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Influence of Concrete Strength on the
Behaviour of Bridge Pier Caps
by
Gavin Mac Leod
March, 1997
Department of Civil Engineering and AppIied Mechanics
McGill University
Montreal, Quebec
Canada
A thesis submitted to the Faculty of Graduate Studies and Research in partid fulfilment of the
requirements for the degree of Master of Eng inee~g
Gavin MaCLeod, 1997
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ABSTRACT
Two full-sale rernforced concrete bridge pier caps were constructeci and tested to
investigate the influence of concrete strength on their behaviour. The arnount of uniformly
distributeci reinforcement required for crack control at service load Ievels was aiso varied in order
to investigate the sui tabi l i~ of current design approaches for these disturbed regions. in addition,
strut-and-tie modeIs, refined strut-and-tie models and non-Iinear finite element analyses are used
CO predict the comp!ete behaviour of the test specirnens.
Deux chapiteaux de pont grandeur réelle en béton armé ont été construits et testés pour
étudier I'infiuence de la résistance du béton sur leur comportement. La quantité d'armature
distribuée uniformément, nécessaire pour contrôler les fissures sous charges de service, a été
variée pour déterminer si les approches de conception actuelles conviennent pour ces structures
spéciales. De plus, des modèles bielle et tirant simple, des modèies bielle et tirant plus détaillés
et des analyses non-linéaires par éléments finis sont utilisés pour prédire Ie comportement complet
des spécimens d'essai.
ACKNOWLEDGEMENTS
The author would Iike to thank Professor Denis Mitchell for his cornpetent supervision,
support and encouragement throughout this research programne. The author would also like to
express his gratitude to Dr. WiiIiam Cook for his advice and assistance durhg this programme.
The efforts of Marek Pnykorski, Ron Sheppard, John Bartczac and Darnon Kiperchuk
in preparing the experiments are gratefully acknowtedged. The author would also like to thank
Homayoun Abrishami, Arshad Khan, Stuart Bristowe, Glenn Marquis, Peter McHarg and Pierre-
Alexandre Koch for their contributions in the construction and testing of the specimens.
The financiai support provided by Concrete Canada, a Network of Centres of Excellence
Pro- hnded by the Minister of State, Science and Technology in Canada, is greatly
appreciated.
iii
TABLE OF CONTENTS
ABSTRACT
RÉSUMÉ .
ACKNOWLEDGEMENTS .
LIST OF FIGURES
LIST OF TABLES
LIST OF SYMBOLS .
1. INTRODUCTION Introduction . Disturbed Regions . Previous Research on Strut-and-Tie Models . Design Using Strut-and-Tie Models . AC1 Design Approaches for Disturbed Regions
1 S. 1 AC1 Provisions for Deep Beams
1.5.2 AC1 Provisions for Brackets and Corbels
Experiments on Deep Beams, Corbels and Pier Caps . 1.6.1 DeepBearns . 1.6.2 Corbels
1.6.3 PierCaps
Detailed Analysis Procedures . 1.7.1 Refined Strut-and-Tie ModeIs . 1.7.2 Non-Linear Finite EIement Analysis .
High-Performance Concrete . 1 .8.1 Compressive Strength . 1.8.2 Flexure and Axial Loads
1.8.3 Minimum Reinforcernent for Flexure and Shear
1.8.4 Strut-and-Tie Provisions
Crack Widths and Crack Spacing
Research Objectives ..
1
. . II
. iii
. viii
2. EXPERIMENTAL PROGRAMME . 39
2.1 Details of Specimens . . 39
2.2 Material Properties . . 43
2.2.1 Concrete . 43
2.2.2 Reinforcing Steel . 46
2.3 Test Setup and htnimentation . 48
2.4 Testing Procedure . . 51
3.1 Load-Deflection Responses . 3.1.1 Specimen CAPN
3.1.2 Specimen CAPH
3.2 Development of Strains
3.2.1 Specimen CAPN
3 -2.2 Specimen CAPH
3.3 Development of Cracking
3.1.1 Specimen CAPN
3.1.2 Specimen CAPH
4. COMPARISONS AND ANALYSES OF RESULTS . . 76
4.1 Cornparison of Responses of Normal- and High-Strength Concrete
Specimens . . 76
4.2 dredictions of Results . . 83
4.2.1 AppIicability of Plane-Sections Anaiysis . 83
4.2.2 Simple Strut-and-Tie Models . . 83
4.2.3 Refined Strut-and-Tie Models . . 85
4.2.4 Non-Linear Finite Element Analysis Using Program FIELDS . 88
4.3 Estimates of Crack Widths . . 101
5. CONCLUSIONS . . 103
REFERENCES . . 105
APPENDK - EXPERIMENTAL DATA .
LIST OF FIGURES
Typical forms of cap beams and pier caps used in bridge construction . Examples of disturbed regions .
Strut-and-tie modelling of a deep beam with a direct support and a tension
hanger support .
Influence of principal tensile strain, E , , on compressive strength of
diagonally cracked concrete . Compressive strength of sûut versus orientation of tension tie passing
through strut .
Provisions for brackets and corbels . Applicability of stmt-and-tie mode1 for predicting series of bearns testeci by
Kani .
Crack control reinforcement required with assurnption of straight-tine
compressive struts . Investigating the effect of distributed reinforcement on deep beams . Evaiuating stresses at Gauss points in quadrüaterai element . Determining average concrete tensile stress, f,,, from suain, E ,
Investigating stress condhon at crack interface
Influence of concrete strength on shape of stress-strain curve .
Crack width parameters
Side-face cracks controlled by skin reinforcement
Test simulation of cantilever cap beams
Specimen details
Concrete properties .
Typical stress-strain resopnses of reinforcing bars . Specirnen CAPN under the MTS testing machine
Different bearing details of specimens CAPN and CAPH
LVDT locations
Strain gauge locations and crdck width lines of measurernent .
Loaddeflection responses of speciniens . 54
Strains in bottom bar of CAPN tension fie, determined from strain gauges . 56
St.4ns distributed reinforcement of CAPN, determined from strain gauges . 58
Longitudinai strains from LVDTs at mid-height and at the level of the tension
tie of CAPN .
