1 1 uo

Reference publications

NBSIR 86-338

JOawocL J.cJta,

741

Punching Shear Resistance of

Lightweight Concrete Offshore

Structures for the Arctic:

Literature Review

David I. McLean

H. S. Lew

Long T. Phan

Mary Sansalone

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Building Technology

Gaithersburg, MD 20899

May 1986

Sponsored by:

Technology Assessment and Research Branch

Mineral Management Service

Department of the Interior

100 ton, Virginia 22091

• U56

86-3388

1986

JUX/>Z/

'w X-2677}

R3S

RESEARCH

INFORMATION CENTER NBSIR 86-3388

PUNCHING SHEAR RESISTANCE OF

LIGHTWEIGHT CONCRETE OFFSHORE

STRUCTURES FOR THE ARCTIC:

LITERATURE REVIEW

David I. McLean

H. S. Lew

Long T. Phan

Mary Sansalone

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Building Technology

Gaithersburg, MD 20899

May 1986

Sponsored by:

Technology Assessment and Research Branch

Mineral Management Service

U.S. Department of the Interior

Reston, Virginia 22091

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
;|vV

.

v- Gv-..'
ABSTRACT

The punching shear resistance of lightweight concrete offshore

structures for the Arctic is being investigated at the National

Bureau of Standards on the behalf of The Minerals Management

Service of the U.S. Department of the Interior in cooperation

with five American oil companies. This report serves as an

introduction to the project and reviews current knowledge on

material relevant to the punching shear behavior of concrete

offshore structures subjected to Arctic ice loads. A brief

review of available information on Arctic ice loads and a discussion of some of the proposed offshore structural concepts

are presented. The general mechanics of punching shear failures

and the factors affecting punching resistance are discussed along

with a comparison of current U.S. and European code provisions on

punching shear. Available literature on experimental and

analytical investigations on punching shear relevant to this

project is also reviewed.

Keywords: Arctic environment; lightweight concrete; literature

review; offshore structure; punching shear; reinforced concrete.

i

11
.

'
PREFACE

In 1984, under the sponsorship of the Minerals Management

Service, Department of the Interior, the National Bureau of

Standards (NBS) initiated a study of the punching shear behavior

of lightweight concrete offshore structures. This project was

conceived following the 1983 International Workshop on the

Performance of Offshore Concrete Structures in the Arctic

Environment, which identified the behavior of lightweight

concrete elements subjected to high local ice forces as a major

research area.

The authors of this report gratefully acknowledge the support,

encouragement, and cooperation provided by Mr. Charles E. Smith

of the Minerals Management Service and the significant technical

contributions made to this project by Professor Richard N. White

of Cornell University.

Any opinions, findings, and conclusions or recommendations

expressed in this report are those of the authors and do not

necessarily reflect the views of the Minerals Management Service,

Department of the Interior.

iii
TABLE OF CONTENTS

ABSTRACT

PREFACE

LIST OF TABLES

LIST OF FIGURES

1.0 INTRODUCTION

1.1 Background

1.2 Purpose and Scope of Research

1.3 Purpose of This Report ....

2.0 ICE LOADS ON ARCTIC STRUCTURES

2.1 Introduction

2.2 Nature of Arctic Ice ... 2.3 Predicting Ice Forces

2.4 Design Values of Ice Loads

3.0 CONCRETE OFFSHORE STRUCTURES FOR THE ARCTIC

3.1 Introduction

3.2 Structure Classification

3.2.1 Island Structures

3.2.2 Gravity Structures

3.2.3 Floating Structures

3.3 Review of Proposed Designs

4.0 PUNCHING SHEAR BEHAVIOR OF CONCRETE SLABS

AND SHELLS

4.1 Introduction

4.2 Comparison of Beam and Punching Shear

4.3 Mechanism of Punching Shear

4.4 Factors Affecting Punching Shear Strength

4.5 Predicting Punching Shear Resistance

Ease

11

iii

vi

vii

1

1

3

4

5

5

5

Oo 12

15

15

15

15

15

10

18

24

24

25

27

29

40

IV
TABLE OF CONTENTS (continued)

Page

4.6 Code Provisions on Punching Shear Strength .... 42

4.6.1 ACI 318-83 43

4.6.2 CEB-FIP 44

4.6.3 CP110 46

4.6.4 Comparison of the Codes 47

4.6.5 Limitations of Code Provisions on

Punching Shear Strength 48

5.0 RECENT RESEARCH IN PUNCHING SHEAR 51

5.1 Punching Shear in Thick Slabs 51

5.2 Punching Shear in Nuclear Reactor Structures .. 53

5.2.1 Reactor Vessel End Slabs Under Pressure

Loading 54

5.2.2 Impact Loading on Nuclear Reactor

Containment Structures 57

5.3 Fiber Reinforced Concrete Subjected to

Punching and Impact Loads 59

5.4 Punching Shear in Offshore Structures 61

5.4.1 BWA Punching Shear Study 62

5.4.2 Punching Shear in Prestressed Cylindrical

Shells: Norwegian Work 71

5.4.3 Other Punching Shear Studies on Offshore

Structures 73

5.5 Finite Element Predictions of Punching

Shear Strength 75

6.0 SUMMARY 82

7.0 REFERENCES 84

v
LIST OF TABLES

Trip le Page

1 Comparison of effective ice pressures for

vertical piles and piers 100

2 Expressions for ultimate shear strength 101

3 Summary of code provisions on punching

shear 103

vi
LIST OF FIGURES

Figure Eaag.

1 Possible ice failure modes 104

2 Local ice pressure design curves 105

3 Example configurations of Arctic offshore

structures 106

4 SOHIO Arctic Mobile Structure (SAMS) 107

5 Brian Watt Associates Caisson System

(BWACS) 108

6 Artist's sketch of the Arctic Cone

Exploration Structure (ACES) 109

7 Typical details of initial constuction

(ACES) 110

8 Concrete Island Drilling System: Super

Series (Super CIDS) Ill

9 Super CIDS brick dimensions and details 112

10 Tarsiut Island, general arrangement 113

11 Structural arrangement for concrete ice

wall 113

12 Shear transfer mechanisms in a cracked

beam 113

13 Crack formation in the column area of a slab 114

14 Arching action in slabs 114

15 Typical curves for an under reinforced

slab 115

16 Punch load vs. flexural reinforcement for

the simple and restrained slabs tested by

Taylor and Hayes 116

17 Shear test data vs. Eg. 11-37 of ACI 318-83

for two-way prestressed slabs 116

18 Idealized connection model of Kinnunen and

Nylander 117

vii
LIST OF FIGURES (continued)

Fjgy.££ Page

19 Punching test results compared with code

predictions 118

20 Comparison of punching shear provisions for

selected parameters: ACI vs. CEB-FIP 119

21 Comparison of punching shear provisions for

selected parameters: ACI vs. CP110 120

22 Different types of cracks observed in

pressure vessels 121

23 Shear-flexure interaction curve 122

24 General characteristics of a typical test

panel used in the BWA study 123

25 BWA punching shear study loading system 124

26 Effect of shear reinforcement quantity on

ultimate shear resistance in BWA study 125

27 Test results of BWA study compared with

"conventional slab methods" 126

28 Test results of BWA study compared with

"conventional slab method" (CP110) 127

29 Comparison of tested vs. calculated ultimate

shear resistance, Vu ("ACI modified punching

shear method") from BV7A study 128

30 Geometry and dimensions for shell specimens

of Reference 149 129

31 Results of punching tests of Reference 152 . . 130

32 Finite element predictions of punching shear

strength: load vs. deflection curves 131

viii
1.0 INTRODUCTION

1 . 1 BACKGROUND

Potentially great sources of oil and natural gas are contained

within the Arctic Ocean region of North America. To exploit

these reserves will require the design, construction, and

maintenance of permanent offshore structures that can withstand

the harsh conditions imposed by the Arctic environment. Few

permanent Arctic offshore structures actually exist and little

information is available on the environmental loads that these

structures might experience. Further, the structural

configurations being proposed are sufficiently different from

standard construction that uncertainties exist in predicting the

behavior of these Arctic structures under load. For safety and

economic reasons, more research is clearly needed if the mineral

resources of the Arctic are to be developed.

Designs of Arctic offshore structures have utilized both concrete

and steel as the construction material, and increasing attention

is being given to composite structures incorporating both

concrete and steel into the design [1,2]. Use of concrete as the

construction material has many inherent advantages in the harsh

Arctic environment. Properly constructed concrete structures can

be extremely durable and maintenance free when exposed to marine

environments, and concrete can provide a structure with the mass

and rigidity needed to withstand the extreme loading conditions

of the Arctic [3]. Offshore structures for the Arctic will

normally be built in temperate climates and towed to the Arctic

region. The structure's weight, buoyancy, floating stability,

dynamic response during tow, and deployment in shallow or icecovered waters must all be considered in design [4]. These

requirements make it desirable to use lightweight, high-strength

concrete in the construction of Arctic offshore structures.

1
Over the last 15 years, concrete has been used successfully in

the construction of offshore structures in the North Sea [3,5,6].

Concrete has also been used for lighthouses both in Canada and in

Northern Europe for over 50 years [6], While this experience

with concrete structures in temperate and sub-arctic regions

provides valuable information, unknowns in structural performance

still exist as a result of the severe ice loading conditions that

exist in the Arctic. Much more research is needed in this area

to better understand and quantify ice loads on structures in the

Arctic

.

Proposed designs of offshore structures for the Arctic typically

have a concrete wall extending around the perimeter of the

structure. These exterior walls will be subjected to tremendous

loads resulting from the impact of ice on the structures.

Designs of the exterior walls call for thick, lightweight, highstrength concrete sections which are heavily reinforced and

possibly prestressed to improve flexural and shear capacities.

Both flat and curved exterior surfaces have been proposed for

use. The proper design of this exterior ice wall is of

particular importance to the integrity of the structure, and it

substantially influences the cost.

The design of offshore structures in the Arctic requires an

understanding of the behavior of the concrete exterior walls

under high intensity ice loads. Both global and local effects of

the ice loading must be considered. Estimates of the ice contact

pressures are typically in the range of 3 to 15 MPa (400 to 2200

psi), depending on the area of contact between the ice and the

structure [6], These structures should be designed so that under

high intensity ice loads punching shear is not the primary mode

of failure. A shear failure is undesirable because it is sudden

and it could lead to the progressive collapse of the structure.

Information on the punching shear behavior of thick, heavily

reinforced, lightweight concrete sections of the type being

2
proposed for Arctic structures is limited. Provisions in

existing standards pertaining to punching resistance have been

derived from tests conducted on thin and lightly reinforced

sections. The increased thickness, the large amount of

reinforcement, and the possible presence of arch action and

prestressing all will influence the punching load capacity.

Thus, there is a need to investigate the punching shear

resistance of heavily reinforced thick slab and shell sections

[3].

1.2 PURPOSE AND SCOPE OF RESEARCH

This research project is being conducted by the National Bureau

of Standards (NBS) to investigate the punching shear resistance

of heavily reinforced, high-strength, lightweight concrete slab

and shell sections in order to aid in the establishment of

criteria for the design of Arctic offshore concrete structures.

The project was undertaken on the behalf of The Minerals

Management Service of the U.S. Department of the Interior in

cooperation with the following five oil companies:

- Chevron Oil Company;

- Exxon Company, U.S. A.;

- Mobil Corporation;

- Shell Oil Company; and

- Standard Oil Company of Ohio.

The research project will consist of both analytical studies and

physical model studies. The analytical phase is directed towards

the development of a finite element analysis program that will

incorporate non-linear material models and failure criteria under

multi-axial states of stress. The physical modeling tests will

be conducted on representative slab and shell sections of Arctic

offshore structures. Both prestressed and non-prest ressed

sections will be studied. The physical tests will initially be

conducted on 1/6-scale models, with larger-scale model tests to

follow

.

3
1.3 PURPOSE OF THIS REPORT

This report is the first in a series of progress reports on the

project being conducted at NBS to investigate the punching shear

resistance of lightweight concrete offshore structures. The

purpose of this report is to introduce the problem and to review

current knowledge on the punching shear behavior of concrete

offshore structures subjected to Arctic ice loads. A general

review of material relevant to the subject is also presented.

The shape and design of proposed Arctic offshore structures are a direct result of the ice loads that the structures will be

expected to resist. A review of available information on Arctic

ice loads is presented, followed by a discussion of typical

structural concepts that have been proposed. The general

mechanics of punching shear failures and the factors affecting

punching resistance are discussed along with a comparison of

current U.S. and European punching shear code provisions.

Finally, available literature on experimental and analytical

research on punching shear relevant to this research is reviewed.

A
2.0

ICE LOADS ON ARCTIC STRUCTURES

2.1 INTRODUCTION

Offshore structures in the Arctic will be exposed to severe ice

loading and successfully designing these structures to resist the

ice forces is a major aspect of the overall design of the

structure. The perimeter wall surrounding an offshore structure

represents a substantial portion of the weight and cost of the

structure. Design of this perimeter wall (sometimes referred to

as the ice wall of the structure) is controlled by the extremely

high ice pressures that develop as an ice formation is crushed

against it. Past experience with marine structures in sub-arctic

and temperate regions, while valuable, does not include

information on loading conditions as severe as those expected for

the Arctic. Development of an understanding of ice action in

the Arctic and quantification of design values of ice loads are

clearly in their early stages. Much more research is needed in

this area. This chapter presents a review of the publicly

available information (much of the recent research is

proprietary) on ice loads in the Arctic.

2.2 NATURE OF ARCTIC ICE

The proposed locations of the offshore Arctic structures will

result in the structures being exposed to a wide variety of ice

forms. Both freshwater ice and sea ice formations are found in

the Arctic Ocean. Freshwater ice formations, such as icebergs

and ice islands, are of glacial origin. Ice islands are the

largest freshwater ice formations and can be as large as 1000 km

(400 square miles) in area and have thicknesses up to 60 m (200

ft) [7], Sea ice is usually classified by age into first-year

and multi-year ice. First-year ice is sea ice of one winter's

growth, with thicknesses ranging from 0.3 to 2 m (1 to 7 ft).

Multi-year ice is ice that has survived at least two summers, and

5
consolidated multi-year ice thicknesses of up to 7 m (23 ft) have

been recorded [7], Pressure ridges are the result of ice sheets

deforming due to pressure and may be 20 m (65 ft) thick. Pack

ice is a term commonly used to refer to any accumulation of sea

ice. Floes are any relatively flat pieces of sea ice having

lateral dimensions on the order of 20 m (65 ft) or more. More

detailed information on the classification of ice formations can

be found in the literature review on ice loading performed by The

American Bureau of Shipping [8].

Ice conditions are a function of the specific region in the

Arctic and the hydrography of that particular location. Bays and

shallow waters are stationary ice areas. For most of the year

the ice is frozen to the sea bed, creating what is known as an

ice foot [7]. When melting occurs during the summer, pieces of

the ice foot can move, resulting in loads on a structure.

However, since the geography of stationary areas limits ice foot

movements, the impact forces imposed on a structure are much less

than those that would be experienced by a structure located in

the open sea. In the Arctic seas the ice cover is made up of

moving pack ice. Winter ice conditions are more predictable than

those that occur during breakup of the ice cover in the warmer

months. The most dangerous ice formations occur during the

spring and summer when multi-year floes invade the southern

Arctic waters.

Action of ice on offshore structures requires calculation of both

local contact pressures and global forces. Forces due to ice

pressure result from thermal expansion, static loads, or dynamic

loads. Some of the possible failure modes for ice impinging upon

a structure are shown in Figure 1 (adapted from References 7,9

and 10). The ice loads imposed on vertical structures are

usually based on the buckling or crushing strength of an ice

sheet [8]. As buckling occurs only for relatively thin ice

floes, ice loads are more commonly specified by the compressive

strength of the ice formation. Ice loads on structures with a

6
sloping surface around their perimeter (usually the structures

are conical in shape) are a function of both the compressive and

flexural strength of the ice [8]. When moving ice collides with

an inclined surface, it tends to ride up the slope, and local

crushing occurs along the bottom of the ice sheet which is in

contact with the structure. As the contact force is normal to

the sloping surface, bending stresses are induced in the ice

sheet. When the tensile strength of the ice sheet is exceeded,

the sheet fails by cracking.

The possibility of dynamic loading conditions for any particular

location depends upon the hydrography of the location. Very fast

currents and strong winds can cause impact loading of an ice mass

on a structure. Dynamic stresses can also occur when failure of

an ice mass in contact with a structure causes instant unloading

[11]. Ice-induced vibration of offshore structures is usually

not a problem, except perhaps for slender, flexible structures in

which the natural frequency of the structure is in the range of

the frequency of ice load oscillation (0.5 to 15 Hz) [8].

However, stresses induced by continuous crushing of an ice mass

in contact with a structure (ratchetting effects) may cause

structural fatigue.

The forces imposed on a structure by moving ice are influenced by

many factors. Enge lbrek tson [11] has identified the following

factors as being of predominant importance:

- structural shape (vertical or inclined face, shape of cross

section , width)

?

- structural response (rigid, flexible, vibrating);

- ice feature (sheet ice, rafted ice, ice ridges, icebergs);

- ice failure mode (ductile or brittle crushing, bending,

shearing)

;

- contact between ice and structure (contact area, degree of

momentary contact, variation of contact); and

7
- ice strength, which is in turn governed by:

- crystalline form and grain size;

- ice temperature;

- brine volume;

- stress condition (confinement); and

- strain rate.

Ice is elastic at low load levels and high strain rates, but

exhibits inelastic behavior under higher load levels and lower

strain rates [8]. Typical strength values for sea ice with a salinity of 4.7% and at -10°C are [8,12]:

flexural 0.6 - 1.0 MPa (85 - 145 psi)

compressive, unconfined 3.5 - 4.1 MPa (500 - 600 psi)

A more complete discussion of the physical and mechanical

properties of ice is given in Reference 8.

