than one -quarter of the design vertical load; or  
b) the horizontal design shear force is less than that required to produce an average design  shear stress 
of 0.45 MPa over the whole wall cross -section.  
NOTE  For concrete of grades lower than grade 25 and for lightweight aggregate concrete, the figure of 0 .30 MPa 
should be used instead of 0 .45 MPa.  
12.5.3.15  Cracking of concrete  
Reinforcement may be needed in walls to control cracking due to flexure or thermal and hydration shrinkage. 
Wherever reinforcement is provided, the quantity should be:  
a) for reinforcement of grade 450: at least 0 .25 % of the concrete cross -sectional area; and  
b) for reinforcement of grade 250: at least 0 .30 % of the concrete cross -sectional area.  
12.5.3.16  Reinforcement in plai n walls for flexure  
If, at any level, a length of wall exceeding one -tenth of the total length is subjected to tensile stress resulting 
from in -plane eccentricity of the resultant force, vertical reinforcement may be necessary to distribute potential 
crack ing. Reinforcement need only be provided in the area of wall found to be in tension under design service 
loads. It should be arranged in two layers and should comply with the spacing rules given in the appropriate 
clause.  DRS 142: 2020  
181                ©RSB 2020  - All rights reserved  
 12.5.3.17  Reinforcement in plain walls to co unteract cracks resulting from shrinkage and  temperature  
12.5.3.17.1  Plain concrete walls that exceed 2 m in length and are cast in -situ, may have to be  reinforced to 
control cracking arising from shrinkage and temperature effects, including temperature ri ses caused by the 
heat of hydration released by the cement. Reinforcement for this purpose should be considered as follows:  
a) in an external plain wall directly exposed to the weather, reinforcement should be provided in both 
horizontal and vertical directio ns; it should consist of bars of small diameter, relatively closely spaced, 
with adequate cover near the exposed surface (see also 12.5.3.15 ); 
b) in an internal wall it may only be necessary to provide reinforcement in that part of the wall where 
junctions wi th floors and beams occur, in which case it should be equally dispersed between each 
face (see also 12.5.3.15 ). 
12.5.3.17.2  In general, it will not be necessary to provide reinforcement to counteract shrinkage and  
temperature effects in walls made of no -fines concrete.  
12.5.3.18  Reinforcement around openings in plain walls  
Nominal reinforcement should be considered.  
12.5.3.19  Deflection of plain concrete walls  
The deflection in a plain concrete wall will be within acceptable limits if the preceding provisions have been 
conforme d to and if, in the case of a cantilever shear wall, the total height of the wall does not exceed ten 
times its length.  
13 Fire resistance  
13.1 General  
13.1.1  When a structural concrete element is subjected to fire, it undergoes a gradual reduction in  strength 
and rigidity. For limit state design, therefore, there are three conditions to be considered:  
a) retention of structural strength;  
b) resistance to penetration of flames; and 
c) resistance to heat transmission.  
13.1.2  The first criterion is applicable to all structura l elements while the other two criteria are applicable to 
walls and floors, which perform a separating function.  
13.1.3  The requirements for fire resistance for various elements in a structure are either checked by  a 
standard test on a specimen or satisfie d by suitable choices based on the data given in this clause.   
©RSB 2020  - All rights reserved                  182 
 NOTE  Standard fire tests are not intended to give information on the use of an element after it has been subjected to 
fire. 
13.1.4  The following factors influence the fire resistance of concrete  structures (some of these factors 
cannot be taken into account quantitatively):  
a) the size and shape of the element;  
b) the type of concrete;  
c) the type of reinforcement or tendon;  
d) the protective concrete cover provided to reinforcement or tendons;  
e) the load supp orted;  
f) the conditions of restraint.  
13.1.5  Concretes made with siliceous aggregates have a tendency to spall when exposed to high  
temperatures but this tendency can be reduced by the incorporation of supplementary reinforcement in the 
concrete cover. Spal ling does not generally occur with either calcareous or lightweight aggregates. The 
insulation properties of concrete made from lightweight aggregates are superior to those of concrete made 
from siliceous and calcareous aggregates. Other measures that may be taken to prevent spalling from 
occurring are:  
a) a finish of plaster, vermiculite, etc., applied by hand or sprayed;  
b) the provision of a false ceiling as a fire barrier; and  
c) the use of sacrificial tensile steel.  
13.1.6  Concrete, prestressing tendons, and re inforcement show a reduction in strength at high  
temperatures. At about 400  °C, tendons are likely to lose about 50 % of their strength at ambient temperature 
and in the case of reinforcement, a similar reduction in strength occurs at about 550  °C. 
13.1.7  The fire resistance of structural elements is generally determined when the element is  supporting its 
service load, which is taken as the sum of all the nominal self -weight and imposed loads.  
13.1.8  Thermal restraint can be assumed to be provided by the su rrounding structure if no gaps or  
combustible materials exist between the structure and the ends of the floor or beam and if the  surrounding 
structure is capable of withstanding the thermal stresses induced by the heated floor or beam.  
13.1.9  Where plaster  or sprayed fibre is used as an applied finish to elements, it may be assumed that the 
thermal insulation provided is at least equivalent to the same thickness of concrete. Such finishes can 
therefore be used to remedy deficiencies in cover thickness. For selected materials, the following guidance 
can be given with respect to allowing the use of additional protection not exceeding 25 mm in thickness as a 
means of providing effective cover to steel reinforcing or prestressing elements.  DRS 142: 2020  
183                ©RSB 2020  - All rights reserved  
 13.2 Beams  
13.2.1  The fire resistance of a reinforced or prestressed concrete beam depends on the amount of  
protective cover, consisting of concrete with or without an insulating encasement, provided to the 
reinforcement or tendons. It is also necessary that the beam have a minimum width to avoid failure of the 
concrete before the reinforcement or tendons reach the critical temperature. For I -beams, the web thickness 
bw of a fully exposed beam should be at least 0 .5 of the minimum width for the fire resistance of various 
beams.  
13.2. 2 The average concrete cover is determined by summing the product of the cross -sectional area  of 
each bar or tendon and the distance from the surface of the bar to the nearest relevant exposed face, and 
dividing the sum by the total area of these bars or t endons. Only those bars or tendons provided for the 
purpose of resisting tension due to ultimate loads should be considered in this calculation. When 
reinforcement is used in combination with tendons, its total area should be used.  
13.2.3  In addition, in c ertain cases where siliceous aggregate concrete is used, it will be necessary to 
consider the provision of supplementary reinforcement to hold the concrete cover in position.  
13.3 Floors  
13.3.1  The fire resistance of a floor depends on the minimum thickness of the concrete section and  the 
average concrete cover to the reinforcement in the tensile zone.  
13.3.2  Non-combustible screeds or floor finishes may be taken into account in the estimation of the  
thickness of concrete.  
13.3.3  The average concrete cover is d etermined by summing the product of the cross -sectional area  of 
each bar or tendon and the distance from the surface of the bar to the nearest relevant exposed face, and 
dividing the sum by the total area of these bars or tendons. Only those bars or tendon s provided for the 
purpose of resisting tension due to ultimate loads should be considered in this calculation.  
13.3.4  In addition, in certain cases where siliceous aggregate concrete is used, it will be necessary to 
consider the provision of supplementary  reinforcement to hold the concrete cover in position.  
13.3.5  In the absence of adequate test data, low -density concrete floors should be treated as dense 
concrete floors even though the fire resistance of the former might be expected to be somewhat superi or. 
13.3.6  In the case of hollow slabs (or beams with filler blocks), the effective thickness d should be  obtained 
by considering the total solid material per unit width te as follows:  
 