Responses of CAPN-A rosettes A6 and A7 .
Responses of CAPN-B rosettes B6 and B7 .
Strains in bottom bar of CAPH tension tie, determined from main gauges .
Strains distributed reinforcement of CAPH, determined from strain gauges .
Longitudinal strains frorn LVDTs at mid-height and at the level of the tension
tie of CAPH - Respomes of CAPH-A rosettes A6 and A7 . Responses of CAPH-B rosettes B6 and B7 . Development of cracks in CAPN
CAPN after failure . Development of cracks in CAPH
CAPH after failure .
Comparison of Ioad-deflection responses of specimens . FIexural crack widttis measured at the level of the tension tie in specimens
Diagonal crack widths measured at mid-height of specimens .
infiuence of distributed reinforcernent ratio on crack control . S imple strut-and-tie mode1 for specimen CAPN
Simple strut-and-tie mode1 for specirnen CAPH
Refined strut-and-t ie models for specirnen CAPN
Refined stnit-and-tie models for specimen CAPH
Predicted load-deflection responses of specirnens
Predictions of deflected shapes of specimens at maximum predicted loads
Predicted strains and stresses in specimen CAPN at a load of 920 kN . Predicted strains and stresses in specimen CAPH at a load of 920 kN .
Predicted strains and stresses in specimen CAPN at a load of 2280 kN
Predicted strains and stresses in specimen CAPH at a Ioad of 2280 kN
Predicted strains and stresses in specimen CAPN at a load of 4980 kN
Predicted strains and stresses in specimen CAPH at a load of 5340 kN
Predictions of stress development in main tension ties of specimens . Comparison of predictions of stress in main tension ties at general yield
vii
LIST OF TABLES
1.1 Effective stress levels in struts . 7
1.2 Effective stress levels in nodal zones . . 10
2.1 Mix design for 35 MPa concrete . 44
2.2 Mix design for 70 MPa concrete 4 4
2.3 Concrete properties . . 46
2.4 ReUrforcing steel properties . . 48
4.1 Cornparison of strut-and-tir: predictions with measured loads at general
yielding - 88
4.2 Cornparison of refined stmt-and-tie predictions and non-linear finite element
predictions with rneasured loads at generai yielding . . 98
4.3 Cornparison of predicted and measured crack widths and principal tensile
strains in the main tension ties of specimens . . 102
4.4 Cornparison of predicted and rneasured diagonal crack widths and principal
tensile strains at mid-height of the specimens . . 102
Readings from vertical LVDTs used to determine the deflection of
specimen CAPN
Readings fiom LVDTs located at the Ievel of the main tension tie in
specimen CAPN-A .
Readings from LVDTs located at the level of the main tension tie in
specimen CAPN-B .
Readings from LVDTs Iocatd at mid-height of specimen CAPN-A .
Readings from LVDTs located at rnid-height of specirnen CAPN-B .
Readings from LVDTs rosettes located in end A of specirnen CAPN . Readings from LVDTs rosettes Iocated in end B of specimen CAPN . Strains fiom strain gauges located in end A of specirnen CAPN
Strains Crorn strain gauges located in end B of specimen CAPN
Readings from vertical LVDTs used to determine the deflection of
specimen CAPH
Readings from LVDTs located at the level of the main tension tie in
specimen CAPH-A .
Readings from LVDTs located at the level of the main tension tie in
specirnen CAPH-B .
viii
A. 13 Readings fiom LVDTs located at rnid-height of specimen CAPH-A . . 124
A. 14 Readings from LVDTs loçated at mid-height of specimen CAPH-B . . 125
A. 15 Readings from LVDTs rosettes located in end A of specimen CAPH . . 126
A. 16 Readings from LVDTs rosettes located in end B of specirnen CAPH . . 127
A. 17 Strains fiom strain gauges located in end A of specimen CAPH . 128
A. 18 Strains from strain gauges located in end B of specimen CAPH . 130
LIST OF SYMBOLS
r?iaximum aggregate size
shear span
effective area of concrete surrounding each reinforcing bar
area of effective embedment zone of concrete where reinforcing bars can influence crack
w idths
effective cross-sectionai area of concrete compression strut
area of reinforcement required to resist moment, Mu, in corbel
area of horizontal stirrup reinforcement in corbel
area of reinforcernent required to resist horizontal rensile force, N,,, in corbel
area of primary tension reinforcement
area of reinforcing steel
minimum area of flexural reinforcement
area of reinforcing steel in main tension tie
area of shear reinforcement perpendicular to axis of member within a distance s
area of shear friction reinforcement
area of shear reinforcement parallel to axis of member within a distance s2
width of member
width of tension zone of member
minimum effective web width within depth d
clear concrete cover
distance from extreme compression fibre to neutral axis
force in compression strut
distance from extreme compression fibre to centroid of tension reinforcernent
depth of compression strut
diarneter of reinforcing bar
distance from exueme tension fibre to centre of closest bar
modulus of elasticity of concrete
modulus of eIasticity of reinforcing steel
modulus of elasticity of tension tie reinforcernent
concrete stress
compressive strength of concrete
concrete cracking stress, equal ro E,E,
limiting compressive stress in concrete compression stnit
average principai tensile stress in concrete
average principal compressive stress in concrete
mdulus of rupture of concrete
average stress in reinforcing steel
calculted stress in reinforcement at specified Ioads
stress in reinforcing steel across crack
limiting compressive stress of diagonaily cracked concrete
overall depth of beam
height of effective embedrnent of tension tie
distance of main tension reinforcement from neutral axis
distance of extreme tension fibre from neutrai axis
post-peak decay t e m for stress-suain relationship of concrete
coefficient that characterizes bond properties of reinforcing bars used in CEB-FIP crack
width expression
rtmforcing bar location factor used in development length expression
coefficient to account for strain gradient used in CEB-FIP crack width expression
reinforcement coating factor used in development le@ expression
reinforcing bar size factor used in deveIopment length expression
length of bearing
development length of reinforcement
straight embedrnent length
clear span
cracking moment
factored mom~nt at a section
factored moment resistance at a section
design ultimate moment
curve fitting factor for stress-strain relationship of concrete