2.3 PREDICTING ICE FORCES

Evaluating the effects of ice forces is an important design

consideration for any structure that will be required to function

in an ice environment. Predicting ice effects on marine

structures requires calculation of both local ice contact

pressures and total ice forces. Bridges, piers, lighthouses, and

ships have existed or operated in ice-infested regions for many

years. With the discovery of oil and gas in the Arctic,

increasing attention is being given to the problem of predicting

ice forces on Arctic structures. A substantial amount of

research has been conducted in recent years by individual

companies and by joint industry groups such as the Alaska Oil and

Gas Association (AOGA) and the Arctic Petroleum Operators

with an ice thickness

of 1.5 m (5 ft)

elastic modulus

Poisson's ratio

4100 MPa (0.6 X 10 6 psi)

0.30 - 0.35

8
Association of Canada (APOA) ; however, much of this work is

proprietary [8]. Despite these considerable efforts, knowledge

and understanding of ice loading on Arctic structures is limited.

Ice forces have been determined using many different techniques

and approaches. It is a very complex problem and no general

consensus yet exists on what values should be selected for design

pressures. An indication of the wide range of ice pressure

values that can be calculated using different theories is given

in Table 1, taken from Croasdale [13]. While this table is for

piles and piers, it nevertheless indicates the difference in

opinions that can exist.

In general, three approaches have been taken in the prediction of

ice loads on structures: theoretical analyses, experimental

laboratory studies, and monitoring of existing structures in

situ. A brief discussion of the three approaches is given, and

some problems and shortcomings associated with these efforts are

noted. A more complete literature survey of the research work

that has been performed on the problem of predicting ice loads on

structures can be found in Reference 8.

Theoretical approaches have applied classical mechanics to the

problem of predicting ice forces, using theories of elasticity

and plasticity. The forces are usually specified by solving an

indentation problem whereby an ice sheet, represented as a viscoelastic-plastic medium, moves into a rigid indentor [8]. Work by

Korzhavin [14] and Ralston [15] has led to the development of

indentation equations for predicting the horizontal force exerted

by ice crushing against a structure. Ralston's equation appears

in API Bulletin 2N [16] and is as follows:

F = I f

c Cx D t (2-1)

where F = horizontal ice force;

I = indentation factor;

9
f c = contact factor;

C

x = unconfined compressive strength of the ice;

D = diameter or width of the structure at the region

of ice contact; and

t = ice thickness.

The indentation factor, I, depends on:

- crystallographic structure of the ice;

- multi-axial strength of the ice;

- strain rate; and

- geometry of the interaction between the ice and the

structure

.

The strain rate for the ice is a function of the ice approach

velocity and the structure dimension, D. The contact factor, f c

, depends on:

- ice movement rate;

- local geometric effects; and

- active defense mechanisms.

Besides the obvious complexity of using this equation, there are

other problems. Parameters to be used in this equation will

depend on the location and configuration of the offshore

structure. Yet there is no rational basis that currently exists

for choosing appropriate values for the parameters. Also, due to

the random nature of the loading, an assessment needs to be made

to determine what conditions and values will be selected, i.e.

what return interval should be used. There are other

considerations. Portions of the structure may interact, altering

the failure mode of the ice feature. Also, non-s imu 1 taneous

failure of the ice may occur across the width of large

structures. Therefore, even if the theory that is used in the

prediction of the ice forces has a rational basis, enough

unknowns exist to render the current applicability of this and

10
similar equations to design questionable [17],

A number of small-scale laboratory tests have been conducted on

the interaction of ice with a structure. Both real and

artificial ice have been used in these model tests. The U.S. Army

Cold Regions Research and Engineering Laboratory has studied the

action of sheet ice on model bridge piers using their large

refrigerated test basin facility (33.5 m long by 9.15 m wide by

2.4 m deep) [18]. Various parameters were investigated,

including the geometry of the bridge piers and the velocity,

thickness, and flexural strength of the ice. It was observed in

the tests that the magnitude of the force required to fail the

ice sheet was strongly influenced by the slope angle of the

inclined structure. The investigators compared their test

results with forces predicted by Ralston's theoretical approach,

and observed some agreement. However, the experimental results

tended to be higher than the theoretical ice forces calculated

from Ralston's formulation. Other model studies have been

conducted on cyl indr ical ly- and conically-shaped structures

[8,19]. These and other model tests have led to the development

of empirical design formulas, but the validity of the formulas

are questionable for actual structures because of scale effects

[8] and many of the same reasons discussed previously for the

theoretical approaches that have been used.

In situ tests involving monitoring of existing structures in the

Arctic have been performed [17]. However, the measured response

of any structure will be influenced by the particular

configuration of that structure. Also, monitoring of actual

Arctic structures has not been performed over a sufficient period

of time to allow appropriate design and overload values to be

selected. Further, much of this work of monitoring of existing

structures in the Arctic is currently proprietary. Continued

coordinated efforts combining analytical and experimental studies

with results of in situ tests are needed before realistic values

of Arctic ice loads can be determined.

11
The discussion of the random nature of the loads that structures

in the Arctic will experience intuitively leads to the conclusion

that the ice and other environmental loads should be treated in a statistical sense, i.e. by applying a reliability-based design

methodology. This has been proposed by Engelbrektson [11], Kry

[20], Vivatrat and Slomski [21], and others. Even though this is

a logical and promising approach, not enough statistical

information has been collected on conditions in the Arctic to

provide the basis for developing such a reliability- based design

method

.

The problem of predicting Arctic ice loads is extremely complex,

and the development of design criteria for Arctic structures is

still in its early stages. With the increased activity in this

region, the need for more research into the interaction of

structures with ice is urgent.

2.4 DESIGN VALUES OF ICE LOADS

Despite the lack of a practical and accurate method for

predicting ice loads in the Arctic, offshore structures have been

designed and a limited number are currently in use in the Arctic.

Values must therefore have been assigned to the ice forces in

these designs. From the limited amount of design information

publicly available, it appears that considerable engineering

judgement was used in selecting design ice pressures.

Although both local ice pressures and global ice forces must be

considered in design, it is local ice pressures that will control

the thickness of the perimeter ice wall of the structure. Local

ice pressures can result in a punching shear mode of failure in

the exterior wall, although other modes of failure may also

occur. As the exterior wall represents a substantial portion of

the total cost and weight of the structure, careful judgement

must be exercised in selecting a value for the local contact

12
pressures

.

Published codes give very little guidance on values of local ice

pressures to be used in design. The American Petroleum Institute

has issued Bulletin 2N, "Planning, Designing and Constructing

Fixed Offshore Structures in Ice Environments," 1982 [16]. While

not a design code per se, the bulletin does identify design

considerations for Arctic offshore structures. No design values

are given for local ice contact pressures. The bulletin simply

states that ice contact failure pressures will be considerably

larger than the uniaxial ice strength because of confinement

effects, but that the relationship between unconfined and

confined compressive strengths is not well established. Values

of local confined pressures of sea ice as high as 24 MPa (3500

psi) have been reported [7], Proprietary research is currently

being conducted in this area.

Bulletin 2N states that the design of concrete structures should

follow the provisions of ACI 357 R-78 (1978), "Guide For The

Design and Construction of Fixed Offshore Concrete Structures"

[22]. No provisions for ice force values are given in ACI 357 R78. Also, no load factor for ice is specified other than stating

that it should be determined for the specific site and location.

A survey of available design information on proposed and existing

structures indicates that a wide range of local ice contact

pressures have been reported as a basis for design:

- 1200 psi on any 50 ft^. Imperial Oil (ESSO), 1983 [23];

- 1300 psi on any 5 ft^ (exploratory structure) and 2000 psi

on any 5 ft^ (production structure), R. G. Bea, 1983 [24];

- 590 to 670 psi over 310 to 200 ft^ respectively, SOHIO,

1984 [25]

;

- 1600 psi on 10 ft^ or less and 1000 psi on 210 ft^, ACES,

1984 [26]; and

- 900 psi on 5 ft X 5 ft area. Super CIDS, 1984 [27].

13
The only agreement on local ice pressure design values is that as

the contact area gets larger, the pressure should decrease.

Bruen et al. [28] have proposed design curves, shown in Figure

2a, taking into account this relationship. A similar ice pressure

design curve, from Byrd et al. [26], is shown in Figure 2b.

Values from the curves are to be considered as uniformly

distributed pressures. It is also stated that these curves

should be calibrated by large-scale field tests.

14
3.0

CONCRETE OFFSHORE STRUCTURES FOR THE ARCTIC

3.1 INTRODUCTION

Although very few Arctic offshore structures have been built, a large number of innovative concepts for offshore structures have

been proposed. The exterior walls extending around the perimeter

of offshore structures must be able to resist both large global

loads and local contact pressures exerted on the walls by moving

ice. The shape of a structure plays an important role in how the

structure will resist the severe ice forces as the failure mode

of the oncoming ice is a function of how the ice features

interact with the structure. However, the choice of the shape

and configuration for an offshore structure is also influenced by

the depth of water in which it will operate, cost,

const ructibi 1 ity, towing requirements, etc. This chapter will

discuss the general types of structural configurations that have

been proposed for Arctic offshore structures. Relevant design

details from several specific proposals are also presented.

3.2 STRUCTURE CLASSIFICATION

Proposed configurations of offshore structures for the Arctic can

generally be classified into three categories [3,23]:

- island structures: non-retained and retained;

- gravity structures: conical, vertical- and step-sided; and

- floating structures.

Representative drawings of the different categories of structures

are shown in Figure 3. Hybrid structures combining features may

also exist.

3.2.1 I SLAND STRUCTURES

Island structures are most applicable for shallow water areas.

Since 1972, about 30 structures of this type have been built in

the Beaufort Sea off Canada and Alaska [23]. Island structures

15
may be non-retained, in effect an artificial island, or the fill

material used to construct the island may be retained with

caissons

.

Non-retained islands (Figure 3a) are economical for use in

shallow water regions of 25 m (80 ft) or less [23], The island

is formed by making a mound using fill material upon which the

working area is constructed. Ice forces are resisted as a result

of the large mass of the structure. Rubble formation around the

island enhances the resistance, however it makes accessabil ity to

the structure difficult. This type of structure has a large work

area which can accomodate many wells. A large amount of locally

available gravel or other suitable construction material is

required for these structures [3].

Retained islands (Figure 3b) have been proposed for water depths

in which non-retained islands would be uneconomical because of

their large material requirements. Retained islands are reported

to be cost effective for water depths of 25 to 60 m (80 to 200

ft) [23]. Retained islands are formed by constructing a rigid

perimeter wall of either steel or concrete and backfilling the

wall with earth. The walls will normally be constructed in

temperate locations and towed to the Arctic. Like non-retained

islands, the retained islands achieve their strength as a result

of their large mass [3].

3.2.2 GRAVITY STRUCTURES

Gravity structures have been proposed for use in water depths in

which island structures are uneconomical. Proposed designs call

for use of gravity structures in water depths of up to 200 m (650

ft) [23,29]. Gravity structures may rest on the sea bed, or they

may be attached to the bottom using piles. The structures may

also be placed on a submerged berm. Proposed configurations of

gravity structures have included structures with sloping sides

(usually the structure is conical in shape), vertical sides, and

16
stepped sides. The different configurations are a result of

attempts to reduce the ice forces that the structure must resist.

Conical structures (Figure 3c) and other structures with sloping

sides have been proposed as a way of reducing ice forces on the

structure by causing the ice to fail in bending rather than

crushing. Conical structures will normally have a large base to

provide stability and a small top section to reduce the ice force

on the structure. The small top section will also result in the

disadvantage of having a small working area [3].

Vertical-sided caisson gravity structures (Figure 3d) are

normally very large and polygonal in shape. The vertical walls

will induce a crushing failure in oncoming ice features, which

will result in high local contact pressures developing on the

structure's exterior wall. The exterior walls of the verticalsided gravity structures may be configured as an arch shape to

induce arching action, thereby reducing principal tension

stresses in the wall [25].

Stepped-sided gravity structures (Figure 3e) have been proposed

for production platforms in water depths of 50 to 200 m (165 to

650 ft) that are subject to impact of large ice features [29],

In deeper waters, vertical-sided structures require large

quantities of structural materials, the draft is deep, and the

maximum ice forces are large. Conical structures, while reducing

the impact forces by causing the ice to ride up, may be difficult

to construct and deploy in deeper water, resulting in higher

costs. Gerwick et al. [29] report that the stepped geometry

enables a more efficient utilization of materials than a vertical-sided gravity structure. Additionally, they report that

this concept will result in reduced ice impact forces by creating

a multi-modal failure of the ice. It is reported that global ice

loads would be reduced by 50% or more when compared to those

developed by a vertical-sided structure [29]. However, high local

ice pressures would continue to be a problem that would need to

17
be addressed in the design.

3.2.3 FLOATING STRUCTURES

Floating structures (Figure 3f) have been reported [23] as being

the most realistic approach for exploration and production in

water depths of 150 m (500 ft) or greater. Floating structures

have a limited capability to resist ice forces, but they may be

moved to avoid large ice features. Cone configurations may be

incorporated into the floating structure to create flexural

failure in the ice. Induced vertical motions may also be used to

achieve the same result [23]. Drill ships have been suggested

for drilling in very deep waters [23].

3.3 REVIEW OF PROPOSED DESIGNS

A brief discussion of some of the published work on specific

proposals for Arctic offshore structures is presented.

1. Schlechten et al. [25], 1984, SOHIO Arctic Mobile Structure

(SAMS)

The SAMS structure consists of a 345 ft wide octagonal ly shaped

concrete base with a plan view as shown in Figure 4a. The height

of the exterior wall of the structure is 70 ft. Approximate

dimensions of the exterior wall are presented in Figure 4b.

Design of the exterior wall was controlled by local ice pressure.

The arch profile on the interior face of the wall was used to

help resist the ice loads in direct compression, thereby

minimizing principal tension in the concrete. Additionally,

orthogonal post-tensioning was used to create a biaxial

compression state to further reduce principal tension. Ice

pressure intensities of 590 to 670 psi (unfactored) over

respective areas of 310 to 200 ft^ controlled the design of the

ice wall by creating limiting compressive stresses at the crown

of the arch. Higher intensity pressures over smaller areas

leading to a punching type of failure did not control the design

18
because of the arched inner surface and post-tensioned induced

state of biaxial compression. Other relevant design details

included

- a semi-1 ightweight^, high-strength concrete was used with a unit weight of 133 pcf and a design compressive strength of

7000 psi at 90 days;

- load factor for ice = 1.3; capacity reduction factor = 0.7

(which reflects the compressive type failure mode

expected)

;

- a 15% increase in effective compressive strength was

allowed, based on the expected triaxial state of stress in

the concrete;

- in designing the exterior wall, a temperature gradient of

+34°F (inside) to -50°F (outside) was considered. Tension

created by this gradient was compensated for by

prestressing the concrete;

- a tension reinforcement ratio of 1% was used in the

exterior wall;

- prestressing in the exterior wall varied from 500 to 1000

psi, depending on location; and

- analysis for the design consisted of three-dimensional

linear analyses of a segment of the exterior ice wall

followed by two-dimensional nonlinear finite element

analyses to check the ultimate capacity of the wall. Shear

reinforcement and confinement steel requirements were

determined from the two-dimensional analyses based on the

location and magnitude of the principal stresses.

One final comment on this concept is that the shear design

requirements were not based on conventional code formulae. The

^For this report, lightweight concrete is defined as concrete

with a unit weight of 120 pcf or less, semi-lightweight as

concrete with a unit weight of 121 to 140 pcf, and regular-weight

as concrete with a unit weight of 141 pcf or greater.

19
designers noted that this would have resulted in excessively

thick plates due to the presence of extremely high ice pressures

and the relatively low shear (tensile) strength of the concrete.

To account for the arch action within the plate, the designers

used Section 11.4.2.2 of ACI 318-77 [30] which allows the

determination of shear strength to be "computed as the shear

force corresponding to dead load plus live load that results in a principal tensile stress of 4 ^/f , c at the centroidal axis of a member." The designers used two-dimensional finite element

analyses to demonstrate that the ice wall successfully limits

principal tension through arch action to resist loads in

compression

.

2. Bhula et al. [31], 1984, Brian Watt Associates Caisson

System (BWACS)

BWACS is a ve rt ica 1 -s ided caisson gravity structure. A

perspective view of the BWACS structure is shown in Figure 5a.

The exterior ice wall is 90 ft high. A detail showing typical

dimensions is given in Figure 5b. Design of the outer wall is

controlled by flexure and out-of-plane shear forces. The arched

outer wall induces compression which enhances its out-of-plane

shear resistance. The external walls were designed for out-ofplane shear in accordance with ACI 318-83 [32]. The ice pressure

curves proposed by Bruen et al. [28], shown in Figure 2a, were

used in the design. Other relevant design details:

- BWACS is to be a monolithic structure constructed of

lightweight, high-strength concrete (compressive strength

at 28 days = 7000 psi)

;

- the structure is to be post-tensioned but no stressing

values are given;

- a mild steel reinforcing ratio of 2% was used with a steel

yield strength of 60,000 psi;

- load factor for ice = 1.3; shear reduction factor for

lightweight concrete = 0.8; and

- the analysis for the design was carried out using finite

element techniques. Some of the ice loading patterns

20
considered on the finite element mesh are shown in Figure

5c.

Brian Watt Associates Inc. conducted an experimental

investigation into the punching shear capacity of thick, heavily

reinforced regular-weight concrete shells [34] with apparent

applications to the BWACS design.

3. Byrd et al. [26], 1984, Arctic Cone Exploration Structure

(ACES)

A perspective cut-away of ACES is given in Figure 6. The hull

has a conical shape in order to induce a bending failure mode in

the ice, resulting in reduced forces on the structure. The

authors feel the concept introduced in the ACES design will be

used as a prototype for heavy duty, bottom-founded mobile rigs

for Arctic offshore drilling. Some typical dimensions of the

exterior wall are shown in Figure 7. Local ice pressures

determined the configuration and sizes of the principal

structural components in the ACES design. The relationship

between local ice pressure and loaded area used in the design is

given in Figure 2b. Other relevant design details:

- a lightweight, high-strength concrete was used in the

design (UW = 115 pcf, 28 day compressive strength = 7000

psi)

;

- the outer shell contained meridional and circumferential

prestressing; and

- load factor for ice = 1.3.

