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IS:2950(PartI)-1981
CODE OF PRACTICE FOR DESIGN AND CONSTkUCTIdN OF RAFT FOUNDATIONS , _
PART I DESIGN -
f Second Revision)
Second Reprint MAY 1994 UDC.
624.153.61:624.0:69.001.3
@ Copvrighl 1982
MkhAK
9 BqHADUR NEW DELHI 110002
IS : 2950 ( P3rt I ) - 1981
CODE OF PRACTICE FOR DESIGN AND CONSTRUCTION OF RAFT FOUNDATIONS
PART I DESIGN
Second Revision I
Engineerhg Sectional Committee, BDC 43
Cen~oor~lding Research
PROF DINFX~ MOHAN
Institute ( CSIR 1,
Institute (
DR R. K. BHANDARI Cen&Rdor~~lding Research
CSIR 1,
SHRI DEVENDRASHARMA ( Alternate ) CHIEF ENGINEER Calcutta Port Trust, Calcutta SHRI S. GUI~A ( Alternate ) SHRI M. G. DANDAVA~ The Concrete Association of India, Bombay SHRI N. C. DUGGAL ( Alternate ) SHRI R. K. DAS GUPTA Simplex Concrete Piles ( India ) Pvt Ltd, Calcutta SI-IRIH. GUHA BISWAS ( Afternate ) SHRI A. G. DASTIDAR In personal capacity ( 5, Hungerford Road 121, SHRI V. C. DESHPANDE DIRECTOR ( CSMRS ) DEPUTY DIRECTOR ( CSMRS SHRI A. H. DIVANJI The Pressure Piling Co ( I ) Pvt Ltd. Bombay Central Water Commission, New Delhi and Construction Co Pvt Ltd,
Hungerford Street, Calcutta )
SHRI A. N. JANGLE ( Alternate ) SHRI A. GHOSHAL Stup Consultams Ltd, Bombay PROF GOPAL RANJAN University of Roorkee, Roorkee DR JAGDISHNARAIN Indian Geotecbnic Society, New Delhi PROP SWAMI SARAN ( Alternate )
) ( Alternate ) Asia Foundations Bombay
( Continued on page 2 ) @I Copyright 1982
BUREAU This publication reproduction is protected OF INDIAN STANDARDS of 1957 ) and under the Indian Copyright Act ( XIV
in whole or in part by any means except with written permission of tbe
publisher shall be deemed to be an infrigement of copyright under the said Act.
IS : 2950 ( Part I ) - 1981 ( Continued from page 1 )
Members Representing SHRIG. S. JAIN G. S. Jain & Associates, Roorkee SHRIASHOK KUMAR JAIN ( Alternate ) JOINTDIRECTOR D ) ( National Buildings Organisation, New Delhi SHRISUNILBURY( Alternate ) Ministry of Railways Jogs? RESEARCH SM ), ( JOINTDIRECTOR RESEARCH ( B & S ), RDSO ( Alternate ) Indian Institute of Technology, Bombay DR R. K. KATTI SHR~SR. KUtKARNl M. N. Dastur & Co Pvt Ltd, Calcutta SHRI S. ROY ( Afternate ) Public Works Department, Chandigarh SHRI0. P. MALHOTRA Central Warehousing Corporation, New Delhi SHRIA. P. MATHUR SHRIV. B. MATHUR Machenzies Limited, Bombay Engineers India Limited, New Delhi SHRIT. K. D. MUNSI SHRIM. IYENGAR Alternate ) ( BokwB,kFrzl Plant ( Steel Authority of India ), SHRIY. V. NARASIMHA RAO B~lo OMBIR SINGH Engi;z$n-&iefs Branch, Army Headquark=, Construction Company Limited,
LT-COL K. P. ANAND Alternate ) ( The gita;an SHRIB .K. PANTHAKY
SHRIV. M. MADGE Alternate ) ( Cemindia Co Ltd. Bomb&y SHRIM. R. PUNJA SHRIS. MUKHERJEE Alternate ) ( The Braithwaite Born & Jessop Construction Co SHRIN. B. V. RA~HVAN Ltd, Calcutta Vijayanagar Steel Plant ( SAI ), New Delhi SHRIA. A. RAJU Nagadi Consultants Pvt Ltd, New Delhi DR Vi V. S. RAO Cement Corporation of Indta, New Delhi SHRIARJUNRIJHSINGHANI SHRI0. S. SRIVASTAVA ( Alternate ) College of Engineering, Guindy DR A. SARGUNAN SHRIS. B~~MINATHANAlternate ) ( Public Works Department, Government of Andbra SHRI K. R. SAXENA Pradesh,.Hyderabad United Technical Consultants Pvt Ltd, New Delhi DR S. P. SHRIVASTAVA DR R. KAPUR( Alternate ) Gammon India Limited, Bombay SHRIT. N. SURBA RAO SHRIS. A. REDDI( Alternate ) Ministry of Shipping and Transport, New Delhi SHR~ SIVAGURU N. SHRID. V. SIKKA Alternate ) ( Central Public Works Department, New Delhi SUPERINTENDING G I N E E R E N ( DESIGNS ) EXECUTIVE ENGINEER DESIGNS V ( ) ( Alternate ) ( Continued on page 24)
IS : 2950 ( Part I ) - 1981
Second Revision)