applied axial tension
horizontal tensile force
spacing of shear reinforcement parallel to axis of member
maximum spacing between longitudinal reinforcing bars
mean crack spacing
mean spacing of diagonal cracks
spacing of shear reinforcement perpendicular to axis of member
force in tension tie
nominai shear strength provided by concrete
shear stress at crack interface
limiting shear stress dong crack
nominal shear strength at a section
nominal shear strength provided by shear reinforcement
factored shear force at a section
average crack width. equal to E , S ,
characteristic crack width, equal to 1 . 7 ~ ~
mean crack width, equai to e#,,,
maximum crack width
limiting crack width parameter, equal to f; @A) '13
ratio of average stress in rectangular compression block to concrete strength
factor accounting for strain gradient, equaI to b l h ,
ratio ûf depth of rectangular compression block to depth to neutral axis
density of concrete
shear strain
yield deflection
ultimate deflection
compressive strain
strain in concrete at peak compressive stress
strain in concrete caused by stress
suain in concrete at cracking
strain in reinforcing steel
strain in reinforcing bar at crack location
horizontai tensile strain
suain in ydirection
principal tensile strain
largest tensile strain in effective embedment zone
principal compressive strain
smdlest tensile strain in effective embedment zone
angle of principal compressive main from horizontal
smallest angle between compression stmt and tension tie crossing suut
effective coefficient of shear fiction
factor to account h r influence of high-strength concrete, eqiial to 0.55 + 1.2Wylf; reinforcement ratio of primary tension reinforcement, equal to AJbd
xii
Pef AiAccf
Pw Aibwd
6 capacity reduction factor, taken as 0.85 for shear material resistance factor for concrete
# matend resistance factor for prestressing steel
6, material resistance factor for reinforcing steel
xiii
CHAPTER 1
INTRODUCTION
1.1 Introduction
Figure 1.1 shows some typical forms of cap bearns and pier caps used in bridge
construction. Although there is a variety of forms for these types of elements, this research
programme will examine a pier cap of fom shown in Fig. l.l(b), which is also representative
of the cantilever portions of the cap beam shown in Fig . 1.1 (a). This chapter first reviews the
behaviour and design of disfurbed regions, highlighting the use of strut-and-tie modeIs for design.
.4 review of experimental work carried out on deep beams, corbels and pier caps is presented to
provide background information on the behaviour of disturbed regions which are similar to those
investigated in this research programme.
1.2 Disturbed Regions
Regions of a member in which the "plane-sectionsn assurnption is appropriate are
sometimes referred to as B-regions (where B stands for beam or Bernoulli hypothesis). Other
regions of a member where the strain distribution is significantly non-linear are referred to as D-
regions, or disturbed regions (Schlaich et ai. 1987). This non-Iinear distribution of strains is due
to a complex interna1 flow of stresses adjacent to abrupt changes of cross-section or the presence
of concentrated loads or reactions. The two maid design assumptions, that plane sections remain
plane and that the shear stress can be assumed to be unifonn over the nominai shear ma, are no
longer valid in disturbed regions-
Several examples of disturbed regions are shown in Fig. 1.2. where the flow of
compressive stresses is shown by dashed lines, and tende ties are indicated by solid lines.
Figure 1.2(a) shows how the presence of a support reaction intempts the uniform diagonal
compression field in a shply supported "slendern beam with stimps. The flow of compressive
stresses fan into the support causing a disturbed region near that location. Figure 1,2(b) shows
a deep beam subjected to concentrated loads. Because of the complex flow of stresses in this
member, the entire member is a disturbed region. The flow of forces from the top of the beam
(a) Continuous cap beam
(b) Cantilever cap bearn
(c) Deep-water pier cap
Figure 1.1 Typical foms of cap bearns and pier caps used in bridge construction
unifom fan field
/' /' D ; B
I ' tension tie 1
(a) Simply supported beam
compressive S u u t
l I \'-- tension tie 1 1
(b) Deep beam
CO m press ive s tnlt
(c) Corbet
Figure 1.2 Examples of disturbed regions
to the reaction areas delineates concentrated compressive stresses as shown. The resisting
mechanism, consisting of the flow of compressive stresses and the presence of the tension tie,
resembles a tied arch. The corbel shown in Fig. 1.2(c) is a D-region characterized by
concentrated compressive stresses flowing from the bearing areas to the column. The horizontal
components of these diagonal compressive stresses must be equilibrated by tension in
reinforcement which is well-anch~red at the outer edges of the bearing areas.
1.3 Previous Research on Strut-and-Tie Models
Truss models have been used since the turn of the century for the design of slender
reinforced concrete beams (Ritter 1899, Morsch 1909). These early truss models had a
compression chord and tension chord with diagonal compressive stmts, typically assumed to act
at 45". These tmss models formed the basis of code developrnents in Europe and North America
for the design of slender beams. Recently, renewed interest has been generated in t m s models
as a design tool, not only for siender beams, but also for the design of disturbed regions.
A strut-and-tie model provides a simple toof for the design of disturbed regions, that is,
regions having a complex flow of stresses. The flow of forces in a disturbed region is ideaiized
using compressive stnits to represent the concentrated compressive stresses and reinforcement to
represent the tension ties (see Fig. 1.2). Figure 1.3 illustrates the development of a strut-and-tie
model for a deep beam with a direct support and a tension hanger support. The first step in
design is to sketch the flow of compressive stresses, in the form of compressive stmts, from the
location of the applied loads to the support regions. The next step is to sketch the tension tie
reinforcement required to complete the strut-and-tie model (see Fig. 1.3(a)). The shaded areas
in Fig. 1.3(a) where compressive struts and tension ties meet are referred to as nodal zones.