where , 
h is the actual thickness of slab;  
ξ is the proportion of soli d material per unit width of slab; and   
©RSB 2020  - All rights reserved                  184 
 tf is the thickness of non -combustible finish.  
13.4 Additional protection to floors  
The fire resistance of any given form of floor construction may be improved by the provision of an insulating 
finish on the soffit or by a  suitable suspended ceiling.  
13.5 Columns  
13.5.1  The minimum dimension of a column is a determining factor in the fire resistance it can provide.  
13.5.2  Supplementary reinforcement shall consist of either a wire fabric not lighter than 0 .5 kg/m2 (2 mm 
diameter wires at centres not exceeding 100 mm) or a continuous arrangement of links at centres not 
exceeding 200  mm, incorporated in the concrete cover at a distance not exceeding 20 mm from the face.  
13.5.3  Columns that are built into fire -resistant walls to thei r full height are likely to be exposed to fire on one 
face only.  
13.6 Walls  
13.6.1  Concrete walls containing at least 1,0 % of vertical reinforcement  
13.6.1.1  Concrete cover to the reinforcement should be at least 15 mm for a fire resistance of up to 1 h, and 
at least  25 mm for a fire resistance for longer periods. Unless shown otherwise by a test, walls containing 
vertical reinforcement of less than 1 .0 % are regarded as plain concrete walls (see 13.6.2) for fire -resistance 
purposes.  
13.6.1.2  Walls exposed to fire on more than one face are to be regarded as columns (see 13.5).  
13.6.2  Plain concrete walls  
From the limited data available, the fire resistance of plain siliceous aggregate concrete walls can be taken as 
follows:  
a) Concrete, 150 mm thick: 1 h;  
b) Concrete, 175 mm thick:  1.5 h. DRS 142: 2020  
185                ©RSB 2020  - All rights reserved  
 ANNEX A  
(normative ) 
Properties of reinforcement suitable for use with this code of practice  
A.1 General  
A.1.1  Table A.1 gives the properties of reinforcement suitable for use with this code of practice. The 
properties are valid for temperatures betwee n -40 ºC and 100  ºC for the reinforcement in the finished 
structure.  
Table A.1 — Properties of reinforcement  
 