4. Wetmore [27], 1984, The Concrete Island Drilling System:

Super Series (Super CIDS)

This structure is one of the few proposed offshore structures for

the Arctic that has been built. The general concept of the Super

CIDS system is shown in Figure 8. The use of large "brick” units

allows the system to be adapted to different locations, i.e. the

bricks can be stacked to accommodate varying water depths. A plan

view of a typical brick is shown in Figure 9. Relevant

design details are:

21
- design local ice load was 900 psi on an area of 5 ft X 5

ft;

- all of the elements of the "brick", except the interior

wall and shear walls, are constructed of lightweight (115

pcf), high-strength (28 day compressive strength = 6500

psi) concrete. The interior wall and shear walls use

normal-weight concrete with a design strength of 8000 psi;

- the outer wall is post-tensioned to 500 psi in the

horizontal direction and 300 psi in the vertical direction;

and

- the load factor for ice is 1.3.

5. Fitzpatrick and Stenning [35], 1983, Tarsiut Island:

Tarsiut Island was constructed of four concrete caissons,

arranged in a square, backfilled and placed atop a submerged sand

berm. The general arrangement is shown in Figure 10. Thickness

of the caisson walls was approximately 250 mm. A lightweight

concrete with a density of 120 pcf was used in the construction.

The final reinforced concrete density, the weight of the steel

and post-tensioning included, was 140 pcf. The concrete had a 28

day compressive strength of 6000 psi.

6. Bruce and Roggensack [1], 1984:

Only a general discussion on designing Arctic platforms is

presented in this paper. It is recommended that arch action be

built into the design of the exterior ice wall of the offshore

structures in order to enhance the capacity of the system. An

arrangement for doing this is shown in Figure 11. Even with the

arch action, shear stresses can still be large, requiring a significant amount of shear reinforcement. To reduce the shear

stresses, transverse prestressing has been suggested, the

potential advantages being:

- the load at which inclined cracking first occurs is

increased

;

-• ultimate strength is increased; and

- the congestion of shear reinforcement in the cross section

22
is reduced.

The practicality of using short tendons to post-tension

section can be questioned, however. The authors also add

the shear lag effects of thick concrete members will ease

problems associated with high local ice impact pressures.

the

that

the

23
4.0 PUNCHING SHEAR BEHAVIOR OF CONCRETE SLABS AND SHELLS

4.1 INTRODUCTION

The mechanism by which failure will occur in a structure must be

considered in the design in order to insure an adequate level of

safety. It is important that the structure behave in a ductile

manner as it approaches failure rather than failing in a brittle

fashion. Flexural failures in properly designed reinforced

concrete members are accompanied by a gradual yielding of the

flexural steel, and relatively large deflections will occur

before failure. The large deflections provide warning prior to

the collapse of the structure, and the ductile behavior allows

load redistribution to occur thus maintaining the load carrying

capacity of the structure even though it has been locally

overloaded. A shear failure, in contrast, is undesirable in a concrete structure because of the sudden and catastrophic nature

of the failure. The designer must recognize the possible modes

of failure and insure that at ultimate loads the structure will

behave in a ductile manner.

In many conventional applications of reinforced concrete slabs

and shells, the design will be governed by flexural effects or

deflection limitations. This is normally the case for slabs or

shells supported on beams or walls that are subjected to

distributed pressures. For this type of situation, the magnitude

of the shear stresses is small relative to the flexural

stresses. However, shear stresses can govern the design of slabs

and shells when concentrated loads are present. Shear forces can

also become critical when the span-to-dept h ratio becomes

relatively small and large amounts of flexural reinforcement are

present

.

Shear failures in a slab or shell can occur as a result of a failure across the width of the section (one-way action) or as

the result of a local shear failure around a concentrated load

24
(two-way action). When the slab or shell fails by one-way

action, it acts as a wide beam with the shear failure surface

extending across the entire width. Failure in shear of a slab or

shell by two-way action can be caused by a concentrated load when

a shear failure surface develops around the perimeter of the

load, i.e. the concentrated load "punches" through the slab or

shell. Situations in which two-way shear action is critical can

arise from: (1) the transfer of forces from slabs to columns, (2)

the transfer of forces from columns to footings, and (3) when a concentrated load is applied to the slab or shell [36], Both

beam shear and punching shear must be evaluated to determine the

shear strength of the slab or shell.

It should be noted that shear stress is normally computed by

dividing the shear force on the critical section by the length

and depth of that section. The resulting shear stress is a nominal stress. It is neither indicative of the actual shear

stresses nor their distribution. Further, the nominal shear

stress is particularly sensitive to the assumed location and

shape of the critical section [37]. Nominal shear stresses are

used to provide a reference stress when designing concrete

members

.

4.2 COMPARISON OF BEAM AND PUNCHING SHEAR

A reinforced concrete slab or shell resists shear forces in many

ways analogous to that of a beam. After the formation of a crack, shear forces are carried by the following mechanisms, as

shown in Figure 12 [39]:

1. shear resistance of the uncracked concrete or by the

concrete lying beyond the inclined crack, Vcz ; 2. aggregate interlock (or interface frictional force

transfer) across the inclined cracks, Va

; 3. dowel action of the longitudinal reinforcement crossing

the inclined cracks, Vd ;

25
4. contribution of any shear reinforcement present, Vs

; and

5. possible arch action from membrane forces.

The mechanism of shear failure in a slab or shell is less well

understood than that of shear failure in a beam. This is a result of the three-dimensional nature of shear in slabs and

shells and the associated conceptual and observational

complications. The developing shear failure mechanism in beams

is comparatively easy to observe and identify, whereas in slabs

and shells the inclined shear cracks initiate within the member

and may not be visible on an exposed surface [37]. A complete

understanding of the mechanism of shear failure in slabs and

shells has yet to be achieved.

The nominal ultimate punching shear stress that can be developed

is usually greater in a slab or shell than in a beam. Criswell

and Hawkins [37] have attributed this difference to six factors:

1. Restricted inclined crack location - The inclined crack

forming the failure surface is confined to the perimeter of

the loaded area because the area resisting shear increases

with the distance from the loaded area. Thus the crack is

less free to develop at the weakest section than in a beam.

2. State of stress at the apex of the inclined crack - Bending moments in a slab create compressive stresses

in the plane of the slab or shell, and the concentrated

load causes local compressive stresses, resulting in a complex state of triaxial stress conditions. This

favorable state of triaxial compressive stresses is often

cited as the main reason higher ultimate shear stresses are

obtainable in slabs and shells than in beams. A transition

from slab to beam behavior will occur because of a diminished ability to resist these higher shear stresses as

the size of the loaded area increases relative to the slab

thickness

.

3. Lack of symmetry - A lack of axial symmetry results in

26
4.

variations in the loads for cracking and inelasticity to

develop at different locations around the loaded area.

Distribution of moments - The relative magnitudes of

the moments in a slab or shell vary with the pattern of

cracking of the concrete and yielding of the reinforcing

steel. This in turn affects the subsequent formation and

opening of the inclined shear cracks.

5. Dowel forces - A greater number of bars will cross the

shear failure surface in a slab than in a beam, and

thus proportionately greater dowel forces may develop

in slabs and shells than in beams.

6. Lack of a simple static analysis - Equilibrium

requirements alone provide basic knowledge on the forces in

a diagonally cracked beam. However, in a slab or shell a simple static analysis is inadequate for accurately

predicting the forces. This is because a slab or shell can

redistribute forces prior to failure. Further, the inplane forces generated by restraints provided by the

supports and non-yielding portions of the slab or shell

cause complications not usually associated with the

behavior of beams.

4.3 MECHANISM OF PUNCHING SHEAR

A concentrated load acting on a slab or shell can cause diagonal

tension cracking around the perimeter of the loaded area leading

to a punching shear failure in the slab or shell. The diagonal

failure cracks form a truncated cone or pyramid shaped surface,

depending on the shape of the loaded area. The cracks forming

the failure surface extend from the edge of the concentrated load

at the compressive surface of the slab to distances away of about

one to two times the slab depth. When the cracks intersect the

flexural reinforcement they may flatten out or even extend

horizontally along the level of the steel. The angle of

inclination of the truncated cone or pyramid with respect to the

plane of the slab varies from 20° to 45°, depending on many

27
factors including the amount and nature of the reinforcement in

the slab [38].

Drawing upon the discussion presented in a comprehensive report

on the shear strength of reinforced concrete members by ASCE-ACI

Committee 426 [40], a summary of the mechanism by which a punching shear failure occurs can be given as follows. The

dominant crack patterns for an axisymmetric loading situation are

shown in Figure 13. First, a roughly circular tangential crack

forms around the perimeter of the loaded area due to negative

bending moments in the radial direction. Radial cracks then form

extending away from the loaded area. Because of the rapid rate

at which the radial moment decreases with distance from the

loaded area, significant increases in load are needed for further

cracking to occur. Inclined cracks originating near middepth

then form and intersect the radial cracks at right angles. The

inclined cracks that form are not likely to be initiated by

flexural cracks, and thus the characteristics of inclined cracks

in slabs or shells is more similar to the web-shear rather than

the flexure-shear cracks of beams'6

. The tangential stiffness of

the slab surrounding the cracked region helps to control the

opening of the diagonal tension cracks. This preserves the shear

transfer by aggregate interlock at higher loads than would occur

in beams.

Yielding of the slab or shell reinforcement may develop first at

the perimeter of the loaded area because of the high radial

9^Flexure-shear cracks are cracks that start as a flexural crack

on the tension face of a beam, and then spread diagonally upward

(under the influence of diagonal tension) toward the compression

face. Web-shear cracks start in the web section of a beam due to

high diagonal tension, then spread both upward and downward.

Web-shear cracks in beams are rare except in beams with

relatively thin web sections or heavy prestressing [38],

28
moments present. However, until general yielding of the slab

reinforcement in the area of the concentrated load occurs,

rotation at the inclined crack will be restrained by increased

tangential moments. Thus, a punching shear failure will not

normally occur until yielding of the reinforcement in both the

radial and tangential direction has occurred. Yielding of the

reinforcement, however, is not necessary for failure to occur,

nor does yielding of the reinforcement necessarily result in a shear failure.

4.4 FACTORS AFFECTING PUNCHING SHEAR STRENGTH

Based on a review of existing literature on the subject

[36-41], a discussion of the factors that influence the punching

shear strength of slabs and shells is presented. The factors are

listed in no particular order.

1. Concrete strength : The compressive strength of the concrete

influences the punching shear strength because the tensile

strength of the concrete is related to the compressive strength,

and shear failures are controlled primarily by the concrete

tensile strength. Current ACI code provisions assume that the

nominal shear strength of the concrete is proportional to the

square root of the compressive cylinder strength. However,

recent research by Carino and Lew [42] has indicated that the

current ACI formula for splitting tensile strength underestimates

the actual splitting strength of concrete with high compressive

strengths. Thus, if shear strength is correlated to the

splitting tensile strength, then it is likely that current ACI

formulas also underestimate the shear strength of high-strength

concretes. However, other research conducted by Elstner and

Hognestad [43] suggests just the opposite. The investigators

found that equations dependent on the square root of the

compressive strength predict too rapid an increase in shear

strength with increasing f' c

. Hawkins, Criswell and Roll [41]

concluded that the shear strength can be said to be dependent on

29
the square root of the compressive strength for compressive

cylinder strengths less than 4000 psi (28 MPa); any application

to higher strength concretes should be made with caution. The

shear behavior of high-strength concretes is an area that

requires further research.

2. Type of aggregate : Most shear studies have been performed

using normal weight concrete. However, lightweight concrete is

used extensively in construction because it reduces dead weight.

The use of lightweight concrete generally lowers the shear

strength because lightweight concrete has a lower splitting

tensile strength than does normal weight concrete. Also, the use

of lightweight aggregate in the concrete will result in less

shear force being transferred through aggregate interlock than

when normal weight aggregate is used.

Ivy, Ivey, and Buth [44] tested fourteen concrete slabs made with

three different lightweight aggregates. Comparisons were made

with previous work on normal weight concrete slabs, and existing

and proposed design methods were evaluated. They recommended

that the limiting stresses calculated for normal weight concretes

be multiplied by 0.75 for all lightweight and 0.85 for sanded

lightweight concretes. Results from this study are currently

used in the ACI code. Hawkins, Criswell and Roll [41] have

suggested that there appears to be no need to differentiate

between all lightweight and sand-lightweight concretes, and that

the shear strength of a lightweight concrete slab should be taken

as 0.85 times the shear strength of a normal weight concrete

slab (concrete compressive strengths being constant).

Compared with the data that have been collected on the shear

behavior of normal weight concrete slabs, there is an inadequate

amount of information on the shear behavior of lightweight

concrete. Further, it appears that most of the work completed to

date on the shear behavior of lightweight concrete slabs has been

performed using moderate strength concrete (compressive cylinder

30
strengths of 5000 psi (34.5 MPa) or less). Because of the

widespread use of lightweight and increasingly high-strength

concrete, further research in this area is needed.

3. Amount of. flexural reinforcement : Dowel forces develop as a result of the flexural reinforcement crossing the inclined shear

cracks, and may be responsible for a larger percentage of the

shear resistance in slabs than in beams. This is because of the

shape of the failure surfaces, resulting in a larger number of

bars crossing the failure surface in a slab than in a beam.

Kinnunen [45] and Anis [46] concluded that dowel forces carry

about 30 percent of the total shear in a slab. However, Moe [47]

found that the contribution of dowel forces was insignificant.

It would be reasonable to expect that an increase in the amount

of flexural reinforcement would result in an increase in the

shear force carried by dowel action. This was observed in tests

by Elstner and Hognestad [43] in which the punching shear

strength increased as the reinforcing ratio increased. However,

dowel action is complex and not totally understood. Dowel action

is influenced by the size and distribution of the flexural

reinforcing bars, and the amount of concrete cover over the bars.

In a recent study conducted by Brian Watt Associates Inc. [34] on

the punching shear resistance of shells, the investigators found

that an increase of 43 percent in the amount of flexural

reinforcement resulted in only a 2 percent difference in shear

capacity. Dowel action will be strongly influenced by the manner

in which cracking of the slab or shell occurs, because dowel

forces cannot be mobilized prior to some type of displacement

that reacts against the dowel stiffness. This may be one of the

main reasons why the percentage of the total shear force carried

by dowel action varies from one experiment to another. Dowel

forces will be very small prior to cracking, and if failure

occurs soon after cracking commences, without any transverse

displacements to mobilize the stiffness of the dowel bars, then

dowel forces will also be small.

31
4. Thickness of. the slab ox. shel l t It has been observed that,

in general, the relative strength of a structural element

decreases as the size of the specimen increases. This phenomenon

is commonly referred to as size effect. In conducting laboratory

tests on scaled models of prototype structures, size effects may

result in higher strengths being observed in the scaled models

than in the prototype structures. In addition, test results

that were successfully applied to typically dimensioned members

may not be valid for applications to members with significantly

increased dimensions.

Roll et al. [48] built 1/2.5-scale models of specimens tested by

Moe [47] and Elstner and Hognestad [43] and found excellent

agreement between the model and prototype shear strengths.

Batchelor and Tissington [49] tested 1/6- to 1/15-scale models of

a hypothetical prototype bridge deck and found no significant

effect of scale on the punching strength of the slabs. However,

Malhotra [50] found that the tensile strength, and therefore by

extension possibly the shear strength, of concrete increased as

the size of the specimen decreased. In experimental tests

conducted at Delft University, Walraven [51] investigated the

influence of depth on the shear strength of both normal- and

lightweight concrete beams without shear reinforcement. He found

that the nominal shear stress that developed at failure decreased

approximately 45 percent in both the normal- and lightweight

beams when the depth was increased from 0.1 m to 0.7 m (4 in. to

28 in.). Bazant [52] applied the theory of fracture mechanics to

diagonal shear failures of concrete beams without shear

reinforcement and concluded that significant size effects exist

with increasing beam depth.

Size effects in the punching shear strength of slabs due to

increased thickness have been reported by Kinnunen, Nylander and

Tolf [53]. They found that the nominal punching shear strength

decreased with increasing effective depth of the slab if the

other parameters were kept constant. They reported a reduction

32
in shear strength of up to 10 percent for slabs with shear

reinforcement and up to 40 percent for slabs without

reinforcement when the depth of the slab was increased from 0.1 m

to 0.62 m (4 in. to 24 in.). Several European codes specify

reductions in allowable shear stresses with increasing thickness,

but the current ACI code does not recognize any effect of

concrete thickness.

5. Size of the l oaded area relative to the s lab thickness ; The

ability of a slab to resist higher shear stresses diminishes as

the size of the loaded area increases relative to the slab

thickness. Tests have shown that the rate of decrease is a function of the shape and size of the loaded area and the

relative magnitude of the principal moments in the slab [37],

Moe [47] was the first to recognize that the ratio of the

characteristic dimension, c, of the loaded area to the effective

slab thickness, d, affected the shear strength. Moe examined

test data for c/d ratios between 0.75 and 3.0 and proposed

equations for predicting the punching shear strength of slabs

with c/d ratios in this range. Moe recommended that a critical

section for punching shear be assumed at a distance of d/2 away

from the perimeter of the loaded area, resulting in the shear

strength equations proposed by Moe becoming independent of the

c/d ratio. Thus, the effect of the size of the loaded area

relative to the thickness is addressed by Moe in an indirect

manner. This work by Moe was used in the development of the

provisions in the ACI code. For larger c/d ratios, these

equations will overestimate the shear strength; new equations for

predicting the punching shear strength of slabs with c/d ratios

higher than 3.0 have been proposed [41]. Another problem that

has been associated with high c/d ratios is the possibility of a

f lexural ly-inf luenced shear failure, termed a f 1 exu ra 1 -shea

r

failure, at lower loads than would be predicted based on punching

shear considerations or flexural considerations alone [54].