These nodal zones are regions of multidirectionaily stressed concrete. In order to examine the
equilibriurn of the model, an ideaiized truss model is created as shown in Fig. 1.3(b). The
dashed lines represent the centreline of the compressive struts, and the solid lines are located at
the centroid of the tension tie reinforcement. The nodes of the idealized t m s occur at the
intersections of the compressive struts and tension ties in the idedized t m s model. One of the
main advantages of using strut-and-tie models is that the flow of forces can be easily visualized
by the designer. Scme experience is required to determine the most efficient strut-and-tie model
for any given situation, as no unique solution exists. As this is a lower-bowid solution technique,
al1 solutions will give conservative resulrs provided that equilibriwn is satisfied, applicable stress
limits are not exceeded and the reinforcement is capable of developing the required stress.
Schlaich and Schafer (1984) and Schlaich et al. (1987) suggest choosing the geometry of a sirut-
- 4 - - 4 - (a) Strut-and-tie rnodel
(b) Tniss idealization
Figure 1.3 Strut-and-tie modelling of a deep beam with a direct support and a tension hanger support
and-tie model such that the angle of each compression diagonal is within * 15" of the angle of
the resultant of the compressive stresses obtained from an elastic analysis. While this approach
gives some guidance in choosing the model geometry, it should be noted that considerable
redistribution of stresses may occur afier cracking.
Once the geometry of the strut-and-tie model has been chosen, forces in the t m s
members can be found from equilibrium. The required arnount of reinforcement for each tension
tie can then be determined while ensuring that this reinforcement is anchored in such a way to
transfer the required tension to the nodal zones of the truss. The dimensions of a concrete
compressive strut mut be made large enough such that the calculated stress in the stmt is less
than its h i t i n g stress.
Considerable research has been carrieci out on limiting stresses in concrete compressive
struts and the influence of anchorage details on the dimensions of these stnits. Thürlirnan et al.
(1983) and Marti (1985) concludeci that the stress in the stmts be limited to 0.60 fCf, while
Ramirez and Breen (1991) suggest a compressive stress limit of 2 . 4 9 K (in MPa units).
Schlaich et al. (1987) proposed stress limits for the struts which depend upon the stress conditions
and the angle of cracking associated with the stmt (see Table 1.1).
Vecchio and Collins (1986) developed expressions for the modifieci compression field
theory which accounted for the strain softening of diagonally cracked concrete (see Fig. 1.4).
The limiting compressive stress, f-. is given as:
where: fCt = concrete compressive strength,
€ 1 = principal tende strain.
The following strain compatibility equation provides a means of detennining the principd tensile
strain, E , , in diagonally cracked concrete:
where: E, = horizontal tensile strain,
€2 = principal compressive strain, 8 = angle of the principal compressive strain from horizontal.
I I - --- - - -- - - 1 Effective
II Conditions of Strut 1 Stress Level
Undisnubed and uniaxial state of
compressive stress that may exist for
prismatic struts
Tensile strains ancilor reinforcement
perpendicular to the axis of the strut may
cause cracking parailel to the strut with
nonnal crack width
Tensile strains andior reinforcement at
skew angles to the axis of the strut may
cause skew cracking with normal crack
II width 1 11 Skew cracks with extraordinary crack 1
width (expected if modelling of the stmts
departs significantly from the theory of
II elasticity's flow of interna1 stresses)
- - -
Uncracked uniaxiaily stresseci struts of
Stmts cracked longitudinally due to
bottle-shaped stress fields with sufficient
transverse reinforcement
Struts cracked longitudinally due to
bottle-shaped stress fields without
transverse reinforcement
Il Struts in cracked zone with transverse
tensions From transverse reinforcement
by - - -. - Schlaich er
al.
( 1987)
MacGregor
( 1997)
Table 1.1 Effective stress Ievels ïii stmts (adaptai from Schlaich et al. 1987, and MacGregor 1997)
(a) Average concrete compressive stress,f;_, from strains E, and E,
(b) Reduction in compressive strength with increasing values of E,
Figure 1.4 Infiuence of principal tensile strain, E,, on corvpressive strength of diagonally cracked concrete (Vecchio and Coilins 1986)
Figure 1.5 Compressive strength of stmt versus orientation of tension tie passing through stmt (Collins and Mitchell 1986)
In order to apply the strain softening expression to diagonal compressive struts, for use
in a stmt-and-tie model, Collins and Mitchell (1986) gave the foilowing expressions for the
limiting compressive stress in the struts:
where: f, = Iirniting compressive stress in the strut,
f: = concrete cylinder strength,
€1 = principal tensile strain.
where: = principal compressive strain in the strut, taken as 0.002,
es = strain in the tension tie crossing the strut,
4 = smallest angle between the stmt and the tension tie crossing the strut.
The variation of the compressive strength, f,, of a strut as a function of the angle, 8,, between
the strut and the tension tie passing through the strut is shown in Fig. 1.5.
It is also necessary to Iimit the compressive stress in the nodal zones of the strut-and-tie
model. The maximum compressive stress Iimits in nodal zones depend on the different straining
and confinement conditions of these zones. Figure 1.3 iIlustrates three types of nodes identifieci
as follows:
1 CCC - nodal zone bounded by compressive struts and bearing areas only,
2. CCT - node with a tension tie passing through it in only one direction, and
3. CTT - node with tension ties passing through it in more than one direction.
The two nodal zones in Fig. 1.3 located under the bearing areas at the top of the deep beam are
examples of CCC-nodes, that is, each node is bordered by a bearing area and two compressive
struts. The node above the direct support at the right end of the beam is an example of a CCT-
node since it contains one principal tension tie passing through the zone. The node at the indirect
support, located at near the bottom-left corner of the deep beam show. in Fig . 1.3 is an example
of a CTT-node since two tension ties pass through it. These nodal zones must be chasen large
enough to ensure that stresses do not exceed the applicable stress limits. Table 1.2 outlines the
effective stress limits for nodal zones as determineci by several researchers .