0.1 This Indian Standard ( Part I ) was adopted by the Indian Standards Institution on 5 October 1981, after the draft finalized by the Foundation Engineering Sectional Committee had been approved by the Civil Engineering Division Council. 0.2 Raft foundation is a substructure supporting an arrangement of columns or walls in a row or rows and transmitting the loads to the soil by means of a continuous slab with or without depressions or openings. Such types of foundations are found useful where soil has low bearing capacity. This standard was first published in 1965 and revised in 1973. In this revision, besides making its contents up-to-date, guidelines have been given to choose particular type of methods in particular situations and giving reference to finite difference method which will be covered at a later stage. 0.3 For the purpose of deciding whether a particular requirement of this standard is complied with, the final value, observed or calculated, expressing the result of a test, shall be rounded off in accordance with IS : 2-1960*. The number of significant places retained ,in the rounded off value should be same as that of the specified value in this standard. 1. SCOPE 1.1 This standard ( Part I ) covers the design of raft foundation based on conventional method ( for rigid foundation ) and simplified methods (flexible foundation ) for residential and industrial buildings, store-houses, silos, storage tanks, etc, which have mainly vertical and evenly distributed loads. *Rules for rounding off numerical values ( revised ). 3
IS : 2950 ( Part I ) - 1981 2. TERMINOLOGY 2.1 For the purpose of this standard, IS : 2809-1972* shall apply.
of terms given in
3. NECESSARY INFORMATION
3.1 For satisfactory design and construction following information is necessary:
of a raft foundation,
Site Plan - Site plan showing the location of the proposed as well as neighbouring structure.
Building plan and vertical cross-sections levels, ducts and openings, etc, layout columns, shear walls, etc. design combination
showing different floor of load bearing walls,
d Loading conditions preferably shown on a schematic plan indicating
of loads transmitted to the foundation.
Environmental Factors - Information relating to geologic history of the area, seismicity of the region, hydrological information indicating ground water conditions and its seasonal variations, climatic factors like vulnerability of the site to sudden flooding by surface run-off, erosion, etc. Geotechnical Information - Giving subsurface profile with stratification details ( see IS : 1892-1979t ), engineering properties of the
founding strata, namely, index properties, effective shear parameters determined under appropriate drainage conditions, compressibility characteristics, swelling properties, results of field tests like static and dynamic penetration tests, pressure meter tests, etc.
Modulus of Elasticity and Modulus of Subgrade Reaction - Appendix A enumerates the methods of determination of modulus of elasticity ( E, ) and Poissons ratio ( k ). The modulus of subgrade reaction ( k ) may be determined in accordance with Appendix B.
g) Limiting values of the angular distortion and differential settlement,
the superstructure can withstand ( see IS : 1904-1978$ ).
A review of the performance locality.
of a similar structure, if any, in the
*Glossary of tempt and symbols relating to soil engineering(first revision ). tCode of practice for subsurfaceinvestigationsfor foundations (first revision ). ICode of practice for structural safety of buildings : Shallowfoundations ( second
revision ).
necessary to assess the possible effects of the new structure on the existing structures in the neighbourhood. the less the for
k) Proximity of mines or major storage reservoirs to the site.