6. Shape the l oaded area : The shape of the loaded area

33
affects the deformations that will develop in a loaded slab or

shell. This in turn will influence the distribution of the shear

forces around the loaded area. In general, for the same c/d

ratios, slabs loaded by a circular area are stronger in shear

than those loaded by a square area [40], Vanderbilt [55] found

that the shear strengths of slabs with circular columns were

consistently higher than slabs with square columns, reaching a maximum of about 35 percent difference for a c/d ratio of 4.

However, Nightingale [56] and Plisga [57] found that with a c/d

ratio of 2.5 strengths for slabs with square columns were 16

percent higher than strengths for slabs with circular columns.

The conflicting results are apparently because the shear

strengths are influenced by the c/d ratio, the reinforcement

pattern, and the method of support, all of which were not held

constant in the tests [40],

There is, however, clear evidence that the limiting shear stress

decreases with increasing rectangularity of the loaded area [40].

There are two reasons for this. In tests [58] in which the

length of the column perimeter was held constant as the aspect

ratio of the sides of the column were varied, the shear strength

decreased because one-way bending became more predominant

resulting in increasing beam shear action developing along the

sides of the column. Criswell [54] notes that a second reason

for a reduction in shear strength is that shear forces tend to

concentrate at the corners of rectangular columns. Shear

distress occurs at the corners before the column faces, and the

failure is sequential resulting in the decrease in strength. He

also notes that this effect decreases for very large or very

small c/d ratios.

7. Interaction qL shear and f.lejuLta.1 effects : In a slab or

shell subjected to a concentrated load, the critical sections for

maximum moment and shear both coincide with the perimeter of the

loaded area, resulting in an interaction between the shear and

flexural forces. This makes it almost impossible to visually

34
classify the failure as being totally flexural or totally shear

in nature. The effects of in-plane forces also complicate this

classification. Hawkins [59] found that, in general, even

lightly reinforced slabs eventually fail by punching unless shear

reinforcement is provided well in excess of the amount needed to

carry the shearing force at the theoretical ultimate flexural

strength of the slab. The transition between a shear failure and

the attainment of the ductilities normally associated with

flexural failures is a gradual change as the flexural strength of

the region is decreased [54], While it is accepted that the

shearing stress for failure decreases as the intensity of the

flexural loading increases [40], this relationship has not been

fully investigated. Moe [47] has proposed an interaction

equation for slabs subjected to combined flexure and shear.

However, Moe also notes that the shear failure mechanism need not

always be related physically to the flexural failure mechanism.

8. Rate of l oading : Criswell [60] tested duplicate sets of

specimens, with one group being subjected to static loading and

the other to dynamic loading. In specimens where the load was

applied with a rise time of 20 to 40 milliseconds, an increase in

strength of about 26 percent resulted for specimens failing in

shear and an increase of about 18 percent resulted for specimens

failing primarily in flexure when compared to static tests on

similar specimens. Criswell attributed these increases in

strength to the increase in material strength properties at the

rapid strain rates of the dynamic loading. Investigations into

the effect of the rate of loading on the punching shear strength

have also been conducted for nuclear reactor structures subjected

to impact loads. Some of these investigations are discussed in

Section 5.2.

9. In-p l ane forces : Many investigators have recognized that

both the flexural and shear strengths of slabs and shells are

influenced by the presence of in-plane forces. Compressive in35
plane forces can significantly increase the strengths, while

tensile in-plane forces may have the tendency to reduce the

strengths. Compressive in-plane forces can be introduced into a slab or shell by lateral restraint provided by the supports or by

the elastic portions of the structure surrounding the yielded

region in the immediate vicinity of the concentrated load. The

supports may be fixed against horizontal movement or they may

provide partial restraint because of increased stiffness around

the perimeter, as is the case for a slab with edge beams. Inplane forces may develop because of the geometry of the

structure, such as in an arched shell, and can also be introduced

by the presence of prestressing. While compressive in-plane

forces can enhance the flexural and shear capacities of slabs and

shells, the compressive forces also tend to reduce the ductility

of the section and brittle failure modes may result.

For a slab subjected to a concentrated load and supported around

its perimeter, outward displacements will occur with yielding of

the slab surrounding the load. Since the region away from the

yielded area will remain elastic, the displacements are

restrained and axial forces develop. The elastic region

surrounding the concentrated load acts as an external frame that

will enhance the flexural and shear capacities of the slab [37].

The magnitude of the compressive forces that can develop will

increase as the stiffness of the elastic region increases

relative to the stiffness of the yielded region, and the

magnitude of the forces will decrease as the reinforcing ratio

increases [37]. Horizontal restraint provided by supports

results in similar behavior.

Criswell and Hawkins [37] have suggested that the jamming action

that occurs in slabs with horizontal restraint can be compared to

the difficulty that is encountered in opening a pair of doors

when the gap between them is insufficient. The mechanism by

which restraining forces at the slab boundaries can result in

compressive membrane (arch) action is illustrated in Figure 14.

36
Based on experimental results for uniformly loaded laterally

restrained reinforced concrete slabs, Moll [61] obtained the

typical deflection and restraining force versus load curves shown

in Figure 15. Moll identified three distinct phases in the

curves

Phase A, Loading: Due to changes in geometry and cracking, the

edges of the slab tend to move outward and as a result a compressive membrane force can develop.

Phase B, Unloading: At some point, the membrane force will begin

to contribute to, rather than reduce, the deformation of the

slab. Once this point is reached, the membrane force begins

to decrease. In the results that Moll examined, he found

that the transition from phase A to phase B occurs when the

deflection is approximately equal to half the slab thickness.

Phase C, Reloading: After substantial deformations occur, the

edges of the slab tend to move inward and a tensile membrane

force may develop.

For unreinforced slabs, only phases A and B can occur.

The beneficial effect of lateral restraint provided by arching

action in slabs increases with decreasing span-to-depth ratios.

Brotchie and Holley [62] tested square slabs with different spanto-depth ratios and variable amounts of flexural steel. For

slabs with lateral restraint provided at the supports, decreasing

the span-to-depth ratio from 20 to 5 resulted in more arch action

and significantly higher capacities. As the amount of flexural

steel was increased, the improvement in capacities was less

marked

.

Taylor and Hayes [63] tested plain and reinforced slabs failing

in punching shear. Two duplicate specimens were made of each

test slab, one simply supported along the edge and the other

similarly supported but confined horizontally within a steel

frame. Three reinforcing ratios of 0.0, 1.57 and 3.14 percent

and a variable loaded area were studied. Results of their tests

are shown in Figure 16. They found that increases in the

37
punching shear capacity caused by the horizontal restraint were

greater with smaller reinforcing ratios. The increase was 24-60

percent when the corresponding simply supported slabs were near

flexural failure at collapse, but only 0-16 percent when the

corresponding simply supported slabs were not near flexural

failure at collapse.

Aoki and Seki [64] tested fourteen square slabs supported around

the perimeter with edge beams of varying dimensions. The

investigators found that arch action was more effective in slabs

with high concrete compressive strength and lower steel ratios,

however the magnitude of the arch action was difficult to

measure. Their test results indicated that the flexural collapse

load was 2.1 times that calculated without considering the

membrane force, and improvements in shear capacity of up to

67 percent were measured. Equations for predicting the

enhancement resulting from edge restraint are presented, however

it has been noted by Hewitt and Batchelor [65] that the equations

suggested by Aoki and Seki are valid only for the relative

restraint provided by their configuration and should not be

applied to other slab systems.

Tong and Batchelor [66] tested 1/15-scale models of a three span

bridge subjected to concentrated loads. They proposed a method

for predicting the ultimate capacity of the slabs taking into

account the enhancement in strength due to compressive membrane

action. They assumed that the compressive in-plane forces could

be represented by a membrane moment which helped to carry the

applied load. Their proposed method for including in-plane

effects was applied to the tests conducted on the models of the

bridge, and good correlation was obtained. The investigators

concluded that recognizing the compressive membrane enhancement

in slabs would result in significant savings in the reinforcement

required for two-way bridge slabs. However, Masterson and Long

[67] note that the particular approach suggested by Tong and

Batchelor would not be widely applicable until further tests arc

38
done on different slab configurations. Hewitt and Batchelor [65]

have proposed an idealized rational model for predicting the

punching strength of slabs with unknown restraints by extending

the theory of Kinnunen and Nylander [68] (the basics of the

theory suggested by Kinnunen and Nylander are discussed in

Section 4.5). Hewitt and Batchelor suggested that it would be

possible to evaluate limits on the range of the restraint effects

and use this information for design purposes. However, they also

note that more tests are needed.

Many investigators [69-71] have studied the effects of in-plane

forces caused by prestressing on punching shear strength, with

the level of prestressing in the tests varying from zero to as

high as 650 psi. Both normal weight and lightweight concrete

slabs subjected to prestress have been investigated. All

investigators reported increases in punching shear strength

resulting from the prestress, with the ultimate shear strength

increasing approximately linearly with increasing prestress.

ACI-ASCE Committee 423 [72] has recommended a lower bound

expression, shown in Fig. 17, for predicting the punching shear

strength of prestressed two-way slabs. This expression is

included in the current ACI building code [32] and is discussed

in more detail in Section 4.6.1 of this report.

An example of a structure in which tensile in-plane forces can

develop is a reinforced concrete containment vessel when

subjected to combined internal pressure and punching shear loads

normal to the containment wall. Tensile in-plane forces may have

the effect of reducing the capacity of a concrete slab section,

but only a limited number of tests have been conducted.

Researchers at the University of Maine [56,57] reported that

tensile forces on uniformly loaded slabs supported by columns

caused the measured loads for a general flexural failure to be

about 20 percent less than the loads predicted using the moments

for pure bending. Researchers at Cornell University [73,74]

found that the punching shear capacity of slabs was only slightly

39
related to the level of biaxial tension. Johnson and Arnouti

[75] also found that little reduction in shear strength occurred.

The limited amount of work that has been done on the effects of

tensile in-plane forces has not led to a comprehensive

understanding of the relationship, and more work is needed.

It is clear from the research that has been conducted that

compressive in-plane forces can enhance both the flexural and

shear capacities of slabs and shells, particularly for low

reinforcing ratios and high strength concrete. However, the

magnitude of the in-plane forces, and thus the degree of

enhancement, is difficult to calculate since it depends on the

complex interaction of the slab, supports and the surrounding

structure. More work is needed in this area before economies

resulting from the enhancement can be realized.

4.5 PREDICTING PUNCHING SHEAR RESISTANCE

Many equations have been proposed for predicting the punching

shear resistance of concrete slabs, and the strengths predicted

by the different equations vary considerably. Criswell and

Hawkins [37] provide a comprehensive review of the methods and

equations that have' been proposed. Two general design approaches

have developed. The first approach is the use of primarily

empirical equations suitable for codification to predict the

punching strength, and the second is the development of an

idealized model that will capture the dominant behavior of the

punching shear mechanism.

Empirical equations that have been proposed can be classified

into two broad groups, those in which the expressions are mainly

dependent on the concrete strength and those in which the

flexural strength or amount of flexural reinforcement is the main

factor. A summary of the equations that have been proposed is

given in Table 2. Development of the equations is discussed in

Reference 37.

40
While most North American efforts have been directed towards

empirical equations to fit test data that would be suitable for

codification, the European approach has been to develop idealized

models that will provide a realistic conceptualization of the

mechanism of failure [37], The most complete model for punching

shear in a slab is that developed by Kinnunen and Nylander [68].

The basic model has been modified by Kinnunen [45] to include

effects of dowel forces, and also by Anderson [85] to extend the

model to slabs with shear reinforcement. The idealized

axisymmetric model of the slab developed by Kinnunen and Nylander

is shown in Figure 18. The slab outside the inclined crack is

divided into sectors bounded by radial cracks, the perimeter of

the slab, and the inclined crack. Each sector is assumed to

rotate as a rigid body about the apex of the inclined crack and

to be supported on an imaginary conical shell which is in turn

supported on the column. Forces on each sector, except for the

load and the reaction, are proportional to the rotation of the

slab. The shear strength is calculated from the equilibrium

conditions at failure, and collapse is assumed to occur when

tangential compressive concrete strain under the root of the

crack reaches limiting values obtained from tests. Hewitt and

Batchelor [65] evaluated the model developed by Kinnunen and

Nylander by comparing results of the model with previous tests.

They examined 137 slab tests reported in literature, and found a very good comparison of the test load and the theoretical load

predicted by the Kinnunen and Nylander model. They also reported

that the comparison was better than that obtained by evaluating

the punching shear equations suggested by Moe [47].

A different approach in which the classical theory of plasticity

is applied to the problem of shear in concrete structures has

been suggested by Nielsen et al. [86] and Braestrup et al.

[87,88], To calculate the ultimate punching load, the external

work done by the punching force is equated with the internal work

41
dissipated along the failure surface. The load found is an upper

bound solution for the ultimate punching load. The concrete is

assumed to behave as a rigid, perfectly plastic material with the

modified Coulomb failure criterion as the yield condition and the

deformations are governed by the associated flow rule (normality

rule). These assumptions about the constitutive model for the

concrete enable the strength and failure deformations of the

concrete to be described by three parameters: the compressive

strength, the tensile strength, and the angle of internal

friction. Elastic deformations are neglected and unlimited

ductility at failure occurs using these assumptions, resulting in

a modification factor needing to be applied to the theory in

order to obtain a better fit of the predicted strengths with test

data. Also, for the theory to work, the tensile strength of the

concrete is taken as essentially zero, a departure from realistic

conditions. In comparisons of the proposed method with both

punching shear tests and pull-out tests, a good prediction of the

failure surface is obtained. However, different modification

factors must be used with different test series in order to

obtain a good fit of the theoretical strengths with the test

strengths. Further, no method is suggested to account for

variations in the amount of flexural and shear reinforcement.

4.6 CODE PROVISIONS ON PUNCHING SHEAR STRENGTH

A review and comparison is presented of the provisions for the

punching shear resistance of slabs and shells in three major

codes of practice for concrete design: the American ACI 318-83

code [32,33], the European CEB-FIP code [89], and the British

Code of Practice CP110 [90], In all the codes that are reviewed,

the punching shear resistance is calculated as an allowable

nominal shear stress multiplied by a specified critical surface.

However, the provisions in the codes differ considerably in the

value of the nominal shear stress that is to be used, and also

in the definition of the critical surface. Treatment by the coder,

of the various factors discussed in Section 4.4 affecting the

42
punching shear resistance also differs.

4.6.1 ACI 318-83

The ACI code provisions for punching shear are based on equations

that use the strength of the concrete as the primary variable.

The amount of flexural reinforcement is not recognized as having

an effect on the punching shear resistance. The shear strength,

Vc

, of nonprestressed slabs is [Reference 32, Section 11.11.2.1]:

vc

» (2 + i//S0

) b0 a < 4 b

0

d (4-1)

where j3c

b o

f

c

d

= the ratio of the long side to the short side of

the loaded area;

= the perimeter of the critical section located at

a distance of d/2 away from the perimeter of the

loaded area (in);

= the compressive cylinder strength of the

concrete (psi); and

= the distance from the extreme compression

fiber to the centroid of the tension

reinforcement (in)

.

For two-way prestressed slabs, an alternate expression is given

[Reference 32, Section 11.11.2.2]:

v0 = <3.5/^ + 0.3 fpc > b0 a + V

p

(4-2)

where fp C = the average value of the compressive stress in

the concrete (after allowance for all prestress

loss) for the two directions (psi); the value

shall not be less than 125 psi, nor taken as

greater than 500 psi;

Vp = the vertical component of all effective

prestress forces crossing the critical section;

and

43
f'

c shall not be taken as greater than 5000 psi

because of limited test data.

The ACI building code commentary [33] notes that the shear

strength predicted by the equation for nonpr es t r essed slabs

corresponds to a diagonal tension failure of the concrete

initiating at the critical section, while the second equation for

two-way prestressed slabs predicts a punching shear failure of

the concrete compression zone around the perimeter of the loaded

area. Consequently, the code includes the term y§c only in the

first equation for nonprestressed slabs.

To determine the punching shear resistance of slabs and shells

made with lightweight aggregate concrete, the ACI code gives two

alternative procedures that can be used to modify the shear

strength as calculated by the equations discussed above. One

method is based on laboratory tests which determine the

relationship between the splitting tensile strength and the

compressive strength for the particular lightweight concrete

being used [Reference 32, Section 11.2.1.1]. As a simplification, a second method recommends the use of reduction

factors which have been established based on the assumption that,

for a given compressive strength of concrete, the tensile

strength of lightweight concrete is a fixed proportion of the

tensile strength of normal weight concrete [Reference 32, Section

11.2.1.2], Specified reduction factors are 0.75 for alllightweight concrete and 0.85 for sand-lightweight concrete. A

summary of the ACI code equations and provisions is given in

Table 3.

4.6.2 CEB-FIP

Punching shear provisions in the CEB-FIP model code include

factors to account for the reduction in shear strength with

increasing slab or shell thickness, the beneficial effect of

higher amounts of flexural reinforcement, and the beneficial

effect of axial compression, in addition to the usual term that

44
relates the concrete compressive strength to the shear strength.

The shear strength, v Rdl' of slabs without significant

longitudinal forces is [Reference 89, Section 13.4.1]:

vRdl = !•« Tsd K (1 + 50,0 ) u d (4-3)

where 7Trc3 = s ^ ear stress which is based on the cylinder

compressive strength and is given in tables

[MPa]?

K = a depth factor, K = 1.6 - d 2 1.0;

yj = the flexural reinforcement ratio, < 0.008;

u = the perimeter of the critical section

located at a distance of d/2 away from the

loaded area (m); special provisions are given

for loaded areas with aspect ratios greater

than 2? and

d = the distance from the extreme compression

fiber to the centroid of the tension

reinforcement (m).

For members subjected to significant axial compression, including

prestress, the shear strength obtained from the above equation

may be increased by multiplication with the following factor

[Reference 89, Section 11.1.2.2]:

ft 1 = 1 + <«o/Msdu> * 2

where M

s du = the maximum design moment in the shear region

under consideration; and

M Q = the decompression moment for the section

where MS(j u is acting.