NOTE  The recommended value for the fatigue stress range with an upper limit of  β fyk and for the minimum relative 
rib area  are given in Table A.2  The recommended value is 0 .6. 
Table A.2  — Properties of reinforcement  
  
©RSB 2020  - All rights reserved                  186 
 A.1.2  The values of fyk, k and εuk in Table A.1 are characteristic values. The maximum % of test results 
falling be low the characteristic value is given for each of the characteristic values in the right hand column of 
Table A.1.  
A.1.3  In order to be deemed to comply with the long term quality levels in Table A.1, the following limits on 
test results should be applied:  
a) where all individual test results of a test unit exceed the characteristic value, (or ar e below the 
characteristic value in the case the maximum value of fyk or k) the test unit  may be assumed to 
comply;  
b) the individual values of yield strength f a nd ε should be greater than the minimum  values and less 
than the maximum values. In addition, the mean value, M, of a test uni t should satisfy the equation  
M ≥ Cv + a (A.3)  
where : 
Cv is the long term characteristic value  
a is a coefficient which depends on th e parameter considered  
NOTE 1 The recommended value for fyk is 10 MPa and for both k and εuk is 0. 
NOTE 2 The minimum and maximum values of fyk, k and εuk for use in a Country may be found in its The 
recommended values of fyk, k and εuk are given in Table A.3. 
Table A.3 — Absolute limits on test results  
Performance 
characteristics  Minimum value  Maximum value  
Yield strength fyk  0.97 xminimum Cv  1.03 xmaximum Cv  
k 0.98 xminimumCv  1.02 xmaximum Cv  
εuk 0.80 xminimum Cv  Not applicable  
 
A.2 Strength  
The maximum a ctual yield stress fy,max shall not exceed 1 .3fyk. DRS 142: 2020  
187                ©RSB 2020  - All rights reserved  
 Bibliography  
[1] Rwanda Building code  
[2] Rwanda Urban Planning Code  
[3] RS 186  (All parts ) Fire safety - code of practice  
[4] ISO 13822 , Bases for design of structures — Assessment of existing structures  
[5] ISO 23469:  2005 , Bases for Design of Structures — Seismic Actions for Designing Geotechnical 
Works  
[6] ISO 18408:  2019 , Simplified Structural Design for Reinforced Concrete Wall Buildings  
[7] ISO 28841:  2013 , Guidelines for Simplified Seismic Assessment And Rehabilitation of Conc rete 
Buildings  
[8] ISO 19338:  2014 , Performance and Assessment Requirements for Design Standards on Structural 
Concrete  
 DRS 142: 2020  
 
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