Conditions of Nodal Zone
Effective Proposed
Stress LeveI
CCC-nodes O. 85f: Collins and
CCT-nodes O. 75f; Mitchell
CTT-nodes 0.60fc (1986)
Nodes where reinforcement is anchored
in or crossing the node
Nodes bounded by compression stnrts 1 .O v2 fcf (') MacGregor
and bearing areas
Nodes anchoring one tension tie 1 O=
Nodes anchoring tension ties in more
than one direction
Table 1.2 Effective stress levels in nodal zones (adapteci from Collins and Mitchell 1986, Schlaich et al. 1987, and MacGregor 1997)
1.4 Design Using Strut-and-Tie Modeis
The CSA Standard A23.3 "Design of Concrete Structures for Buildings" (CSA 1984,
1994), the Ontario Highway Bridge Design Code (OHBDC 199 l), the Canadian Highway Bridge
Design Code (CHBDC 1997, currently under development) and the AASHTO LRFD
specifications (AASHTO 1992) have adopted the strut-and-tie design methods developed by
Collins and Mitchell (1986). In cornparing different codes, it is important to realize that the
Canadian standards use material resistance factors (@, for concrete. t$s for reinforcing steel and
4p for prestressing steel), while the U.S. codes use capacity reduction factors, 9, which depend
on the type of action- Both the CSA Standard and the CHBDC use the s a m material resistance
factors for steel with t$$ = 0.85 and #p = 0.90. The CSA Standard uses 9, = 0.60, while the
CHBDC uses 9, = 0.75. In this section reference will be made to the requirements of the
Canadian Highway Bridge Design Code. The CHBDC states that strut-and-tie models shall be
considered for the design of deep footings and pile caps or other situations in which the distance
between centres of applied load and the supporting reaction is less than twice the cornponent
thickness .
The design procedure, with reference to the relevant code requirements, is sumrnarized
in the following steps-
1. Sketch the strut-and-tie model, assuming straight compression struts to mode1 the flow
of forces from the points of application of the loads to the supports (see Fig. 1.3fa)).
2. Choose the size of each bearing such that the limiting compressive stress of the adjacent
nodal zone is not exceeded. The nodal zone stresses are limited to 0.85 4, fCf for a CCC-
node, 0.75 &, fCt for a CCT-node, and 0.604,f; for a CTT-node. The tension tie
reinforcement must be distributed over an effective area of concrete such that the force
in the tension tie does not exceed the appropriate stress limit, given above, times this
effective area.
For example, the bearing area of the direct support on the right end of the deep beam
shown in Fig . 1.3(a) is adjacent to a CCT-node, so the area of the bearing plate, 1, b,
must be chosen Iarge enough to ensure that the factored reaction force of the support does
not exceed 0.75 6, fer k b. in addition. the reinforcernent making up the tension tie musc
be detailed such that the effective area surroundhg the bars (defmed as that area having
the same centroid as the tension tie, that is, h,b) is large enough such that the tension in
the tie does not exceed 0.75 d,f: ha b.
3. Draw the t m s rnodel ideaiizing the strut-and-tie mode1 (see Fig. 1.3(b)). All nodes are
tocated at the intersections of the lines of action of suuts, tension ties, applied loads and
bearing reactions .
In order to detennine the line of action of compressive stnits, it is necessary to determine
the dimensions of the struts, such that the compressive stress lirnits are ~ o t exceeded.
Since the design of deep beams usuaily commences by considering equilibrium at the
location of maximum moment, it is useful to realize that the depth of the horizontal stmt,
da, cm be found by :
where C = T = @&As, of the main tension tie.
The line of action of this strut is located a distance of dJ2 from the top surface of the
beam (see Fig. 1.3). The CCT-node at the right-hand direct support of the deep beam
in Fig. 1-3 is located at the point of intersection of the lines of action of the vertical
bearing force, and the horizontal tension tie. The CTT-node located at the left-hand
hanging (indirect) support in Fig . 1 -3 is located at the inters~ction of the centroids of the
horizonta1 and vertical tension ties.
4. Calculate the factored forces in the tniss mcmbers (compression struts and tension ties)
through static equilibriurn.
5 . Choose tension tie reinforcement such that the calculated tension force, T, in each tie
does not exceed A,, wheref, and A, are the yield stress and cross-sectionai area of
the tension tie reinforcement. Distribute this reinforcement over an effective area of
concrete at least equal to the force in the tie divided by the stress limit of the nodal zone
which anchors it. Figure 1.3(a) shows the effective anchorage ara, h, b, of the CCT-
node of the deep beam.
6 . Check the development of the reinforcement. For example, the tension tie reinforcernent
in the deep beam shown in Fig. 1.3(a) m u t be anchored over the length lb so that it is
capable of resisting the caiculated force in the tension tie, T, at the inner edge of the
bearing .
7. Check the compressive stresses in the stmts. The dimensions of the strut shall be large
enough to ensure that the caiculated compressive force in the strut does not exceed
&faA,, where fa and A, are the Iimiting compressive stress and effective cross-
sectional area of the strut, respectively. Equations 1.3 and 1.4 give the limiting
compressive stress in the strut. The iimiting compressive stress, f,, decreases as the
principal tensile strain, E , , increases. The principal strain, E , . increases as the angle, O,,
between the strut and the tension tie passing through the strut decreases (see Fig. 1.5).
It is necessary to determine the area, A,, of each strut. For example, the area of the
diagonal stmt at the intersection with the nodal zone at the right-hand end of the deep
beam in Fig. 1.3(a) equals (lbsinûs + h,cosû,)b. This stress must not exceed the limiting
compressive stress in the stmt, f,, as detennined by Eq. 1.3 and 1.4. In caiculating f,,
the strain in the tension tie passing through the strut, E,, rnay be taken as the factored
force in the tie divided by q5,AstEsr, where E,, is the modulus of elasticity of the tension
tie reinforcement.
8. Choose crack control reinforcement. The CSA Standard and the CHBDC require the
inclusion of uniforrnly distributed reinforcement in the horizontal and vertical directions,
having minimum reinforcement ratios of 0.002 and 0.003, respectively, in order to
control cracking. The maximum spacing of this un i fody distributed reinforcement is
300 mm.
1.5 AC1 Design Approaches for Disturbed Regions
The Amencan Concrete Institute Standard 318-95 "Building Code Requirements for
Structurai Concreteu (AC1 1995) has separate provisions for the design of deep beams and for
the design of brackets and corbels. These two different design approaches are discussed below.