3.2 Parameters for the Analysis - These are obtained by averaging parameters ( see 3.1 ) which can be determined only for relatively number of points of the foundation soil. The accuracy with which average values represent the actual conditions is of decisive importance the final results. 4. DESIGN CONSIDERATIONS
4.1 Choice of Raft Type 4.1.1 For fairly small and uniform column spacing and when the supporting soil is not too compressible, a flat concrete slab having uniform thickness throughout ( a true mat ) is most suitable ( see Fig. 1A ). 4.1.2 The slab may be thickened under heavily loaded columns to provide adequate strength for shear and negative moment. Pedestals may also be provided in such cases ( see Fig. 1B ). 4.1.3 A slab and beam type of raft is likely to be more economical for large column spacing and unequal column loads, particularly when the supporting soil is very compressible ( see Fig. 1C ). 4.1.4 For very heavy structures, provision of cellular raft or rigid frames consisting of slabs and basement walls may be considered. 4.2 Allowable Bearing Pressure - The allowable bearing pressure shall be determined in accordance with IS : 6403-1981*. 4.2.1 In granular soils, the ultimate bearing capacity of rafts is generally very large. However, for rafts placed at considerable depth ( for example basement rafts ), the possibility of punching mode of failure should be investigated. The influence of soil compressibility and related scale effects should also be assessed. 4.2.2 For rafts on cohesive soils stability against deep seated failures shall be analysed. 4.2.3 In cohesive soils, the effect of long term settlement due to consideration shall be taken into consideration. 4.3 Depth of Foundation less than 1 m. The depth of foundation shall generally be not
*Code of practice for determination of bearing capacity of shallow foundation (first revision ).
IS :295O(PartI)-1981
1A Fiat Plate
1B Flat Plate Thickened Under Columns
SECUON CC
1C Two-Way Beam and Slab ID
Flat Plate with Pedestals
TYPES RAFT FOUNDATIONS OF FIG. 1 COMMON
IS:29!5o(PartI)-1981 4.4 Sub-soil Water Pressure considered in the design. The uplift due to the sub-soil water shall be
4.4.1 All construction below the ground water level shall be checked for flotation. 4.5 General 4.5.1 Dimensional Parameters - The size and shape of the foundation adopted affect the magnitude of subgrade modulus and long term deformation of the supporting soil and this, in turn, influence the distribution of contact pressure. This aspect shall be taken into consideration in the analysis. 4.5.2 Eccentricity of the building and portion it coinciding resultant force. In pressure distribution
of Loading -
A raft generally occupies the entire area often it is not feasible and rather uneconomical to prothe centroid of the raft with the line of action of the such cases, the effect of the eccentricity on contact shall be taken into consideration.
4.5.3 Properties of the Supporting Soil - Distribution of contact pressure underneath a raft is affected by the physical characteristics of the soil supporting it. Considerations must be given to the increased contact pressure developed along the edges of the foundation on cohesive soils and the opposite effect on granular soils. Long term consolidation of deep soil layers shall be taken into account in the analysis. This may necessitate evaluation of contact pressure distribution both immediately after construction and after completion of the consolidation process. The design must be based on the worst conditions. 4.5.4 Rigidity of the Foundation - Rigidity of the foundation tends to iron out uneven deformations and thereby modifies the contact pressure High order of rigidity is characterized by large moments and distribution. relatively small, uniform settlements. A rigid foundation may also generate high secondary stresses in gtructural members. The effects of rigidity shall be taken into account in the analysis. 4.5.5 Rigidity of the Superstructure - Free response of the foundations to soil deformation is restricted by the rigidity of the superstructure. In the extreme case, a stiff structure may force a flexible foundation to behave as rigid. This aspect shall be considered to evaluate the validity of the contact pressure distribution. 4.6 Heavy Vibratory Loads - Foundations loads should preferably be isolated.
subjected to heavy vibratory
IS : 2950 ( Part I ) - 1981 4.7 Expansion Joints -
In case the structure supported by the raft consists of several parts with varying heights and loads, it is advisable to provide expansion joints between these parts. Joints may also be provided wherever there is a change in the direction of the raft.