For lightweight aggregate concrete, the above provisions apply

except that the factor K is set equal to 1.0 independent of the

value of d [Reference 89, Section 20.11.1], Thus, for slabs with

an effective depth greater than or equal to 0.6 m, no reduction

45
in the nominal punching strength is required by the code when

lightweight aggregates are used. A summary of the provisions on

punching shear of the CEB-FIP code is given in Table 3.

4 . 6.3 CP110

The British CP110 code also includes provisions to account for

the reduction in shear strength with increasing slab thickness

and for the beneficial effect of higher amounts of flexural

reinforcement, in addition to relating the concrete compressive

strength to the shear strength. However it differs from the ACI

and CEB-FIP codes in two major ways. First, the concrete

compressive strength is determined using compressive tests on

cubes of concrete, whereas ACI and CEB-FIP use standard

cylinders. The apparent strength of cubes is approximately 1.25

times higher than that of cylinders due to the state of stress

that exists in a cube under compressive loading. The second

major difference is that the critical perimeter is assumed to be

located at a distance of 1.5 times the total thickness of the

slab away from the perimeter of the loaded area, rather than at

half the effective depth away as in the ACI and CEB-FIP codes.

Part of the motivation for selecting this perimeter as the

critical section is to enable both beam and two-way punching

shear to be calulated using the same nominal shear stress values.

According to the British code, the shear strength, V, of slabs is

given by [Reference 90, Section 3.4.5]:

(4-4)

where v = the nominal shear stress (N/mm 2

) = e 0 vQ

£ 0 = depth factor given in tables; a 20 percent

increase in the shear capacity is permitted

as the slab depth decreases from 300 mm to

150 mm;

v Q = the ultimate shear stress (N/mm ), which

46
is determined from the characteristic

concrete compressive strength and from the

longitudinal tension reinforcement ratio and

is given in tables;

u cr ^ t = the perimeter of the critical section located

at a distance of 1.5 h ( h = the total

thickness of the slab) away from the loaded

area (mm);

d = the distance from the extreme compression

fiber to the centroid of the tension

reinforcement (mm).

Special provisions apply for prestressed slabs. For lightweight

aggregate concrete the above equation applies except that the

specified ultimate shear stresses are multiplied by 0.80

[Reference 90, Section 3.12.7]. The punching shear provisions of

CP110 are summarized in Table 3.

4.6.4 COMPARISON OF THE CODES

Braestrup [87] performed a comparison of the various punching

shear code provisions by making plots of the ratio of the

predicted punching strength versus the calculated punching

strength for four test series: Elstner and Hognestad [43],

Kinnunen and Nylander [68], Taylor and Hayes [63] and Base [91].

The results of his comparison are shown in Figure 19. Braestrup

noted that while the ACI 318-71, CEB-FIP, and British CP110 code

were all rather conservative, the ACI and CEB-FIP were both, in

general, more conservative than the CP110 code. Regan [92]

examined the way various factors affecting punching shear

strength are treated in the ACI 318-71 code and the British CP110

code. Regan showed that the relative strengths predicted by the

two codes will vary depending on the specific parameters being

studied. Under some circumstances the ACI code will be more

conservative, while under others the CP110 code will be more

conservative. However, he concludes that the treatment of

47
several of the factors is superior in the CP110 code.

Numerical comparisons of ACI, CEB-FIP, and CP110 punching shear

provisions, for selected values of slab depth, flexural

reinforcing ratio, and loaded area, as a function of concrete

strength are shown in Figures 20 and 21. These comparisons are

for nominal punching shear strength as material reduction factors

have been included. It should be noted that the different load

factors used by the various codes are not incorporated in the

comparison. Since CP110 provisions are based on characteristic

compressive strengths obtained from cube tests instead of the

standard cylinder tests used by ACI and CEB-FIP, the approximate

relationship that the cube strength is 1.25 times the cylinder

strength was used to convert cube strengths to equivalent

cylinder strengths. Based on an examination of the selected

parameters, punching shear strengths predicted by the CEB-FIP

model code are more conservative than those predicted by the ACI

code, particularly for lower reinforcement ratios and thicker

slabs. However, the CEB-FIP code becomes less conservative

relative to the ACI code as the compressive strength of the

concrete increases. The punching shear strengths predicted by the

CP110 code for the selected parameters also tend to be more

conservative than those predicted by the ACI code. However, the

ACI code provisions become more conservative than the CP1I0

provisions for larger reinforcement ratios and thicker slabs.

It is also interesting to note that, with increasing concrete

strength, the CP110 code becomes more conservative relative to

the ACI code, just the opposite of what was observed in the

comparison of the ACI code and the CEB-FIP model code.

4.6.5 LIMITATIONS OF CODE PROVISIONS ON PUNCHING SHEAR

Current punching shear design provisions are based on data

obtained from experimental and analytical studies of relatively

thin and lightly reinforced members, such as building slabs, roof

shells and footings. Although these provisions have been proven

48
to be adequate for conventional construction, their applicability

to the design of thick, heavily reinforced, lightweight highstrength concrete offshore structures can be questioned for many

reasons

.

Failure modes in the thick, heavily reinforced walls of the

offshore structures will involve both flexural and shear

mechanisms, and design formulas will need to incorporate both

effects. Such interaction formulas have been proposed for thick,

prestressed nuclear reactor vessel end slabs subjected to

pressure loadings and are discussed in Section 5.2.

Insufficient data exists concerning the shear strength behavior

of high-strength concretes. Current ACI design formulas base the

shear strength of the concrete on the square root of the

compressive strength. This relationship was proposed before the

widespread use of high-strength concrete and, as discussed

previously, this relationship may not be valid at higher

strengths. In addition, there is the question concerning the

shear strength of high-strength concretes made with lightweight

aggregates. It does not seem probable that the reduction factors

specified for lightweight aggregates typically used in normal

strength concretes will apply.

There will clearly be a beneficial effect if in-plane compressive

forces are present. However, with the exception of the CEB-FIP

model code, no provisions are made to take this into account in

calculating the punching strength (other than for prestressed

slabs). Further testing is needed to quantify what effect inplane restraint will have in both slabs and shells in order to be

able to take advantage of this beneficial effect in design.

The current ACI code does not recognize any effect on the

punching shear strength of the amount of flexural reinforcement

or the thickness of the slab or shell. Because of the large

amounts of reinforcement that will be present in the walls of

49
Arctic offshore structures, and because of the very large

relative thicknesses that will be used, it seems likely that

neglecting these factors will be more significant in the design

of concrete offshore structures than in the design of

conventional concrete structures. A better understanding of

shear transfer mechanisms in thick, heavily reinforced, possibly

prestressed, lightweight high-strength concrete slabs and shells

is essential.

50
5.0 RECENT RESEARCH IN PUNCHING SHEAS

5.1 PUNCHING SHEAR IN THICK SLABS

The punching shear behavior of thick concrete slabs was studied

by Kinnunen, Nylander and Tolf [53] at the Royal Institute of

Technology in Stockholm, Sweden. Static punching shear tests

were performed on five rectangular concrete slabs supported on

circular center columns. Both prestressed and nonprest ressed

slabs were investigated. The thicknesses of the test slabs were

approximately those of typical full size bridge decks. The main

objective of the investigation was to study the influence of slab

thickness on the punching shear strength of slabs with and

without shear reinforcement.

In the series conducted on nonprestressed slabs, three 0.73 m (29

in.) thick slabs reinforced with high-strength deformed bars were

tested. Two of these slabs were provided with shear

reinforcement in accordance with the Swedish concrete code. The

results of these tests were compared with results obtained in a previous investigation conducted by Nylander and Sundquist [93]

on similar but smaller scale slabs. When the punching failure

loads were compared, it was found that the ratio between the

measured and calculated failure load decreased as the effective

slab thickness increased. For the slabs without shear

reinforcement, the reduction in shear strength was 25 percent and

45 percent for effective slab depths of 0.2 m (8 in.) and 0.62 m

(24 in.), respectively, than for an effective slab depth of 0.1 m

(4 in.). For the slabs with shear reinforcement, the reduction

in strength was considerably less, approximately 10 percent.

In the series conducted on prestressed slabs, two 0.55 m (22 in.)

thick slabs with prestressing running in one direction were

tested. The prestressing resulted in a mean compressive stress

in the concrete of 5.36 MPa (777 psi) in the prestressed

51
direction. One of the prestressed slabs was provided with shear

reinforcement in accordance with the Swedish concrete code. The

results of these tests were also compared with results obtained

in a previous investigation conducted by Nylander, Rinnunen and

Ingvarsson [94] on similar but smaller scale prestressed slabs.

For the prestressed slabs without shear reinforcement, the shear

strength was 30 percent lower for an effective slab depth of

0.471 m (19 in.) than for an effective slab depth of 0.207 m (8

in.). For the prestressed slabs with shear reinforcement, the

reduction in strength with the larger depth was only 5 percent.

To monitor the progression of shear cracks within the slabs, four

vertical brass tubes, with a diameter of 10 mm (0.40 in.) and a wall thickness of 1 mm (0.04 in.), were placed in each specimen

at a distance of half the effective slab depth away from the

periphery of the column on each of the four major axes. The

brass tubes were smooth and equipped with anchor plates at each

end, and strain gages were mounted at the midheight of the tubes.

In the slabs with shear reinforcement, gages were placed on the

shear reinforcement at the middepth of the slab. Close agreement

was observed between the predictions of crack progression

based on results obtained from gages on the tubes and the

predictions based on results obtained from gages on the shear

reinforcement. It was observed that the load level at which

shear cracking first occurred was approximately the same for the

shear-reinforced slabs as for the slabs without shear

reinforcement. However, the load at which failure occurred was

greater relative to the first cracking load in the slabs with

shear reinforcement. In the prestressed slabs, the load level at

which shear cracking first occurred was higher than that in the

nonprestressed slabs, and also the first cracking load was closer

to the ultimate load. It was also noted by the investigators

that shear cracking did not develop uniformly around the column,

but rather cracking progressed around the column as the load

increased

.

52
The shape of the shear cracks was examined after failure. The

angle of the failure surfaces with respect to the plane of the

slab varied from 29° to 42° in the nonprestressed slabs, although

in some cases it was noted that the cracks followed along the

flexural reinforcement layer towards the periphery. The flatter

cracks were observed in the slab without shear reinforcement. In

the prestressed slabs, the crack inclinations were strongly

influenced by the presence of prestress. Shear cracks that

formed perpendicular to the direction of prestressing were very

steep, developing at approximately an angle of 45°. In contrast,

shear cracks that developed in the prestressed direction were

very flat, ranging from 14° to 18°. In none of the tests on

prestressed slabs did the shear cracks parallel to the

prestressing direction penetrate through the thickness of the

slab

.

Eased on this study, the investigators concluded that size effect

has a significant influence on punching shear strength and must

be considered when evaluating the results of model tests and

drawing conclusions about prototype behavior. They also

concluded that size effect is highly decreased if the slab is

provided with shear reinforcement. The results of this

investigation and the previous investigations on thinner slabs

were incorporated into the Swedish code for concrete structures,

BBK 79, and the CEB-FIP Model Code for Concrete Structures, by

introducing a depth factor into the punching shear design

equations

.

5.2 PUNCHING SHEAR IN NUCLEAR REACTOR STRUCTURES

The behavior of nuclear reactor containment structures under

extreme load has been studied extensively in the last 20 years.

Thick, heavily reinforced and prestressed concrete walls are

normally used in the construction of the containment vessels.

Many experimental and analytical investigations have been carried

out in order to obtain a better understanding of the complex

53
failure mechanisms that can occur in these vessels. Punching

shear failures may occur in a reactor structure in at least two

ways: (1) the punching out, under internal pressure, of the end

caps on the reactor vessel, and (2) the local punching failure of

the reactor walls under impact of missiles (projectiles). A

review of some of the investigations conducted in this area is

presented

.

5.2.1 REACTOR VESSEL END SLABS UNDER PRESSURE LOADING

The configuration of a prestressed concrete reactor vessel (PCRV)

is typically that of a cylindrical barrel with flat end slabs.

The behavior of the barrel section under pressure loading is

relatively well defined, however the behavior of the PCRV end

slabs is more complex [95]. The end slabs are significantly

thicker than would be encountered in conventional slab

construction, with span-to-depth ratios typically in the range of

2 to 3.5 [96]. Under internal pressure, the end slabs are

subjected to high flexural and shear stresses. Although flexural

failures in PCRV end slabs have been reported in model

investigations conducted at the University of Illinois [97], most

end slabs of conventional design would fail in shear [96].

Observed modes of failure in PCRV end slabs are similar to the

shear failures occurring in slabs at column intersections.

Cracking occurs first in the negative moment region near the

connection of the end slab to the barrel section and in the

postive moment region on the exterior surface of the end slab

opposite the applied load, as shown in Figure 22 [98]. As

loading progresses, the radial cracks spread toward the edge of

the slab and a compression zone develops due to flexural

distortion. At some point an inclined tensile crack forms near

the middepth of the end slab at approximately 45 degrees. This

inclined crack propagates outward to the unloaded surface of the

slab and inward to the compression zone. Thus the load is

resisted by a dome carved out of the end slab, as shown in Figure

54
22. This dome will fail by shear-compression (failure of the

compression zone) or by punching shear when a plug of concrete in

the form of a truncated cone is extruded [95],

A study of the behavior of 20 model PCRV end slabs was conducted

by Langan and Garas at Taylor Woodrow Construction Ltd. [96].

Some of the conclusions from their study may be relevant to

punching shear in offshore structures. An increase in the

thickness in relation to the span had the effect of increasing

the shear strength in the end slabs. Reducing the span-to-depth

ratio from 2.5 to 2.0 in otherwise identical models increased the

shear strength by 20 percent. The effect of concrete strength on

the shear strength was examined in similar models where the

compressive cylinder strength of the concrete varied from 3000 to

8000 psi (20.7 to 55.2 MPa). The ultimate shear strength was

found to be approximately proportional to the square root of the

compressive strength for the range of concrete strengths tested.

The presence of hoop prestress provided lateral restraint which

resulted in an increase in the ultimate shear strength, but the

rate of increase in shear strength progressively fell. Beyond a prestress level of 1200 psi (8.3 MPa), the restraint provided had

no significant effect on the shear strength. The investigators

noted that while restraint provided by the supports will have a beneficial effect on the shear strength, beyond a certain level

the beneficial effects will be negligible, as they found in the

slabs with hoop prestressing. The researchers concluded that the

contribution of dowel effects is very small in slabs of this

nature when subjected to punching shear.

The researchers developed an empirical equation for predicting

the shear capacity of end slabs, taking into account the effect

of lateral prestress, depth-to-span ratio and the strength of the

concrete:

(5-1)

55
where P = the pressure resulting in failure, psi;

d = the depth of the end slab;

D = the diameter of the loaded area;

f' c = the compressive cylinder strength, psi;

<t> = the total diameter of the end slab; and

f^ = the average compressive stress from the

prestress, psi.

lateral

The researchers noted that this equation is based on a limited

number of tests on a specific structural configuration, and

additional data is needed before a more generally applicable

expression can be developed.

Cheung, Gotschall and Liu [95] examined results from 69 model

tests on PCRV end slabs in which the effects of major parameters

on the ultimate strength were investigated. Recognizing the

similarity of the failure mechanism in end slabs to that of the

shear failure that can occur at slab and column intersections,

and drawing upon previous investigations on slabs, notably that

of Elstner and Hognestad [99] and Hoe [47], Cheung et al.

developed a shear-flexure interaction expression for end slabs.

The proposed interaction expression was based on yield line

theory and had the following general expression:

(5-2)

where P

C,K

the failure load = 'TtR^G'g;

the ultimate shear load = K 2 TT R D

' c ; the ultimate flexural load = TT R

2 G"F

; the radius of the critical section;

the depth of the head (end slab)

;

the failure pressure of the head;

the pressure corresponding to the flexural failure

of the head; and

constants which are determined by minimizing the

56
standard deviation between theoretical and

experimental results.

By substituting the values of P, P

s and Pp into the equation and

solving for cTg/ the following expression was obtained for the

failure pressure of the head:

2 K D/s/f 7!

^9 — (5- 3)

R + C 2 K Da/F7^

<T f

The constants K and C were determined for end slab designs of

practical interest and then modified to take into account the

contribution of bonded reinforcement, the effects of compression

in the concrete, and the strain capacity of the prestressing

elements. As a result, the following equation for predicting the

ultimate strength of end slabs was obtained:

70 DaJP^

<T

g

= (5-4)

R + 60 D<\/f ' c ~*F

A comparison of the proposed shear-flexure interaction equation

(equation 5-4) with experimental results is shown in Figure 23.

While Arctic offshore structures will not have as high span-todepth ratios as the PCRV end slabs, the procedure used in the

development of the shear-flexure expression may be useful in

developing a similar expression for Arctic structures.

5.2.2 IMPACT LOADING ON NUCLEAR REACTOR CONTAINMENT STRUCTURES

Under hypothetical accident conditions, a nuclear power plant may

be subjected to impact loads from high velocity missiles, such as

turbine blades, aircraft and free falling weights. The impact

57
loads are of a very short duration, 10 to 400 milliseconds, and

may have impact velocities of as high as 1500 fps (450 mps).

Protection against a punching type of failure due to these

impacts is an important consideration in nuclear power plant

design, and considerable effort has been made to develop impact

design criteria for nuclear reactor containment structures.

Experimental programs [100-119] have been conducted to study the

failure mechanisms due to impact loads, obtain load-time

functions of missile penetrations, establish performance

criteria, and develop design formulas to predict the capacity of

the reactor structures under impact loads. Both full- and smallscale model tests have been performed, and in most cases

satisfactory agreement was obtained between the model and fullscale tests when careful attention was given to the modeling

requirements. The investigations found that the high velocity

impact of a missile on a reinforced concrete slab or shell was a localized phenomenon as large deformations and damage occurred

only in the immediate zone of the impact.

Several factors limit the applicability of these experimental

results to offshore structures. First, the loading conditions

and the structural response of the reactor structures when

subjected to impact loads are dynamic. A considerable increase

in punching strength occurs due to the increased strain rate

[116], with the increase in strength with increasing rate of

loading possibly being described by a power law function [101].