1.5.1 AC1 Provisions for Deep Beams
The AC1 Standard requires that:
where: Vu = factored shear force at the section considered,
Vn = nominal shear suength at that section, and
Q = strength reduction factor, taken as 0.85 for shear.
The nominal shear strength is defined as:
where: V, = nominal shear strength provided by the concrete, and
v~ = nominal shear suength provided by the shear reinforcement.
The AC1 Code defines a member as as deep beam when ZJd is Iess than 5 (where I, is
the clear span measured from face to face of supports). The shear strength, Vn, for deep flexural
memtrers shall not be taken greater than:
V,, r 1 E b , d for iJd< 2 3
At the upper lirnit of IJd = 5, V, 5 0.83 @b,d (the same for ordinary beams) .
The criticai section for shear shall be taken at a distance of O. 15 I, from the face of the
support for uniformiy loaded beams, and at a distance of 0.50a (where a is the shear span) from
the support face for beams with concentrated loads, but shall not be taken at a distance greater
than d from the face of the support. Unless a more detaiied caiculation is made in accordance
with Eq. 1.10, V , shall be computed as follows:
The nominal shear strength provided by the concrete may also be calculated as:
where: p, = AJb,d
except that the value of the first bracketed term shall not exceed 2.5. and V, shall not be taken
greater than 0 . 5 0 g b W d . Mu is the factored moment occurring simuitaneously with Vu at the
critical section defined above. Where the factored shear force, Vu, exceeds the concrete
resistance, @ V,. shear reinforcement shall be provided to satisw Eq. 1.6 and 1.7, where V' shall
be computed by:
where: A, = area of shear reinforcement perpendicular to the flexural tension reinforcement
within a distance S. and
A, = area of shear reinforcement parallel to the flexural tension reinforcement
within a distance s2, and
s = spacing of shear reinforcement in a direction parallel to the flexuraI tension
reinforcement, and
$2 = spacing of shear reinforcement in a direction perpendicular to the flexurai
tension reinforcement.
In addition, the area of shear reinforcement, A,, shall not be less than 0.00 15 bws and s shall not
exceed d/5, nor 500 mm, and A, shall not be less than O.ME5 b,s2 and s2 shalI not exceed 6/3,
nor 500 mm. The shear reinforcement calculated for use at the critical section shall also be used
throughout the span.
1.5.2 AC1 FVovisious for Brackets and Corbels
The AC1 Code limits the applicability of the design provisions for brackets and corbels
to cases where the shear span-to-depth ratio, ald, is not greater than unity. These brackets and
corbels tend to act as t r w e s or deep beams rarher than flexural memben (see Fig. 1.6).
According to the Commentary, the upper limit of uniîy for ald is specified because, for larger
shear span-to-depth ratios, the diagonal tension cracks are less steeply inclined and the use of
horizontd stirrups alone as shown in Fig. 1.6@) may not be suitable. Also, the specified method
of design has only been validateci experimentally for ald not exceeding unity , and for a factored
horizontal tensile force, N,, not greater than the factored shear force, Vu. lt is assumed that a
corbel may fail by shearing dong the column-corbel interface, by yielding of the main tension
tie, by crushing or splitting of the compression strut, or by Iocalized shearing or bearing failure
under the loading plate. In order to limit the size and shape of the corbel, it must have a
minimum depth at the outside edge of the bearing area of 0.5d. This limit is specified so that
a premature failcre will not occur due to the propagation of a major diagonal tension crack from
below the bearing area to the outer sloping face of the corbel. The section at the face of the
support shall be designed to resist a shear. Vu, a moment [V,a + Nuc(h-d)]. and a horizontal
tensile force, N,,, simuItaneously. In al1 design calculations, 4 is taken equd ro 0.85 since the
behaviour of corbeis is predominantiy controlled by shear.
The design procedure is suIIlfnanzed in the folIowing steps:
Select the initial geometry of the corbel ensuring that the shear span-to-àepth ratio, ald,
does not exceed unity, and that the minimum depth at the outside edge of the bearing
area is 0.5d. Also, the shear strength, Vn, shall not exceed 0.2f:bWd nor 5.5bwd (in
Newtons).
Caiculate the area of shear friction reinforcement, A* across the shear plane necessary
to resist the applied shear force, Vu, as:
where L( = 1.40 for normal weight concrete.
Determine the area of reinforcement, A/, required to resist the moment at the face of
support of the corbel at the level of the p:timary reinforcement. It is necessary to
estimate the distance (h -d ) from the top face of the corbel to the centroid of the main
tension reinforcement. The design uitimate moment, Mu, to be resisted is:
tension tie
plane
(a) Strut-and-tie action of corbel
'4, (primav - reinforcement)
, L stirmps orties
(b) Detailing of corbel
Figure 1.6 Provisions for brackets and corbels
The area of reinforcement, Al. necessary to resist Mu shall be caiculated in accordance
with the flexural provisions of Clauses 10.2 and 10.3 (AC1 1995) using a capacity
reduction factor, #, of 0.85.
4. Cdculate the area of reinforcement, A,, required to resist the horizontal tensile force,
N,, frorn:
where # is taken as 0.85. The value of N, shail not be taken less than 0.2 Vu, uniess
speciai provisions are made to avoid tensile forces.
Caiculate the total area of prirnary tension reinforcement, A,, frorn:
Provide a minimum area of primary tension reinforcement. Ensure that p = A,lbd is at
leas t equal to 0.04 Cf,' If, )
Calculate the total cross-sectionai area of horizontal stirrup reinforcernent, A,, as:
Distribute this reinforcement uniformly within two-thirds of the effective depth of the
corbel adjacent to the primary tension reinforcement.
Experiments on Deep Beams, Corbek and Pier Caps
This section provides a bief surnmary of some of the experimental studies that have been
carried out by other researchers investigating the performance of deep beams, corbels and pier
caps.