5. METHODS OF ANALYSIS
5.0 The essential task in the analysis of a raft foundation is the determination of the distribution of contact pressure underneath the raft which is a complex function of the rigidity of the superstructure, raft itself and the supporting soil, and cannot except in very simple cases, be determined with exactitude. This necessitates a number of simplifying assumptions to make the problem amenable to analysis. Once the distribution of contact pressure is determined, design bending moments and shears can be computed based on statics. The following methods of analysis are suggested which are distinguished by the assumptions involved. Choice of a particular method should be governed by the validity of the assumptions in the particular case. 5.1 Rigid Foundation ( Conventional Method ) - This is based on the assumptions of linear distribution of contact pressure. The basic assumptions of this method are: a) The foundation is rigid relative to the supporting soil and the compressible soil layer is relatively shallow. b) The contact pressure variation is assumed as planar, such that the centroid of the contact pressure coincides with the line of action of the resultant force of all loads acting on the foundation. 5.1.S This method may be used when either of the following conditions is satisfied: a) The structure behaves as rigid ( due to the combined action of the superstructure and the foundation ) with a relative stiffness factor K > 0.5 ( for evaluation of K, see Appendix C ). b) The column spacing is less than 1*75/X( see Appendix C ). 5.1.2 The raft is analysed as a whole in each of the two perpendicular directions. The contact pressure distribution is determined by the procedure outlined in Appendix D. Further analysis is also based on statics. 5.1.3 In cases of uniform conditions when the variations in adjacent column loads and column spacings do not exceed 20 percent of the higher value. the raft may be divided into perpendicular strips of widths equal to the distance between midspans and each strip may be analysed as an independent beam with known column loads and known contact pressures.
IS : 2950 ( Part I ) - 1981 Such beams will not normally satisfy statics due to shear transfer between adjacent strips and the design may be based on suitable moment coefficients, or on moment distribution.
Nore - On soft soils, for example, normally consolidated clays, peat, muck, organic silts, etc. the assumptions involved in the conventional method are commonly justilied.
5.2 Flexible Foundation 53.1 Simplijed Method - In this method. it is assumed that the subgrade consists of an infinite array of individual elastic springs each of which is not affected by others. The spring constant is equal. to the modulus of subgrade reaction ( k ). The contact pressure at any point under the raft is, therefore, linearly proportional to the settlement at the point. This method may be used when the following conditions are satisfied (see Appendix E ): The structure ( combined action of superstructure and raft ) may be considered as flexible ( relative stiffness factor K > 03, see Appendix C ). Variation in adjacent column load does not exceed 20 percent of the higher value. 5.2.1.1 General method - For the general case of a flexible foundation not satisfying the requirements of 5.2.1, the method based on closed form solution of elastic plate theory may be used. This method is based on the theory of plates on winkler foundation which takes into account the restraint on deflection of a point provided by continuity of the foundation in The distribution of deflection and contact pressure orthogonal foundation. on the raft due to a column load is determined by the plate theory. Since the effect of a column load on an elastic foundation is damped out rapidly, it is possible to determine the total effect at a point of all column loads within the zone of influence by the method of super imposition. The computation of the effect at any point may be restricted to columns of two adjoining bays in all directions. The procedure is outlined in Appendix F.
Nom - One of the recent general methods based on the above mentioned theory is numerical analysis by either finite difference method or finite element method. This method is used for accurate analysis of the raft foundation. The details of this method could be covered at a later stage.
6.1 The general design for loads, shrinkage, creep and temperature effects and provision of reinforcement and detailing shall conform ot IS : 4561978*, the foundation being considered as an inverted beam or slab. *Code of practice for plain and reinforced concrete ( r&f rev&ion).
IIS: 2950 ( Part I ) - 1981
APPENDIX [ CZause 3.1( f) ]
DETERMINATION OF MODULUS OF ELASTICITY AND POISSONS RATIO ( p ) A-l. DETERMJNATION OF MODULUS OF ELASTICITY
(E, )
A-l.1 The modulus of elasticity is a function of the composition of the soil, its void ratio, stress history and loading rate. In granular soils it is a func-
tion of the depth of the strata, while in cohesive soils it is markedly influenced by the moisture content. Due to its great sensitivity to sampling disturbance accurate evaluation of the modulus in the laboratory is extremely dimcult. For general cases, therefore, determination of the modulus may be based on field tests ( A-2 ). Where a properly equipped laboratory and sampling facility are available, Es may be determined in the laboratory ( see A-3 ). A-2. FIELD DETERMINATION A-2.1 The value of Es shall be determined from plate loan test given in TS : 1888-1982.
where intensity of contact pressure, least lateral dimension of test plate, settlement, P== Poissons ratio, I, = Influence factor, and = 0.82 for a square plate. 4= B= S=
A-2,1.1 The average value of E, shall be based on a number of plate load tests carried out over the area, the number and location of the tests, depending upon the extent and importance of the structure.