These results would not be applicable to offshore structures

subjected to long duration impact loads by slowly moving ice

masses. A second factor limiting the applicability of the

reactor structure results is that the ultimate state behavior of

the specimens in the tests was highly sensitive to the loading

conditions selected for use in the experiments. The material

used to model the missile (deformable, hard or semi-hard), the

size and shape of the missile, and the impact velocity used in

the tests all strongly influenced the behavior, resulting in wide

58
variation and often conflicting results being reported.

Analytical studies have been performed in an attempty to predict

the behavior of reactor structures to impact loads [120-133].

These analytical studies have been conducted both in conjunction

with and separate from the previously discussed experimental

studies. The analytical models used were based on finite

difference and, more commonly, finite element methods. The

models typically incorporate geometric or material nonlinearities

or both, as well as various failure criteria for the concrete and

steel. The techniques used to study the behavior of the reactor

structures under impact, particularly the techniques for

simulating the nonlinear response of the reinforced concrete

structures, are of interest and may be applicable to offshore

structures under ice loading.

5.3 FIBER REINFORCED CONCRETE SUBJECTED TO PUNCHING AND IMPACT

LOADS

The use of steel fiber reinforcement in a concrete structure can

significantly improve the performance of the structure under

loads. In fiber reinforced concrete, cracks can propagate only

by stretching and debonding the fibers. As a result, large

amounts of energy must be input to the structure before a complete fracture of the composite material can occur. Tests

have shown that the toughness of fiber reinforced concrete can be

an order of magnitude higher than that of plain concrete

[134,135]. Kormeling [136] found that the increased energyabsorbing characteristics of fiber reinforced concrete is present

over a wide range of temperatures. The greater ductility

exhibited by fiber reinforced concrete can result in a greater

level of safety in a structure by increasing the structure's

capacity for internal redistribution of forces when overloaded.

Fiber reinforcement can also prevent the total disintegration and

shattering of concrete that is often associated with impact

loads. In marine environments, fiber reinforced concrete

59
structures may be advantageous because of their high resistance

to crack formation, fatigue and seawater corrosion, and also

their improved freeze-thaw and abrasion characteristics

[137,138]. A guideline for specifying, mixing, placing and

finishing fiber reinforced concrete has been developed by ACI

Committee 544 [139].

Swamy and Ali [140] investigated the behavior of reinforced slabcolumn connections made with steel fiber concrete and subjected

to static loadings. The addition of steel fibers delayed the

formation of diagonal cracks within the slab, reduced

deformations at all stages (particularly after initial cracking),

and transformed brittle-type shear failures into gradual and

ductile shear failures and in some instances into flexural

failures. The addition of fibers also increased the ultimate

punching shear capacity. As the volume of fiber reinforcement

was changed from 0.6 to 1.2 percent, the ultimate punching load

increased from 23 to 46 percent with respect to an unreinforced

slab

.

Walraven [141] conducted a series of tests to determine if steel

fibers were suitable as a substitute for traditional punching

shear reinforcement. The tests were carried out on circular

slabs supported along the edge and loaded in the center. Both

normal weight and lightweight concrete specimens were included in

the test series. The amount of steel fibers added to the slabs

ranged from 0 to 1 percent by volume. Walraven found that the

addition of steel fibers increased the ultimate punching capacity

of both the normal weight and lightweight slabs, with the

increase being more pronounced in the specimens made with

lightweight concrete. The increase was found to be approximately

proportional to the increase of the concrete strength measured on

the control specimens. In addition to the increased punching

resistance, the use of steel fibers also considerably enhanced

the post-failure behavior of the slabs.

60
The behavior of reinforced and prestressed slabs made with steel

fiber reinforced concrete and subject to impact loadings also

shows significant improvements over the behavior of slabs made

with conventional reinforced concrete [134,142-145]. In some of

the tests, the addition of fibers increased the tensile strength

of the concrete sufficiently to prevent a punching type of

failure without the addition of shear reinforcement. Impact

tests were conducted on lightweight concrete specimens and

increased strength and impact resistance were reported [134,146].

Arockiasamy et al. [137,147] conducted impact tests on normal and

fiber reinforced cylindrical panels representative of offshore

structures and found that the fiber reinforced concrete panels

were 1.65 to 1.70 times stronger than those of normal reinforced

concrete. The investigators also developed a three-dimensional

nonlinear finite element program to predict the behavior of the

fiber reinforced panels. Nonlinear material properties for the

fiber reinforced concrete were determined by testing fiber

reinforced concrete cylinders.

Gerwick, Litton and Reimer [148] have suggested that the use of

steel fibers in practical proportions for the reinforcement of

offshore structures will not result in adequate ultimate capacity

for the extreme ice loading conditions associated with the

Arctic. However, steel fibers may be added to the structure to

supplement the conventional reinforcement, resulting in improved

performance of the structure and reduced amounts of conventional

reinforcement, particularly shear reinforcement. Combining fiber

and conventional reinforcement may offer significant advantages

over the use of either type of reinforcement alone [140].

5.4 PUNCHING SHEAR IN OFFSHORE STRUCTURES

Only a limited amount of research has been performed to date on

the punching shear behavior of thick slabs and shells that are

representative of offshore structures. Further, results from

many of the investigations that have been conducted are currently

61
proprietary information. The experimental study by Brian Watt

Associates, Inc. (BWA) [34] represents the only major

investigation into the punching shear resistance of offshore

structures for the Arctic in which results are currently in the

public domain. Because of the significance of this investigation

with respect to the current study of punching shear in

lightweight concrete offshore structures for the Arctic, the BWA

investigation is reviewed in depth. Much of the other work that

has been conducted to date has been directed primarily towards

the behavior of North Sea offshore structures subject to ship

collisions. Colbjornsen and Lenschow [149] studied punching

shear in models representative of Norwegian North Sea

structures, and their report is reviewed in some detail. Some

other work on punching shear in North Sea structures is also

briefly reviewed.

5.4.1 BWA PUNCHING SHEAR STUDY

The punching shear resistance of thick slab and shell sections

representative of Arctic offshore structures was investigated by

Brian Watt Associates, Inc. (BWA) [34], The project is listed

by the Alaska Oil and Gas Association (AOGA) as Project No. 152,

and was undertaken on the behalf of eight oil companies.

Ten model specimens were subjected to punching loads: one slab,

one arch and eight cylindrical shells. All of the specimens were

supported along two opposite edges and a concentrated load was

applied at the center of the specimens. The general dimensions

and loading arrangements for a typical specimen are shown in

Figure 24. The main variables investigated in the study as

having a possible effect on the punching resistance were:

1. flexural reinforcement ratios;

2. shear reinforcement ratios;

3. ratio of shell radius-to-thickness (R/t) ; and

4. cyclic loading.

62
The investigators identified radius-to-thickness ratios in the

range of 16 to 42 as being representative of proposed concrete

structures for the Arctic. For the shell specimens, two radiusto-thickness ratios of 12 and 36 were selected as being

reasonably representative. Specimens with these ratios would

also be expected to respond differently to the punching loads

because of the significantly different moment-to-thrust ratios

that would develop in each. Five of the shell specimens were

cast with radius-to-thickness ratios of 12 and three shell

specimens were cast with radius-to-thickness ratios of 36. One

of the shell specimens was subjected to cyclic loading.

The concrete used in the study had an average cylinder

compressive strength at 28 days of 7000 psi (48 MPa), and in none

of the specimens did the strength vary from this value by more

than 7 percent. Regular weight aggregate with a maximum size of

0.4 in. (10 mm) was used which resulted in an average density of

the concrete of 146 pcf (22.9 kN/m^). Even though air

entrainment is expected to be used for concrete structures in the

Arctic because of the resulting improved freeze-thaw

characteristics, air entrainment was not used in the model

concrete because of an adverse interaction with a superplasticizer being used in the model concrete mix to provide

needed flow characteristics.

Two flexural reinforcing ratios of 2.33 percent and 1.67 percent

were used in the test specimens, with all but one specimen having

a ratio of 2.33 percent. These reinforcing ratios represented

the amount of flexural steel on each face and in each direction.

These ratios were selected as being representative of the level

of flexural reinforcement likely to be used in offshore

structures of this type. The average yield strength of the bars

used in the models was 75 ksi (518 MPa).

Determining the effect of different amounts of shear

63
reinforcement on punching shear resistance was one of the main

objectives of the test program. Three shear reinforcing ratios

were investigated: 0, 0.22 and 0.49 percent. Shear

reinforcement was provided in the specimens using conventional

shear stirrups. The yield strength of the shear reinforcement

actually used in the test program was substantially higher than

the targeted yield strength of 40 ksi (276 MPa). The shear

reinforcement used in the models had yield strengths of 53 ksi

(366 MPa) and 106 ksi (731 MPa), depending on the size of bar

being used to provide the shear reinforcement. To account for

the difference in yield strength, an effective shear

reinforcement ratio was used in all calculations. The effective

shear reinforcement ratio was defined as the actual shear

reinforcement ratio multiplied by the ratio of the actual yield

strength to 40 ksi (276 MPa).

The radius-to-thickness ratios of the shell specimens, the rebar

size and spacing, and the material strengths were prescribed in

order to be representive of those proposed for Arctic

structures. The thickness of the specimens was chosen as 6 in.

(15 mm) in order to allow normal concrete to be used instead of

microconcrete. The investigators noted that this thickness would

probably allow for a good representation of aggregate interlock,

dowel effects, etc. A span length and transverse length of 7.5

ft (2.3 m) were selected for the slab and shell specimens in

order to eliminate any support and edge effects on the stresses

and deflections in the vicinity around the applied load.

However, these conclusions were based on linear elastic analyses

and were therefore valid only in the linear elastic response

range of the specimens. Upon completion of the tests, the

investigators observed that the amount of support rotations and

displacements was not constant from specimen to specimen, and

they noted that this may have had an effect on the behavior of

some of the specimens. It is not clear that the investigators

attempted to satisfy modeling similitude requirements in choosing

the thickness, span and transverse dimension, and perhaps other

64
parameters used in their study. Further, the span-to-depth ratio

of their specimens was 15, which may be unrepresentatively high

for proposed Arctic offshore structures.

The investigators recognized that it would not be possible in the

test program to duplicate the actual distribution of ice contact

pressures. Therefore they decided to apply the loads on the

models as a uniform pressure acting over a circularly-shaped

area. This method of applying the loads was chosen as being the

most reasonable loading that could be practically achieved in the

model investigation. This type of loading is also advantageous

in that a uniform pressure is easily applied to a structure in an

analytical model.

Conventional means of applying the loads through a stiff platen

were rejected by the researchers since this would have resulted

in stress concentrations around the edge of the platen. The

loading system shown in Figure 25 was developed to apply a nearly

uniform distribution of pressure on the specimens. Load is

applied through a steel piston acting on a layer of natural

rubber constrained by a steel cylinder. Under pressure, the

rubber will flow, closely simulating fluid behavior. Extrusion

of the rubber is prevented by leather discs. Friction between

the rubber and cylinder is limited by applying silicon grease

along this interface. A somewhat similar loading system was used

in punching tests on PCRV end slabs conducted by Langan and Garas

[96].

In selecting the area of loading to be used in the test program,

it was desired that the applied pressure on the specimens at

failure be representative of the ice contact pressures that might

be experienced by structures in the Arctic, i.e. pressures in the

range of 2000 to 2500 psi (13.8 to 17.3 MPa). Using this range

for the applied pressures and estimating the nominal shear stress

that might be expected to develop in the specimens at failure,

the investigators selected a load diameter of 18 in. (0.46 m) for

65
the shell specimens. Recognizing that the flexural capacity of

the slab specimen would be less than that for the shell

specimens, a load diameter of 6 in. (0.15 m) was chosen for the

slab specimen in order to prevent a premature bending failure of

the specimen before a punching failure could develop.

A special test rig was designed and built for testing the

specimens. Steel end beams were used to transfer the reaction

loads from the specimens into a prestressed concrete base. A

cementitious grout was injected into the interface between the

shell specimens and the steel support beams. This reportedly

produced a fixed support condition, although it is more likely

that the actual support condition was somewhere between fully

fixed and pinned. The supported edges of the slab specimen were

held down by beams which were prestressed to the test rig and

which also provided support conditions somewhere between

perfectly fixed and pinned.

To try to insure that a punching failure rather than a flexural

failure developed first, both the shear and flexural capacities

of the specimens were calculated prior to the beginning of the

testing program. To determine the flexural capacity, a method

was developed to account for force redistribution in the slab and

shells by averaging the moments obtained from elastic analyses.

In the test on the slab specimen, the load which resulted in

failure was much higher than the predicted flexural load capacity

of the slab. However, even though yielding of the flexural steel

did occur, the slab failed in punching and not in flexure,

indicating that the approximate method developed for predicting

flexural capacity was conservative.

As a means to predict, and also to later evaluate, the punching

shear performance of the specimens, the shear provisions of four

codes were examined:

- ACI 318-77 (American) [30]

66
- CEB-FIP Model Code (European) [89] - CP110 (British) [90] - DnV Rules (Norwegian) [150]

Three approaches were used in calculating the punching shear

resistance of the specimens. In the first approach, the shear

resistance was calculated using the conventional punching shear

provisions in the four codes. The ACI and CP110 codes do not

account for any beneficial effects due to compressive inplane

forces (other than for prestressed slabs, see the discussion in

Section 4.6). The CEB-FIP code does contain provisions to

account for membrane compression. The ACI, CEB-FIP and CP110

codes severely limit the maximum permitted shear stresses. The

DnV code does not distinguish between slabs and other elements.

Recognizing that compressive inplane forces would have a significant effect on the punching resistance of the shell

specimens, the investigators considered a "modified punching

shear method" as a second approach. Slab provisions on punching

shear recommended by the codes were used but beam provisions on

membrane compression effects were incorporated. In addition, the

higher limits allowed for beams were used for the maximum

permissible shear stresses. A third approach using beam

provisions on a critical section at a distance of the effective

depth of the specimen away from the perimeter of the load was

also considered.

The slab and all shell specimens failed in punching shear when

subjected to the local loading. Cracking of the specimens

primarily occurred only in the vicinity around the load.

Observed crack inclinations in the failed specimens ranged from

24° to 53° with respect to the plane of the specimen, the flatter

crack inclinations occurring in the transverse direction of the

specimens. Failure in the specimens was relatively ductile in

that there was no significant sudden loss of load and the

specimens were capable of sustaining at least 60 percent of the

67
ultimate capacity at deformations substantially greater than

those at the ultimate loads. This was true even for the case of

the shell specimen with no shear reinforcement.

The nominal shear stresses at failure in the test specimens,

defined on a critical section at a distance equal to half the

effective depth away from the edge of the loaded area, were:

vu = 13.5 slab;

vu

= (11.0 to 14.0) shells with R/t = 36; and

vu

= (15.0 to 18.0) Vf' c shells with R/t = 12.

These nominal shear stresses are considerably higher than the

upper limits on shear stresses allowed by the four codes

examined. It is worth pointing out that the nominal shear

stresses that will develop will be influenced by the size of the

loaded area relative to the thickness (see Section 4.4). Thus,

it may not be appropriate to compare the slab failure stresses,

obtained with a load diameter of 6 in. (0.15 m) , to the shell

failure stresses, obtained with a load diameter of 18 in. (0.46

m) .

Shear cracking initiated in the specimens when the nominal shear

stresses, defined on a critical section at a distance equal to

half the effective depth of the specimen away from the perimeter

of the loaded area, reached the following levels:

v cr

= (3.5 to 5.0) */f

c slab, shells with R/t = 36; and

vcr

= t0 V^'c shells with R/t = 12.

The reason that the load at which shear cracks first occurred is

higher in the shell specimens with greater curvature is due to

the higher levels of membrane compression generated in these

shells

.

Approximately 78 to 89 percent of the ultimate shear capacity of

68
the shear reinforced specimens was found to be provided by the

concrete. The remaining 11 to 22 percent of the ultimate

capacity was carried by the shear reinforcement. Increasing the

amount of shear reinforcement had a greater effect on the

shallower shells. Average gains in the ultimate punching

strength of 6 percent and 12 percent were realized for every

0.001 increase in the shear reinforcement ratio for the shell

specimens with r adius-to-thickness ratios of 12 and 36,

respectively. The effect of increasing the amount of shear

reinforcement on the ultimate capacity is shown in Figure 26.

Increasing the shear reinforcement ratio also resulted in an

increase in the load at which shear cracking first occurred.

Two identical shell specimens were tested except that one shell

had 43 percent more flexural reinforcement than the other. No

significant difference in ultimate capacity or general failure

mode was observed in the tests on the two specimens.

The specimen subjected to cyclic loading underwent 100 cycles of

loading at different load levels prior to progressing to failure.

When the cycled loads were below that which caused the initiation

of shear cracking, no significant difference in performance was

observed from the specimen loaded to a similar load level

monotonically. However, when the load cycles extended above the

level at which shear cracking initiated, progressive development

of the shear cracks occurred with each cycle. This would be

expected to result in a degradation of the shear capacity.

However, the specimen subjected to the cyclic loads failed at a higher load than did the comparable specimen loaded

monotonically, suggesting that further tests on the effects of

cyclic loading are needed.

The investigators found that the conventional punching shear

provisions of all four codes examined were highly conservative in

predicting the capacity of the test specimens. This was

particularly true for the ACI code provisions where the measured69
to-predicted capacity ratios were between 3.3 and 6.5.

Comparisons of the test results with the predicted capacities are

shown in Figures 27 and 28. Use of the modified punching shear

method suggested by the investigators, which allows for membrane

compression effects, resulted in closer agreement between the

measured and predicted capacities. The "ACI Modified Punching

Shear Method" resulted in measured-to-predicted capacity ratios

between 2.01 and 2.26 (see Figure 29). Punching shear

resistances predicted using the beam shear provisions in the

codes resulted in the closest agreement with the measured

resistances, however the investigators suggested that use of this

third method to predict the punching shear capacity may not

provide an adequate factor of safety for design. Based on the

limited number of tests conducted, the investigators recommended

their suggested "ACI Modified Punching Shear Method" as being

the most appropriate for designing Arctic offshore structures to

resist punching shear.