Figure 1.7 illustrates the marner in which the shear strength reduces as the shear span-to-
depth ratio, ald, increases. This series of tests were carried out by Kani in the 1960's and are
reported by Kani et al. (1979). The beams in this senes had the same flexural reinforcement and
no shear reinforcement. The two main variables were the shear span and the size of the bearing
plates. Aiso shown in this figure are the predicted capacities (Collins and Mitchell 1991) using
the modified compression field theory and stmt-and-tie models. This figure demonstrates that
for beams with ald less than about 2.5 strut-and-tie rnodels give more accurate predictions. The
1995 AC1 Code provides special provisions for deep flexural rnernbers with clear span-to-depth
rstios, IJd, tess than 5, that is beams with ald l e s than 2.5 (see Section 1.5.1).
Franz and Niedenhoff (1963) used photoelastic mode1 studies to investigate the stresses
in isouopic homogeneous deep bearns before cracking. These beams had a uniformly distributed
load applied dong their top surface and were sirnply supported. Franz and Niedenhoff found that
the srnailer the span-to-depth ratio, the more pronounced the deviation of stress distribution from
that assurned by the Bernoulli hypothesis. For beams with a spart-to-height ratio of one, the
extreme fibre tensile stress can be more than twice that predicted by traditional engineering beam
theory. It has also been demonstrated that the flexural lever a m for the elastic solution is las
than 0.67h, which corresponds to that for a slender beam (Park and Paulay 1975). Furthemore,
the interna1 iever arm for very deep beams does not significantly increase after cracking. For
very deep beams, Franz and Niedenhoff also found that the depth of the tension zone near the
bottom of the beam is relatively srnall (roughly 0.251 thick).
Franz and Niedenhoff (1963) also tested reinforced concrete pier cap specimens which
when inverteci resemble simply supported deep bearns . Two di fferent reinforcing bar layouts
were investigated, one which had concentrateci reinforcing bars representing a tension tie and the
other contained bent-up bars for the main tension reinforcement. The specimen with the
horizontal bars had a capacity which was 23 % higher chan that with the bent-up bars due to the
larger arnount of tension tie reinforcement at the inside edge of the bearing.
Leonhardt and Walther (1966) carried out experirnents on deep bearns to investigate the
influence of detailing of the reinforcement and the influence of type of loading. They made the
following conciusions and recomrnendations:
1. The main tension tie reinforcement should be distributed over a depth of 0.25 h -0.05 1
from the bonom (tension) face, for cases where h 5 f.
O 152 x 76 x 9.5 mm plate rn 152~152~25mrnplate + 152 x 229 x fl mm plate
\ = 372 MPa
max agg. = 19 mm
d = 538 mm b = 155 mm
A, = 2277 mm2
strut-and-tie rnodel-\ sectional mode1
Figure 1.7 Applicability of strut-and-tie model for predicting series of beams tested by Kani (adapted from Collins and Mitchell 1991 )
2. At least 80% of the maximum calcuiated force in the main tension tie reinforcement
should be developed at the b e r face of the supports.
3. Small diameter bars of mechanicd anchorages should be used as the main tension tie
reinforcement to prevent premature anchorage faiiure,
4. A minimum web reinforcement ratio of 0.2% in both directions, as in reinforced concrete
walls, is adequate to conuol cracking. This reinforcement shouid be provided in the
form of s d l diameter bars.
5. Near the supports, closely spaced horizontal and vertical bars of the same size as the web
reinforcement should be provided.
In their tests of sirnply supported deep beams, the location of the application of load was
varied. For the case of a point load applied on the top surface at midspan, the load path
resembles a ~k3-arch. When a unifonnly distributed load was suspended from the bottom of the
beam instead of being applied to the top (compression) face of the beam, a more severe loading
condition was created. For this case, the load must first be transferred by vertical or inclined
tension reinforcement up to the compression region of the beam before it can be transferred to
the supports by means of tied-arch action. Therefore, verticai s t imps must be provided to satisQ
this force requirement as well as to control cracks.
Rogowsky et al. (1986) carried out tests on 7 simply supported and 17 two-span
continuous deep beams. Variables included: the shear span-to-depth ratio, the flexural
reinforcement ratio, the amount of vertical stirrups and the amount of horizontal web
reinforcement. Two main types of behaviour were observeci. Near failure, beams without
vertical stirrups or with minimum verticai stirmps approached tied-arch action regardless of the
arnount of horizontal web reinforcement present. These beams failed suddenly with Iittle plastic
defonnation, while those with large amounts of vertical stirrups failed in a ductile manner.
The AC1 Code provisions for deep beams (see Section 1 S. 1) have been developed based
solely on past experiments of single-span, simply supported deep beams Ioaded on their top
(compression) face. Rogowsky et al. (1986) concluded that the AC1 Code expressions gave
conservative results for the simply supported beams and the continuous beams with large amounts
of vertical reinforcement tested. However, these expressions proved unconservative for the
continuous beams without web reinforcement and for those containing only horizontai web
reinforcement. They determined that the AC1 Code predictions were unconservative due to the
fact that they are based on an incorrect mechmical mode1 for the shear strength of deep beams . RogowsIq and MacGregor ( 1986) proposed the use of stnit-and-tie models as a more rational and
consistent means of analyzing single- and multiple-span deep beams .
Franz and Niedenhoff (1 963) carrieci out photoelastic experiments on corbels having a
shear span-to-depth ratio, ald, of less than 1.0. These experimental studies of the elastic response
of corbels indicated that:
1. The tensile stress dong the top edge of the corbel is almost constant between the bearing
area and the face of the column.
2. The compressive stress flowing in from the bottom of the corbel into the c o l m are
almost parailel and resemble a compressive strut.
3. Rectangular corbels exhibited a nearly stress free zone at the outer-bottom corner of the
corbel.
Franz and Niedenhoff developed a simple truss analogy based on their observations of
the stress trajectories. In addition, they gave the following detailing recommendations:
1. The prirnary tension reinforcement should be anchored at the outside face of the corbel.
They recornmended providing the main tension reinforcement in the form of closed
hoops . 2. A minimum amount of compression reinforcement, with appropriate ties to prevent
buckling, should be placed parallel to the compression face of the corbel.