A-2.1.2 Eflect of Size - In granular soils, the value of Es corresponding to the size of the raft shall be determined as follows:
*Method of load test on soils ( second revision ).
IS : 2950 ( Part I) - 1981 where Bj,BP represent sizes of foundation modulus determined by the plate load test. and plate and E, is the
A-2.2 For stratified deposits or deposits with lenses of different materials, results of plate load test will be unreliable and static cone penetration tests may be carried out to determine I&. A-2.2.1 Static cone penetration tests shall be carried out in accordance with IS :4968(Part III )-1976. Several tests shall be carried out at regular depth intervals up to a depth equal to the width of the raft and the results plotted to obtain an average value of E,. A-2.2.2 The value of Es may be determined ship: from the following relation-
E, = 2 Cra
where Cud = cone resistance in kgf/cm2. A-3. LABORATORY DETERMINATION OF Es
A-3.1 The value of Esshall be determined by conducting triaxial test in the laboratory [ see IS : 2720 ( Part XI )-19717 and IS : 2720 ( Part XII )-1981x ] on samples collected with least disturbances. A-3.2 In the first phase of the triaxial test, the specimen shall be allowed to consolidate fully under an all-round confining pressure equal to the vertical effective overburden stress for the specimen in the field. In the second phase, after equilibrium has been reached, further drainage shall be prevented and the deviator stress shall be increased from zero value to the magnitude estimated for the field loading condition. The deviator stress shall then be reduced to zero and the cycle of loading shall be repeated. A-3.3 The value of & shall be taken as the tangent modulus at the stress level equal to one-half the maximum deviator stress applied during the second cycle of loading.
*Method for subsurface sounding for soils : Part III Static cone penetration test (firsi revision ). tMethods of test for soils : Part XI Determination of shear strength parameters of a specimen tested in unconsolidated undrained triaxial compression without the measurement of pore water pressme. 2Methods of test for soils : Part XII Determination of shear strength parameters .of soils from consolidated undrained triaxial compression test with measurement of pore water pressure (first revision ).
[Clause 3.1(f)]
DETERMINATION OF MODULUS B-l. GENERAL B-l.1 The modulus of subgrade reaction ( k ) as applicable to the case of load through a plate of size 30 Y 30 cm or beams 30 cm wide on the soil is given in Table 1 for cohesionless soils and in Table 2 for cohesive soils. Unless more specific determination of k is done ( see B-2 and B-3 ), these values may be used for design of raft foundation in cases where the depth of the soil affected by the width of the footing may be considered isotropic and the extrapolation of plate load test results is valid.
TABLE 1 MODULUS OF SUBCRADE REACTION ( k ) FOR COHRSIONL.ESS SOILS
SOIL CHARACTERISTIC *MODULUS OF SULIGRADE REACTION ( k ) IN kg/cm3
OF SUBGRADE REACTION
c_--_--_------_~ Relative Density (1) Loose Medium Dense
Standard Penetration Test Value ( N) (2) < 10 10 to 30 30 and Over
r--------For Dgap, (3)
*-_--_-_ For $ttzerged (4) 0.9 0.9 to 29 29 to lo.8
1.5 1.5 to 47 4.7 to 18.0
*The above values apply to a square plate 30 x 30 cm or beams 30 cm wide.
TABLE 2 MODULUS
OF SUBCRADE REACTION ( k ) FOR COHESIVE SOILS
*MODULUS OF SU~GRADB RENTION ( k,) IN kg/cm
#--_---,--Consistency (1)
-----7 Unconfined Compressive Strength, kg/cm* (2)
(3) 2.7 2-7 to 5.4 5.4 to 108 are based on the ultimate bearing
Stifi 1 to 2 Very stiff 2 to 4 Hard 4 and over *The values apply to a square plate 30 x 30 cm. The above values assumption that the average loading intensity does not exceed half the capacity.
IS:2950( B-2. FIELD DETERMINATION
PartI)-
B-2.1 In cases where the depth of the soil affected by the width of the footing may be considered as isotropic, thevalue of k may be determined in accordance with IS : 9214-1979*. The test shall be carried out with a plate of size not less than 30 cm.