A conclusion of the BWA study was that linear elastic analyses

could be used to adequately predict the ultimate punching shear

capacities of the slab and shell sections of offshore structures.

However, large safety factors would have to be used in the design

in order for this analysis tool to be used with any measure of

confidence. Further, results from the investigation point out

the inability of the elastic analysis techniques to describe the

ultimate state response of the slab and shell specimens when

subjected to punching loads.

Upon the completion of their testing program, the investigators

identified several areas where further work was needed in order

to improve the understanding of shear behavior in arctic offshore

structures. These include investigations into:

- the effect of support flexibility on punching shear

resistance;

- the strength of repaired members;

70
- the use of lightweight concrete in the models;

- the effect of longitudinal prestressing;

- the use of headed stirrups for shear reinforcement as

rebar congestion with conventional stirrups is a problem;

and

- improved analytical methods.

The first two areas that were identified have been investigated

under AOGA Project Nos. 152 and 198, the results of which are not

yet publicly available. The remaining four areas identified are

being addressed by the current research project at the National

Bureau of Standards on the punching resistance of lightweight

slabs and shells.

5.4.2 PUNCHING IN PRESTRESSED CYLINDRICAL SHELLS: NORWEGIAN

WORK

A study was undertaken in Norway to investigate the behavior of

marine structures in the North Sea subjected to punching loads

resulting from ship collisions [149]. Six 1/10-scale models of

cylindrical shells representative of the Condeep structures were

tested. The shell models contained conventional reinforcement

and were prestressed in the longitudinal direction. To

approximate continuity conditions, an edge beam was cast onto

each end of the shell specimens. The general geometry and

dimensions of the test specimens are shown in Figure 30.

The variables selected for study in the investigation were the

size and shape of the loaded area. Two specimens were tested

with applied load areas of 5 cm X 5 cm (2 in. X 2 in.), two with

areas of 5 cm X 15 cm (2 in. X 6 in.), and two with areas of 5 cm

X 25 cm (2 in. X 10 in.). For the tests on specimens with

rectangular load areas, the direction of the long dimension of

the load was alternated in the two tests between the circular and

longitudinal direction. Steel plates were used to apply the

loads to the specimens, with a layer of plaster being placed

71
between the specimens and the steel plate.

The concrete used in the specimens had an average cube strength

of 38.8 MPa (5600 psi), corresponding to an approximate

compressive cylinder strength of 31 MPa (4500 psi). Mild steel

flexural reinforcement was provided in both directions and on

both faces, with flexural reinforcing ratios of 3.14 percent in

the circumferential direction and 2.00 percent in the

longitudinal direction (the reinforcing ratios being based on the

total area of steel in both faces). The flexural reinforcement

consisted of 6 mm (0.24 in.) diameter bars with a yield strength

of approximately 410 MPa (60 ksi). No shear reinforcement was

provided in any of the test specimens. Prestressing was provided

in the longitudinal direction resulting in an effective

centroidal prestress in that direction of 7 MPa (1014 psi).

The ultimate punching capacity of the shells was found to be

significantly higher than would be expected based on results of

previous tests conducted on slabs. The investigators attributed

this increase in strength to the presence of prestressing and the

arch action that developed because of the cylindrical shape of

the specimens. Increases in load carrying capacity were observed

with increasing area of loading, which is to be expected as the

failure surface is also increasing. In tests conducted on

specimens with the same area of loading, the greater capacity was

found to occur in the case where the long dimension of the

rectangularly-shaped loaded area was in the circumferential

direction rather than in the longitudinal direction of the shell.

Crack angles in the failed specimens ranged from 20° to 70° with

respect to the plane of the specimen, with the steeper cracks

forming in the circucumferential direction and the flatter cracks

forming in the prestressed longitudinal direction.

The investigators attempted to accurately estimate the true area

of the failure surface in the specimens. Using this area, the

investigators then calculated a nominal failure stress on this

72
surface and found that in all six tests, even though the ultimate

capacity varied considerably, the failure stress was almost

constant at 1.7 MPa (250 psi). For comparison, the nominal shear

stress can be calculated at a critical surface of half the

effective depth of the specimen away from the perimeter of the

loaded area, as per ACI code provisions. Results from the tests

indicate that nominal shear stresses of between 9.0 and 11.0 f

c developed, based on an f'

c value of 4500 psi. This is

significantly higher than the stresses specified in the current

ACI code.

5.4.3 OTHER PUNCHING SHEAR STUDIES ON OFFSHORE STRUCTURES

Sorensen [151] conducted a theoretical and experimental

investigation on the impact resistance of tubular structural

members of concrete offshore structures. Sorensen noted that

punching shear in cylindrical tube walls representative of

offshore structures would differ from punching shear in slabs in

two major ways. First, the cylindrical shape would result in

compressive membrane forces developing which would increase the

punching resistance. Compressive membrane forces would also

occur if prestressing was provided in the tube walls. The second

reason for a difference is that wall thicknesses in the offshore

structures will be larger than the thicknesses of previously

tested slabs so that possible extrapolation from slab test

results, expecially concerning shear failures, may give

misleading results.

In discussing the stresses in the specimens, Sorensen notes that

the real stress distribution is complex. In a thick tube,

inclined cracks will not develop simultaneously in all directions

and stress redistribution may occur. Sorensen suggests that the

ultimate punching resistance may be calculated using the tensile

strength acting on a conical ultimate fracture surface. He

suggests the following formula for calculating the punching

resistance of thick tubes:

73
P (5-5) u = 'Tf M h (d + M h) f c

where P

u = the ultimate load capacity;

h = the thickness of the tube;

d = the diameter of the circular loaded area;

f c

= the tensile strength of the concrete;

M = V 1 + CTm/fc ; and

<Tm

= the effective membrane stress.

The magnitude of the effective membrane stress will depend on the

radius-to-thickness ratio of the tube and the level of prestress.

Regan and Hamadi [152] conducted tests to investigate the

behavior of concrete caisson and tower members subjected to

combined bending and shear, including some tests aimed at

gathering information on the punching resistance. The specimens

tested were hollow cylinders with an external diameter of 0.80 m

(31.5 in.) and a wall thickness of 0.04 m (1.57 in.). The

concrete used in the specimens had an average cube strength of 50

MPa (7250 psi), corresponding to an approximate compressive

cylinder strength of 40 MPa (5800 psi). Both prestressed and

nonprest ressed specimens were tested. The models used in the

investigation provided a reasonable representation of the lower

ends of towers of North Sea platforms with a scale factor of

approximately 1:20 to 1:25.

Crack angles of approximately 20° in the longitudinal direction

and approximately 30° in the circumferential direction were

observed on the failure surfaces. Results of this investigation

into the punching behavior are summarized in Figure 31. Two

lines are shown on the figure. The top line gives a reasonable

fit to the test data and corresponds to a nominal shear stress of

4.5 MPa (625 psi) acting on a critical section at a distance of

half the depth of the wall away from the perimeter of the load.

The bottom line represents the predictions of the ACI code, and

74
gives shears which are approximately half those of the top line.

The investigators identified three factors in addition to the

general conservatism of the code that might explain why the

experimental strengths were far greater that the predicted

values:

1. the presence of prestress in some of the specimens;

2. the curvature of the shells resulting in compressive

membrane action; and

3. the effects of scale in the model tests.

While results of these tests are of interest, the investigators

noted that further work is needed before conclusions can be drawn

about the punching resistance of curved shells.

Kavyrchine [153] conducted statical and low speed dynamic tests

on cylindrical concrete shells. The specimens had an exterior

diameter of 0.716 m (28 in.) and a wall thickness of 0.058 m

(2.28 in.). Reinforcement was provided at the mid-thickness of

the specimens. The ultimate strength of the specimens was

essentially the same in both the static and dynamic loading

tests, and might be attributed to the relatively low speeds used

in the dynamic tests. The presence of prestressing in the

specimens was found to have a negligible effect on the punching

behavior. The investigators used the analytical procedure

suggested by Braestrup (see Section 4.5) to predict the

capacities of the tested specimens. After some manipulation of

the factors in the procedure to account for different loading

mechanisms, the investigators obtained experimental-to-predicted

capacity ratios in the range of 0.81 to 1.26.

5.5 FINITE ELEMENT PREDICTIONS OF PUNCHING SHEAR STRENGTH

Finite element models of reinforced concrete structures are based

on representing the concrete and steel reinforcement by an

assembly of finite elements and specifying appropriate

75
constitutive relationships to govern the behavior of the

materials. The problem of predicting the punching shear behavior

of reinforced concrete slabs and shells is very complex and has

not yet been completely solved for the general case.

Consideration must be given to the nonlinear behavior of the

concrete and reinforcing steel, possible dowel action and bond

failure of the reinforcement, and, most importantly, cracking of

the concrete. Further, the stress and strain distributions

through the thickness must also be considered, so the problem

becomes three-dimensional.

A brief discussion of the problems that are encountered in using

finite elements to predict punching shear strength is given,

along with a presentation of some of the approaches that have

been suggested for solving these problems. For illustrative

purposes, three examples of finite element analyses of punching

shear in slabs are presented. A comprehensive review of finite

element applications to reinforced concrete structures can be

found in the ASCE "St ate-of-the-Art Report on Finite Element

Analysis of Reinforced Concrete Structures" [154]. A literature

review of finite element techniques for modeling shear in

reinforced concrete structures has been performed by Noguchi and

Inoue [155].

An accurate description of the nonlinear, multiaxial stressstrain relationship of concrete is very complicated. Three

constitutive models have been shown to be promising [154].

Ottosen [156,157] has developed a constitutive model using four

parameters to define the material behavior, and the model has

been shown to provide a close approximation of experimental

results over a wide range of stress states for short-time,

monotonic loading of concrete [154]. Another important

constitutive model is the Wil lam-Warnke failure criterion [158]

which uses five parameters to numerically represent the failure

surface of concrete under three-dimensional states of stress. A

third constitutive model for concrete that has been successfully

76
used is the "endochronic theory of plasticity" proposed by Bazant

and Bhat [159]. The endochronic theory uses increments of strain

as a measure of intrinsic time (always positive). This intrinsic

time is used to measure the extent of change (or damage) of the

internal structure of the concrete when it is subjected to

deformation histories [154], Another important aspect in

addition to describing the behavior of the material under any

state of stress is that the constitutive model must also describe

the behavior beyond the peak stress, i.e. tension and compression

softening of the the concrete once the peak stresses have been

reached

.

Material modeling of the steel reinforcement is fairly well

defined. The steel can be represented using an elastic-perf ectly

plastic material model, or if added refinement is needed, it may

be modelled as a bilinear material. Reinforcing bars can be

represented in the finite element model as truss elements

connected at node points, or as beam elements if dowel effects

are to be included in the analysis. The reinforcement may also

be represented by an equivalent smeared layer of steel. Bond

between the reinforcement and the concrete has been modelled

using linkage elements (e.g. Scordelis [160]). More recently,

fracture mechanics has been used by Ingraffea et al [161] to

study and model bond-slip behavior. Fortunately, in many

practical applications perfect bond between the concrete and

reinforcement may be assumed with little loss in accuracy.

Tensile cracking in concrete has been recognized as the dominant

nonlinear effect in reinforced concrete structures [154], Two

approaches have been used for representing cracks: discrete

crack modeling and smeared crack modeling. Historically, the

first approach used to represent cracks in finite element

analyses of reinforced concrete members was to model the cracks

as discrete discontinuities along element boundaries (e.g. Ngo

and Scordelis [162] and Nilson [163]). This approach suffers

from the drawback that the finite element mesh must be updated

77
after the formation of each crack, and the model also lacks

complete generality in possible crack direction [154], These

problems associated with the discrete cracking model have led

many investigators to adopt the so-called "smeared" cracking

model where instead of one discrete crack forming, many finely

spaced (or smeared) cracks form perpendicular to the principal

stress direction once the limiting tensile stress has been

exceeded. After cracking has occurred, the modulus of elasticity

of the material is set to zero for the direction perpendicular to

the principal stress. Using the smeared crack approach, the

finite element mesh does not need to be updated during the

analysis, which is a significant improvement over the discrete

crack approach. However, some drawbacks do exist with the

smeared crack approach. In some instances, the smeared cracks

may be excessively diffused, resulting in an inability to predict

dominant crack patterns. In addition, aggregate interlock and

dowel effects can be accounted for only indirectly with the

smeared crack approach.

Recently, attention has again been given to representing cracks

as discrete discontinuities, particularly in combination with

using fracture mechanics for the criteria for crack propagation

(e.g. Kesler, Naus and Lott [164], Ingraffea and Gerstle [165],

and Ingraffea and Saouma [166]). However, it should be noted

that there is some question about the practical applicability of

fracture mechanics to reinforced concrete, at least at its

current state of development [154],

Once cracking occurs in the concrete, shear will be transferred

across the crack by aggregate interlock. Relatively simple

linkage elements at discrete cracks have been used to model

aggregate interlock (e.g. Ngo and Scordelis [162]). More

elaborate shear transfer models have also been developed, such as

those of Walraven [167], Pruijssers [168], and Bazant and

Gambarova [169]. A more common approach to modeling of aggregateinterlock has been to assume that some portion of the shear

78
stiffness of the element remains after the element cracks. Many

investigators (e.g. Hand, Pecknold and Schnobrich [170] and Lin

and Scordelis [171]) have used this "shear retention factor" to

include not only the effects of aggregate interlock, but also to

include dowel effects and any remaining shear transfer in the

concrete. The shear retention factor has thus become a "catch

all" for mechanisms of shear transfer that are otherwise not

explicitly incorporated into the analytical model.

Loseth, Slatto and Syvertsen [172] used finite elements to

predict the punching shear capacity of the circular slabs tested

by Kinnunen and Nylander [68], Because of the nature of the test

slabs, Loseth et al. were able to achieve an accurate formulation

of the problem using an axisymmetric finite element model rather

than a full three-dimensional model, resulting in a huge

reduction in the amount of computational time needed to solve the

problem. Moreover, the investigators noted that a full threedimensional program with the necessary capabilites was not

available. A modified version of the endochronic theory was used

for the concrete material model. For comparison purposes, a simple elastic-plastic constitutive model was also used. Tension

failure in the concrete was modeled by assuming a gradual

softening of the material, and tensile cracks were represented

using the smeared crack approach. The steel reinforcement was

modelled in the slabs as smeared layers. Aggregate interlock,

friction and dowel action of the reinforcement were accounted for

by applying a shear retention factor. An example of their

analyses is shown in Figure 32a. The modified endochronic theory

using a shear retention factor of 0.2 provided the best results.

Tao and White [173] used finite elements to predict the punching

shear capacity of slabs tested at Cornell University [74]. The

slabs were modelled as a layered system of concrete and steel,

drawing upon the work of Scanlon [174] and Hand, Pecknold and

Schnobrich [170]. The stiffness matrix for an element is

obtained by integrating the contribution of each layer. Each

79
layer is assumed to be in a state of plane stress, and thus a biaxial material model is sufficient to describe the behavior of

the concrete. Shear deformation through the thickness of the

slabs is approximately accounted for using this method. Cracking

was represented using the smeared crack approach. A shear

retention factor was incorporated into the program to account

for dowel action and aggregate interlock, based on the approach

of Lin and Scordelis [171]. An axisymmetric finite element

formulation was used in order to simplify the program. An

example analysis of a test slab is shown in Figure 32b.

Borst and Nauta [175] used a finite element program to predict

the shear strength of reinforced concrete beams and slabs. A

modified smeared cracking approach was developed in which the

total strain at a point was decomposed into a concrete strain

component and a crack strain component, as originally suggested

by Litton [176] and Bazant and Gambarova [169]. This

decomposition allows for treatment of both concrete nonlinearity

and cracking at one integration point. Borst and Nauta's

approach also allows cracks to develop at any arbitrary

inclination angle and multiple cracks can occur in one

integration point. In their study, the investigators assumed

that the nonlinear behavior of the reinforced concrete beams and

slabs was dominated by tensile cracking, and they therefore used

a simple linear elastic material model for the concrete in

compression. Axisymmetric finite element analyses were performed

of punching shear tests on slabs conducted at Delft University.

An example of their analyses, using a shear retention factor of

0.2, is given in Figure 32c.

To date, most of the attempts to predict punching shear strength

using finite elements have been performed using an axisymmetric

formulation of the problem. Offshore structures, particularly

those with cylindrical shapes and one-way prestressing in the ice

walls, are not adequately described by an axisymmetric model.

Rather, a full three-dimensional model is needed. Gerwick et al.

80
[148] have performed nonlinear finite element analyses of

offshore structures using a two-dimensional plane strain

formulation, but this formulation is actually modeling a line

load acting on the structure rather than a localized punching

load. An important advancement in the ability to analyze

offshore structures subjected to punching shear will be the

availability of a three-dimensional finite element program

incorporating the features that are currently included only in

two-dimensional programs. It may be possible to simplify some of

the criteria to reduce the computational requirements of the

problem and yet retain the dominant behavior, as was done by

Borst and Nauta when they used a linear elastic material model

for the concrete in compression.

81
6.0 SUMMARY

The punching shear resistance of lightweight, high strength,

heavily reinforced slab and shell sections representative of

proposed Arctic structures is being investigated at the National

Bureau of Standards. The project is being sponsored by The

Minerals Management Service of the U.S. Department of the

Interior and five American oil companies. Both analytical and

experimental studies are planned. This report reviews current

knowledge on punching shear and other subjects relevant to the

project

.

Arctic offshore structures will be required to withstand

tremendous global and local ice pressures. Knowledge of the

behavior of ice action on Arctic structures is limited. Current

investigations include analytical, experimental, and field

measurement studies of ice forces. A coordinated effort using

all three approaches is necessary before design values of ice

forces for Arctic structures can be selected with any measure of

confidence. Design values of ice forces used in proposed designs

are based to a considerable extent on engineering judgement.