B-2.2 The average value of k shall be based on a number of plate load tests carried out over the area, the number and location of the tests depending upon the extent and importance of the structure. B-3. LABORATORY DETERMINATION
B-3.1 For stratified deposits or deposits with lenses of different materials, evaluation of k from plate load test will be unrealistic and its determination shall be based on laboratory tests [ see IS : 2720 ( Part XI )-1971t and IS : 2720 ( Part Xl1 )-1981$]. B-3.2 In carrying out the test, the continuing cell pressure may be so selected as to be representative of the depth of average stress influence zone (about 0.5 B to B ). B-3.3 The value of k shall be determined from the following relationship:
where E, = Modulus of elasticity of soil ( see Appendix A ), fi= p I Youngs modulus of foundatipn material, = Poissons ratio of soil ( see Appendix A ), and = Moment of inertia of structure foundation. if determined or of the
B-3.4 Im the absence of laboratory test data, appropriate values of E, and p may be determined in accordance with Appendix A and used in B-3.2 for evaluation of k.
*Method of determination of subgrade reaction ( k value ) of soils in the field. tMethods of test for soils : Part XI Determination of shear strength parameters of specimen tested in unconsolidated undrained triaxial compression without the measurement of pore water pressure. tMethods of test for soils : Part XII Determination of shear strength parameters of soil from consolidated undrained triaxial cdrnpression test with measurement of pore water pressure (first revision ).
IS:29SO(PartI)-1981 B-4. CALCULATIONS B-4.1 When the structure is rigid ( see Appendix C ), the average moduhrs of subgrade reaction may also be determined as follows: k, =: Average contact pressure Average settlement of the raft
APPENDIX C ( Clauses 5.1.1, 52.1 and B-4.1 )
RIGIDiTY OF SUPERSTRUCTURE AND FOUNDATION C-l. DETERMINATION OF THE RIGIDITY OF THE STRUCTURE
C-l.1 The flexural rigidity EI of the structure of any section may be estimated according to the relation given below ( see also Fig. 2): EI = where EL = modulus of elasticity material ) in kg/cma, Ii b H= = length or breadth bending, of the infilling material ( wall
= moment of inertia of the infilling in cm4, of the structure in the direction of
total height of the intiling in cm,
Es = modulus of elasticity of frame material in kg/cmg, IO = moment of inertia of the beam in cm, Zt4 = I& = I* K h
I,, =
Ib -9
= spacing of the columns in cm,
length of the upper column in cm, If -_( I moment of inertia of the lower column in cm4, and moment of inertia of the foundation beam or raft in cm.
h, = length of the lower column in cm,
II I/
= moment of inertia of the upper column in cm,
NOTE The summation is to be done over all the storeys, including the foundation beam of raft. In the case of the foundation, Ifreplaces Ia and Ir becomes zero, whereas for the topmost beam; I becomes zero.
1 FOUNDATION RAFT FIG. 2
ATION DETERMIN OF RIGIDITY OF A &RUCTURE
C-2. RELATIVE STIFFNESS FACTOR K C-2.1 Whether a structure behaves as rigid or flexible depends on the relative stiffness of the structure and the foundation soil. This relation is expressed IS
IS : 2950( Part I ) - 1981 by the relative stiffness factor K given below: a) For the whole structure K = EE&
b) For rectangular rafts or beams K =
c) For circular rafts K = i2~~
where EZ = flexural rigidity of the structure over the length ( a ) in Wm2, Es = modulus of compressibility of the foundation soil in kg/cm, b I length of the section in the bending axis in cm, a d R= = length perpendicular to the section under investigation in cm, = thickness of the raft or beam in cm, and radius of the raft in cm. 0.5, the foundation OF CRITICAL may be considered SPACING as rigid
C-2.1.1 For K > ( see 5.2.1).