Design curves have been proposed, but the magnitudes of ice

pressure vary from curve to curve. The only agreement on local

ice pressure design values is that as the contact area gets

larger, the pressure should decrease. There is a need for more

research into the interaction of Arctic structures with ice.

Proposed structures for the Arctic can generally be classified

into three categories: island structures, gravity structures and

floating structures. The choice of a particular structural

concept will depend upon the location, usage, and depth of

operation for which the structure is intended. Only a limited

amount of design information is publicly available on existing

and proposed Arctic offshore structures.

82
The basic theory of punching shear and the mechanism by which it

occurs were discussed, and a comparison was made of beam and

punching shear action. Nine factors that may have an effect on

the punching shear resistance of a slab or shell were identified.

Most methods to predict punching shear strength have been based

on empirical equations, although some conceptual models for

predicting punching shear strength have been developed. Code

provisions of three major codes of concrete practice, the ACI,

CEB-FIP , and CP110 codes, were reviewed and a comparison made.

Some limitations of the current code provisions were noted.

Various investigations of punching shear strength relevant to the

project were reviewed. Size effects due to increased slab

thickness were observed in tests conducted in Sweden. Punching

shear tests on nuclear reactor structures due to internal

pressure loading and impact loading, while not directly

applicable to offshore structures, are useful in that the

techniques used to conduct the tests and the approaches used to

develop design equations may provide guidance for the testing

and design of offshore structures. Further, the analytical

tools developed to analyze the reactor structures may also be

useful for analyzing offshore structures. Fiber reinforcement

has been shown in model tests to significantly improve the

punching shear performance of slabs and shells. A limited number

of investigations has been conducted on the punching shear

resistance of offshore structures, the most notable of which is

the study conducted by Brian Watt Associates, Inc. In all of the

investigations reviewed, the observed strengths of the test

specimens were considerably higher than those predicted by any of

the codes. Current finite element approaches for predicting

punching shear strength yield good results for particular cases.

However, the general, three-dimensional problem of punching shear

in a slab or shell has yet to be completely solved.

83
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87
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173. Tao, Xuekang and White, R.N., "Finite Element Prediction of

Punching Shear Failure of Axisymmetric Reinforced Concrete

Slabs," Report No. 84-9, Cornell University, Ithaca, New

York, July, 1984.

174. Scanlon, A., "Time Dependent Deflections of Reinforced

Concrete Slabs," Dissertation, Department of Civil

Engineering, University of Alberta, Edmonton, Canada, Dec.,

1971.

98
175. Borst, R. de and Nauta, P., "Smeared Crack Analysis o Reinforced Concrete Beams and Slabs Failing in Shear,

Proceedings of the International Conference on ComputerAided Analysis and Design of Concrete Structures, Part I,

Sept., 1984, Split, Yugoslavia, pp. 261-273.

176. Litton, R.W., "A Contribution to the Analysis of Concrete

Structures Under Cyclic Loadings," Dissertation, University

of California, Berkeley, 1976.

99

3

H)
Table 1 Comparison of effective ice pressures for vertical

piles and piers (from Reference 13)

Source

Range of Pressures

Specified or Implied

(psi), kPa

Korzhavin 1962: USSR rivers, spring break-up (70 - 270 psi)

490 - 1860

AASHO and CSA (old). Highway bridge codes (400 psi)

2760

New CSA Code S-6 (1974), Highway Bridges (100 - 400 psi)

690 - 2760

USSR Code SN 76-66: River Structures (45 - 190 psi)

295 - 1320

Canada Ministry of Transport - Navigation

Lightpiers, St. Lawrence

(140 - 175 psi)

965 - 1210

Canada Dept, of Public Works - Wharf Piles (200 - 250 psi)

1380 - 1720

Wedge Formula

(warm ice -1 . 5" C)

3 m dia structure (250 psi) 1755

30 m dia structure (200 psi) 1390

Michel and Toussaint

(warm ice -1.5*C)

Ductile (690 psi) 4810

Brittle (230 psi) 1620

Tryde (-1.5*0 3 m dia structure (555 psi) 3860

30 m dia structure (370 psi) 2580

Wedge Formula

(cold ice -10*C

3 m dia structure (585 psi) 4095

30 m dia structure (460 psi) 3255

Michel and Toussaint

(cold ice -10*C)

Ductile (1600 psi) 11230

Brittle (580 psi) 4050

Tryda (-10*C) 3 m dia structure (1300 psi) 9070

30 m dia structure (860 psi) 5990

100
Table 2 Expressions for ultimate shear

Reference 37)

strength (adapted from

Investigator

Nominal

Shear

Stress Limiting Shear

Stress

Eq.

No. Remarks

EXPRESSIONS DEPENDENT PRIMARILY ON CONCRETE STRENGTH

Hognestad [76]

Elstner and

Hognestad [43]

Moe 147]

U

= (0.035 + f' + 130 psi (1) f' > 1800 psi (126 kgf/cm2

) 7/8 bd

O

V 0.046 f

f VTbd ' 333 psi +

$ ~

O V 15(1 - 0.075c/d) /V

u _ c bd

1 + 5.25 bd/f 7

Stages I and II, Fig. 2

.( 2 )

Not intended for c/d ratios much

.(3) larger than 3.0

Moe [47]

Tasker and

Wyatt j 77]

~ = (9.23 - 1.12 c/d) SF for c/d < 3 . . bd c —

. . . .(4a)

v Modifications of Eq. 3 for rx = (2.5 + lOd/c) /F for c/d > 3 . . . . Du C design

Vttt = [8.27 (1 + 1.21 d/c) - 5.25 4> ] /F b a o c

. . . .(5) Modification of Eq. 3

Tasker and

Wyatt [ 77 ]

Herzog [78]

Mowrer and

Vanderbilt

u

_ 10> /F ( 6 ) Lower bound of Eq. 5 for design

b'd + 1 + c/d' r c

V

4 (c + d)d

(2.64 + 0.00477 pf ) /F < 6.3 f

1 . (7) For design

V 9.7 ( 1.0 + d/c) SF

u c bd

=

1 + 5.25 bd /F -^r

c —

( 8 )

Long [84]

or

vu _

/ofy

d (1 - 0.59) /°fv/f e bd b (0.2 - 0.9 c/L)

Vu 20 (c + d) (100 p ) * 25 JFl

bd b (0.75 + 4 c/L)

. (9a)

(9b)

Whichever is smaller

EXPRESSIONS DEPENDENT PRIMARILY ON FLEXURAL EFFECTS

Whitney [80]

Blakey [82]

Gesund and Kaushik [83]

V M /dJF

= 100 psi + 0.75 ———

i

d

2

pf.

4d (r + d) . U0)

Yitzhaki [81] = 8 (1 - £

(149.3 + 0.164 pf ) (1 + |-) . (11) c y •id

— 2tt (m + m ) v = x y U c In + 1.31

= Yield line capacity if Q=

If Q > 4 Shear failure.

2 2 4 pf d *10

y. /F bB

c

(12) Expression for V , not a nominal

shear stress

£ 2 . .(13) Based on f = 40 ksi (2812 kgf/cm2

)

P = negative moment steel ratio

unless positive steel stops

short of column

then p = p t p

1

101
Table 2 (continued) Notation used in expressions

(adapted from Reference 37)

b = perimeter of loaded area

b' = perimeter of column collar (Eqs. 5 and 6)

b = perimeter of critical section located d/2 from column

perimeter

c

d

fy

h

1

s

L

m f m

x y

u

V flex

side length of square column or diameter of circular column

effective depth

concrete cylinder compressive strength

yield strength of reinforcement

overall depth of slab

shear span of slab=distance from face of column or cap to line of contraflexure

span between center of columns

moments in x, y direction per unit width

ultimate nominal shear stress

ultimate shear force

ultimate flexural capacity determined from yield line analysis

4> = V /V,. ^o u flex

p = negative moment reinforcement ratio

p' = positive moment reinforcement ratio

102
103

Table

3

Summary

of

code

provisions

on

punching

shear
Buckling Crushing

Flexure Rubble formation

Adfreeze bond fails then

ice fails in flexure

Ductile flow of ice

around structure

Figure 1 Possible ice failure modes (adapted

from References 7, 9 and 10)

104
Pressure

(psi)

5 10 100 1000

Area (ft ^

)

(a) — Comparison of pressure from first and multiyear floes (from Reference 28)

LOADED AREA («q. ft.)

( b ) —Local Oaaign ca pcaaaura tor noqa and floa mpaci K>acB (from Reference 26)

Figure 2 Local ice pressure design curves

105
Seabed

a) artificial island b) caisson-retained island

c) conical gravity structure d) caisson gravity structure

e) stepped structure f) floating structure

Figure 3 Example configurations of Arctic offshore

structures (adapted from References 3 and 29)

106
345 - 0

'

iQi -oV i42'-iofr«' ipr-oV j

(a) plan view

2 '- 6

"

(b) detail of wall

Figure 4 S0HI0 Arctic Mobile Structure (SAMS)

(from Reference 25)

107
(b) wall detail

aRjiii

4 «4C

(c) typical extreme ice load patterns for BWACS design

Figure 5 Brian Watt Associates Caisson System (BWACS)

(from Reference 31)

108
| III! ^'

; i,

—j.

1 r

i i

!

l| nli P

rrr

[ III H” T:

!|

Figure 6 Artist's sketch of the Arctic Cone Exploration

Stucture (ACES) (from Reference 26)

109
MAIN

SCAFFOLD UNDER

INTERMEDIATE

CELL WALLS

FORM WORK AND SHORING

FOR BASE SLAB

PRECAST CONCRETE SKIRT

MOVEMENT BEARING

CRIBBAGE

GRAVING DOCK FLOOR

Figure 7 Typical details of initial construction (ACES)

(from Reference 26)

110
Concrete Island Drilling System: Super

Series (Super CIDS) (from Reference 27)

111

Figure 8
1. OUTER WALL 5. SILO CONNECTING HALL

2. SMEAR HALLS 6. 0R1LLING MOONPOOL

3. INTERIOR HALL 7. SERVICE MOONPOOL

4. HONEYCOMB SILO 8. MANIFOLD CHAMBER

(a) brick structural arrangement

Figure 9 Super CIDS brick dimensions and details

(from Reference 27)

112
45m

Figure 10 Tarsiut Island, general arrancement

(from Reference 35)

continuity of reinforcement

and prestressing —

possible transverse

stressing

Figure 11 Structural arrangement for concrete

ice wall (from Reference 1)

Figure 12 Shear transfer mechanisms in a cracked

beam (adapted from Reference 39)

113
BOND SLIP OF REINFORCEMENT MITHIN COLUMN CONTRIBUTES

Figure 13 Crack formation in the column area of a slab

(from Reference 40)

I STRESS I INFLANE

I DISTRIBUTIONS | FORCES

COMPRESSIVE

MEMBRANE

FORCE

FIXEO

BOUNOARY

MOMENT

Figure 14 Arching action in

(from Reference

114

slabs

61)
DEFLECTION

(a) load-deflection curve

APPLIED LOAD

(b) load-restraining force curve

Figure 15 Typical curves for an underreinforced slab

(from Reference 61)

115
UHimetf load

» cm

* c

\1

t**

o

ft A

0

* A

* Pune* 7~L~ 6- S»noi* O D A • ft

0% 1.57% ] 14S R»>nlorc»«**nt

Figure 16 Punch load vs. flexural reinforcement for

the simple and restrained slabs tested by

Taylor and Hayes [63] (from Reference 87)

i° p

9 -

8 -

7 -

6 -

• • • *• •%

o

•- •'•8

t . .1

r

03V

4

3

Extoriof column*

Slab foilad in Htxurx

2

I -

0 i i i i i i i i i i 0 I 23436789 10

0<d not (all in punching tbaar ; maximum attained

Figure 17 Shear test data vs. Eq. 11-37 of ACI 318-83

for two-way prestressed slabs (from Ref. 72)

116
(B) ASSUMED GEOMETRY OF CONNECTION

LEGEND

P Applied Load at the Slab Periphery

T * Inclined Compressive Force Acting on the Conical Shell

R^ Resultant Perpendicular to Radial Crack of the Reinforcement

R^ Resultant Perpendicular to Shear Crack of the Reinforcement

R^ Resultant of Shear Reinforcement, If Any

R^ * Tangential Resultant of the Concrete Compressive Stresses

Figure 18 Idealized connection model of Kinnunen and

Nylander [68] (from Reference 37)

117
(a) American

building

code

too

mt ACl Jli-71 1 t‘Nl |

!

' ' !

i

;

1 i !/ 1

300

i

i

. /.* '

! i • 1 /* •• ./» f -• • • • CUtnw t Wfwtloi / * • * • o t Kjr^- y ^ * Tofior A M«r«» / o * • i • tlx X I

;

! i

:

0 100 XO X» 10D too HI n l*«)

(b) European

Model

Code

Prediction o* CEB -PIP

(kNl

1 I L

• Edtner l Hognestod

o Kinnunen l Nyionder i

• Bo - i

! X

1 i : '

; 1 / i

: / 1

: •

./ • • .

#

• *9°

X* • *' /L **«»•

/ ®o= , 1 A i 0t>«erved »tre ngfh

0 100 . 200 300 1 00 WO 600 ItNl

(c) British

code of

practice

r igure 19 Punching test results compared with code

predictions (from Reference 87)

118
COMPARISON OF ACI AND CEB-FIP

PUNCHING SHEAR PROVISIONS

(Thousands)

COMPRESSIVE STRENGTH (psl)

(a) diameter of load = 12 in. , d = 12 in. , Rr =

-- 0.005

(b) diameter of load = 12 in . , d = 12 in . , P,- == 0.01

(c) diameter of load = 36 in . , d = 18 in . , Pf

=

= 0.01

(d) diameter of load = 36 in . , d = 36 in. , P-? == 0.02

Figure 20 Comparison of punching shear provisions for selected

parameters: ACI vs. CEB-FIP

119
RATIO

OF

ACI

TO

CPI

10

COMPARISON OF ACI AND CPI 10

PUNCHING SHEAR PROVISIONS

(a) diameter of load = 12 in. , d = 12 in . , ft = 0.005

(b) diameter of load = 12 in. , d = 12 in. , ft = 0.01

(c) diameter of load = 36 in . , d = 18 in. , a

= o.oi

(d) diameter of load = 36 in . , d = 36 in . , ft = °- 02

Figure 21 Comparison of punching shear provisions for selected

parameters: ACI vs. CP110

120
FLEXURAL CRACKING

INCLINED CRACK

CRACK AT THE /g

REENTRANT CORNER

CRACKS IN THE WALL

Figure 22 Different types of cracks observed in pressure vessels

(from Reference 98)

121
30

Figure 23 Shear-fl exure interaction curve (adapted from

Reference 95)

122
Figure 24 General characteristics of a typical test

panel used in the BWA study [34]

123
STEEL

PISTON

IC-U

STEEL

CYLINDER

NATURAL

RUBBER

LEATHER

Figure 25 BWA punching shear study loading system

(from Reference 34)

124
20

15

I

p 10

, ?>£

.s

<vu>t- < V

cr>t[1 + 0 - 06 ( .o3I

>]

i (7)

.do;.

(9)

.(3)

,( 5 )

,( 6 )

(8)

SYMBOL SPECIMEN

SHELL (18'R)'

SHELL (6'R)

.003 .006 .009

P v (eff)

Figure 26 Effect of shear reinforcement quantity on ultimate

shear resistance in BWA study [34]

125
ev <««)

Figure 27 Test results of BWA study compared with "conventiona

slab methods" [34]

126
20

15

10

5

0

I

Pv

(eff)

ire 2 8 Test results of BWA study compared with "conventional

slab method" (CP110) [34]

127
800

700

600

500

400

300

200

100

0

29 Comparison of tested vs. calculated ultimate shear

resistance, Vu ("ACI modified punching shear method")

,

from BWA study [34]

128
END VIEW

Figure 30 Geometry and dimensions for shell specimens of Reference 149

129
Figure 31 Results of punching tests of Reference 152

130
(b)

from Reference 173

Deflection (In)

(c)

from Reference 175

Figure 32 Finite element predictions of punching shear strength:

load vs. deflection curves 131
NBS.1T4A (WEV. 2-«C> U.S. DEPT. OP COMM. 1. PUBLICATION OR 2. Performing Organ. Report NoJ 3. Publication Date BIBLIOGRAPHIC DATA

REPORT NO.

SHEET (See instructions) NBSIR 86-3388 MAY 1986

4. TITLE ANO SUBTITLE

Punching Shear Resistance of Lightweight Concrete Offshore

Structures for the Arctic: Literature Review

5. AUTHOR(S)

David I. McLean, H. S. Lew, Long T. Phan, . Mary J. Sansalone

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANOAROS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

S. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME ANO COMPLETE AOORESS (Street, City. State, ZIP

)

Technology Assessment and Research Branch; Mineral Management Service

U.S. Department of the Interior

Reston, VA. 22091

10. SUPPLEMENTARY NOTES

I | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Hie punching shear resistance of lightweight concrete offshore structures for the

Arctic is being investigated at the National Bureau of Standards on the behalf

of the Minerals Management Service of the U.S. Department of the Interior in

cooperation with five American oil companies. This report serves as an introduction to the project and reviews current knowledge on material relevant

to the punching shear behavior of concrete offshore structures subjected to

Arctic ice I.pads . A brief review of available information on Arctic ice leads

and a discussion of seme of the proposed offshore structural concepts are presented. The general mechanics of punching shear fa i lures and the factors

affecting punching resistance are discussed along with a comparison of current

U.S. and European code provisions on punching shear. Available literature on

experimental and analytical investigations on punching shear relevant to this projeer

is also reviewed.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons

Artie environment; lightweight concrete; literature review; shore structure

;

punching shear; reinforced concrete.

13. AVAILABILITY

| j Unlimited

PH For Official Distribution. Do Not Release to NTIS

i H Order From Superintendent of Documents, U.S. Government Printing Office. Washington, D.C. 20402.

I I Order From National Technical Information Service (NTIS). Springfield. VA. 22161

14. NO. OF

PRINTED PACES

15. Pnc«

UlCOuu.QC |04)*W«