C-3. DETERMINATION
C-3.1 Evaluation of the characteristics h is made as follows: h-4 -where k = modulus of subgrade reaction in kg/cm* for width B in cm ( see Appendix B ). B = width of raft in cm EC = modulus of elasticity of concrete in kgf/cms Z = moment of inertia of the raft in cm* footing of kB J- 4E,Z
APPENDIX ( Clause 5.1.2 )
CALCULATION OF PRESSURE DISTRIBUTION BY CONVENTIONAL METHOD D-l. DETERMINATION OF PRESSURE DISTRIBUTION
D-l.1 The pressure distribution
( q ) under the raft shall be determined by
4= +i
Qe;
IYrtI,X e
Q = total vertical load on the raft,
A- = total area of the raft,
ek, ei, ZL, Z; = eccentricities and moments of inertia about the principal axes through the centroid of the section, and x, y = co-ordinates of any given point on the raft- with respect to the x and y axes passing through the centroid of the area of the raft. Zi, $, ei, e; may be calculated from the following equations:
z; =I,z; = Iv ei = ee -
T--,
7 i?
ev, and
e;=ev where
zy em zv
I,, Zv = moment of inertia of the area of the raft respectively about the x and y axes through the centroid, 17
IS : 2950 ( Part I ) - 1981 I,, = J xydA for the whole area about x and y axes through the centroid, and ee, o,, = eccentricities in the x and y, directions centroid. For a rectangular raft the equation simplifies to: of the load from the
where LIand b :.=-: dimensions of the raft in the x and y directions the respectively.
NOTE - If one or more of the values of ( q ) are negative, as calculated formula, it indicates that the whole area of foundation is not subject to only a part of the area is in contact with the soil, and the above formula good, provided appropriate values of L,. I,. I,., e z and ey are used with area in contact with the soil instead of the whole area. by the above pressure and will still hold respect to the
APPENDIX ( Clause 5.2.1 )
CONTACT PRESSURE DISTRIBUTION AND MOMENTS BELOW FLEXIBLE FOUNDATION E-l. CONTACT PRESSURE DISTRIBUTION
E-l.1 The distribution of contact pressure is assumed to be linear with maximum value attained under the columns and minimum at mid span. El.2 The contact pressure for the full width of the strip under an interior column load located at point i (pi ) can be determined as ( see Fig. 3B ):
pi = 7 , 48_Mi I?
where I = average length of adjacent span ( m ), Pi = column load at poiflt i ( t ), and Md = moment under an interior columns located at i. 18
IS : 2950 ( Part I ) - 1981 E-l.3 The minimum contact pressure for the full width of the strip at the middle of the adjacent spans p,,,~ and pmr can be determined as ( see Fig. 3A ):
PmZ =
ZPi~--ppt7;
pmr = 2Pi -k - pi;
hi pm = Pmr f
2 where I,, 16as shown in Fig. 3A. El.4 If E-2.3( a) governs the moment under the exterior columns, contact pressures under the exterior columns and at end of the strip pd and pe can be determined as ( &see Fig. 3C ):
4P* + ps = po = -C-a- -
6M. -
3M. PC 2
Ps, pm, M,, II, C as shown in Fig. 3C. where E-l.5 If E-2.3 ( b ) governs the moment under the exterior columns, the contact pressures ps and pe are determined as ( see Fig. 3C ): pc = pc =
L!!&?$
E-2. BENDING MOMENT DIAGRAM E-2.1 The bending moment under an interior Fig. 3A ) can be determined as: M<=-g ( 0.24ti + 016 )
at i ( see
E-2.2 The bending moment at midspan is obtained as ( see Fig. 3B ): M, = Mo + MI where M,, = moment of simply supported beam
I, pr( I ), pd( r ), jrn are as shown in Fig. 3B. 19
3A Moment and Pressure Distribution
at interior Column
3B Pressure Distribution
Over an Interior Span
3C. Moment and Pressure Distribution FIG.
at Exterior Column
MOMENT AND PRESSURE DISTRIBUTION COLUMNS AT 20
IS : 2950 ( Part I ) - 1981 E-2.3 The bending moment M, under exterior columns can be determined as the least of ( see Fig. 3C ): a)
..I+ ( 013h6 + 1.06 AC - 0.50 ) ( 4P* _. ~_ 4c_+
p& __ 2 r, ) C
APPENDIX ( czuuse 5.2.1 .l )
FLEXIBLE FOUNDATION -
F-l. CLOSED FORM SOLUTION OF ELASTIC PLATE THEORY F-l.1 For a flexible raft foundation with nonuniform column spacing and load intensity, solution of the differential equation governing the behaviour of plates on elastic foundation ( Winkler Type ) gives radial moment ( M, ) tangential moment ( Mt ) and deflection ( w ) at any point by the following expressions:
PL= w=40za
where P = column load; r = distance of the point under investigation load along radius; 21 from column
IS : 2950 ( Part I ) - 1981 L = radius of effective stiffness; 4 D k J k = modulus of subgrade reaction for footing of width B;
D = flexural rigidity of the foundation; Et2
12 ( 1 - Pa ) t = raft thickness;
E = modulus of elasticity of the foundation
p = poissons ratio of foundation
Z,, Z;, Z, = functions of shear, moment and deflection ( see Fig. 4 ). F-l.2 The radial and tangential moments can be converted to rectangular co-ordinates:
M, _= M, co.9 4 -I- Mt sina 4 Mv = M, sin8 4 + Mt cos2 4
where 4 = is the angle with x axis to the line joining origin to the point under consideration.
F-l.3 The shear Q per unit width of raft can be determined by:
&z;(+)
where 2; = function for shear ( see Fig. 4 ). F-l.4 when edge of the raft is located within the radius of influence, the followmg corrections are to be applied. Calculate moments and shears perpendicular to the edge of the raft within the radius of influence, assuming the raft to be infinitely large. Then apply opposite and equal moments and shears on the edge of the mat. The method for beams on elastic foundation may be used.
F-1.5 Finally all moments and shears calculated for each individual column and walls are superimposed to obtain the total moment and shear values. 22
IS : 29Jo ( Part I ) - 1981
3 r/L
4 FUNCTIONS FORSHEARMOMENTAND
( Continued from page 2 )
SHRI M. D. TAMBEKAR DR A. VARADARAJAN DR R. KANLRAJ Alternate ) ( SHRI G. RAMAN, Indian
Bombay Port Trust, Bombay
Director General, BfS ( Ex-officio Member )
SHRIK. M. MATHUR
Director ( Civ Engg )
Deputy Director ( Civ Engg ). BIS
Bearing Capacity of Foundation
Convener SHRI S. GUHA
BDC 43
Calcutta Port Trust, Calcutta
STANDARDS Researc~rcsigns & Standards
DEPUTY DIRE~OR EXECWWE ENGINEER DESIGN) V ( SHRIT. N. MUKHERJEE
( B & S ), CB-II
SHRI AMAR S~NGH ( Alfernate ) Engineering Research Laboratories, Hyderabad SHRI K. R. SAXENA Cement Corporation of India, New Delhi SHRI 0. S. SRIVASTAVA SHRIS. K. CHAPERJEE( Alternate )
SHRI B. G. RAO
Central Public Works Department, New Delhi Martin & Bums Co Ltd, Calcutta Central Building Research Institute, Roorkee
DR SWAMISARAN
University of Roorkee, Roorkee
Headquarters Telephones Regional Central
Manak Bhavan, 9 Bahadur Shah Zafar Marg. NEW DELHI 110002
: 331 01 31
: Manaksanstha
331 13 75 Offices :
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DECEMIIER
CODE OF PRACTICE FOR 2950. ( Part 1) - 1981 DESIGN AND CONS11~UCIION 01: RAF1 FOUNDATIONS
PART 1 DESIGN
( Second
[ Puge 4, cfawe 3.1(g) ] 1978f. ( Page 4, foot.note
for the existing foot-note: And
tC0do ol prnclico
IS : 1904.
IS : 1904-1987SJofor
with $ mark ) -- Substitute
corvtrrlction of ~~~r~ntlnlions
roqrtirornancn [ Past
for dcnign ( fhird rruision ), 9, clause
in soila: (Zcnctnl < 0.5 fir
5.2.1 (a),
2 ] -
.rr4 !J.l.l.fir
_ffc
> 0.5. ( Iaga 16, clause C-2.1.1 ) ) Suhatitutc
5.2.1. the existing
( Puge 19, clause E-l.4 matter: j,O m MO: ( Page ap _+_ _
_!$ j Substitute the
19, clause E-2.2
rollowing
~rPcw+mn+P~(~)l
, clause E2.3
(b) J -
matter: _ (4 Pa - flm II ) --. - C* -4c + 11 2 Substitute (<\fir fs in v&e
Sllba~itlltc
( Page 21, clause F-l.1 ) ( Pqa
22, clarlse F-1.1, f,fIS of lnst line J -
( Page 2% &use
<,&r
appcarirlg
( BDC
Kcprogmphy
Urtit, New BIS,
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