3. A minimum amount of uniforrniy distributed reinforcement, having an area of at Ieast
25% of that provided by the primary tension reinforcement, should be provided.
In 1964, Kriz and Raths tested 195 corbels, of which 124 were subjected vertical Ioads
alone and 7 1 others were loaded verticaily and horizontally (Kriz and Raths 1965). The variables
studied in these tests included size and shape of the corbel, amount of main tension tie
reinforcement and its detailing, concrete strength, ratio of shear span to effective depth, and ratio
of horizontal to vertical loading. Kriz and Raths gave the foltowing recomrnendations:
1. The ratio of the arnount of main tension reinforcernent to the gross cross-sectional area
of the corbel should not be l e s than 0.004 in order to control cracking.
2. A cross bar should be welded to the main tension tie reinforcement near each end in
order to provide proper anchorage (see Fig. l.b(b)). The size of this cross bar should
be at least equal to the largest bar used in the main tension tie reinforcement, and it
should be located as near to the outer face of the corbel as cover requirements permit.
3. Closed horizontal stimps shouid be provided having an area not less than 50% of that
provided by the main tension tie reinforcement. These stirnips shouId be uniforxnly
distributed throughout the upper two-thirds of the effective depth of the corbel.
4. The total depth of the corbel at the outer edge of the loading plate shoitid be at least
equal to one-haif the depth of the corbel at the colurnn face.
5 . The outer edge of the bearing plate shouid be at least 50 mm from the outer face of the
corbel.
6 . When corbels are designed to resist horizontal forces, the steel bearing plates should be
welded to the main tension tie reinforcement to transfer the horizontal force directly to
these bars (see Fig . I .6(b)). 7. Bearing stresses at ultimate load should not exceed OS$.
Mast (1968) inuoduced the "shear-friction" concept for the design of corbels. His goal
was to develop a simple rational approach based on physical models of behaviour which could
be used in the design of a number of different concrete connections. The approach assumes
nurnerous failure planes for which reinforcement m u t be chosen to prevent failure dong these
planes.
The shear-friction concept assumes that a crack interface has some roughness and hence.
as shear is applied, the defocmations include not oniy some shear displacernent dong the crack
interface, but also some widening of the crack. The crack opening causes tension in the
reinforcement crossing the crack which is balanced by compressive stresses in the concrete across
the crack interface. The shear on the interface is assumed to be related to the compression across
the interface by a coefficient of friction, p, which depends on the roughness of the interface
surface. The nominal shear capacity is thus given as:
In detennining the shear strength, Mast made the following assumptions:
1. The reinforcement crossing a crack is sufficientiy anchored such that the bars can yield.
2. The cohesive strength of concrete is negligible.
3. The effective coefficient of shear friction, p, depends on the surface roughness but is
independent of concrete strength.
This concept was applied to test data reported by Kriz and Ratlis where the shear span-to-
depth ratio, ald, was less than or equal to 0.7 and where the reinforcement had yielded. The
shear-friction concept gave reasonably conservative strength predictions for both vertical and
combineci vertid and horizontal loading cases.
Mattock et al. (1976) tested 28 reinforced concrete corbels subjected to vertical and
horizontal loading. The variables included in these tests were: the ratio of shear span to effective
depth, the ratio of horizontal to vertical load, the maunts of main tension tie and distributed
reinforcement, concrete strength and type of aggregate.
The design procedure first introduced in the 197 1 AC1 Code was based on the research
of Kriz and Raths (1965) with later modifications to include the design procedure developed by
Mattock (1 976) and Mattock et al. (1 976). This approach is still in use today (see Section 1 -5.2).
1.6.3 Pier Caps
Al-Soufi (1990) carried out an experimental investigation which involveci testing six
reinforced concrete pier caps. Parameters which were varied in these specimens included: the
geometry of the pier caps, the amount and distïibution of unifonnly distributed reinforcement,
and the anchorage details of this reinforcement. He made the following conclusions and
recornmendations :
After yielding of the main tension tie reinforcement, yielding spreads to the distributed
reinforcement.
The unifonniy distributed reinforcement contributes significantly to the strength and plays
a key role in controlling cracks.
Standard 90" end hooks rnay be provided to anchor the reinforcement of the main tension
tie provided that these bars can develop their yield force at the inner edge of the bearing
plates.
The unifonnly distributed horizontal reinforcement may be provided in the form of U-
shaped stirrups properly lap spliced over the central region of the pier cap. The
uniformly distnbuted vertical reinforcement rnay be provided in the f o m of closed
stirrups or lap-spliced U-shaped stirnips.
The column reinforcement, which was extended into the pier cap, provided additional
horizontal (column ties) and vertical reinforcement in the central region of the pier cap.
This additional reinforcement controlled cracks and provided some confiement for the
lap splices of the uniforrnly distriburai horizontal reinforcement.
Stnit-and-tie models provided a usehl tool for evaluating the strength of these pier caps,
while non-linear finite element analysis provided a means of predicting behaviour at service load
Ievels (see Section 1 -7.2).
1.7 Detailed Analysis Procedures
This section discusses more detailed anaiysis procedures, including refined stnit-and-tie
modelling, and non-Iinear finite element analysis.
1.7.1 Refined Strut-and-Tie Modds
Simple strut-and-tie models typically assume that the compressive struts can be
represented by straight lines between loading and support bearhg areas, and usuaily ignore the
contribution of uniformiy distnbuted reinforcement. More refmed strut-and-tie models attempt
to include the effects of bulging and curving compressive stnits due to the presence of tensile
stresses in the concrete and uniformiy distributecl reinforcement. Accounting for the presence
of unifonnly distributed reinforcement also increases the total amount of tension tie
reinforcement, and hence the strength of the member.
Figure 1.8 shows a simply supported deep bearn with a concentrated load applied on its
top surface. In Fig. 1 .&a), the flow of principal compressive and tensile stresses are indicated
with dashed and solid lines, respectively. The diagonai compressive struts buige between the
loading point and the supports due to the presence of tensile stresses in the concrete. A possible
strut-and-tie mode1 which acccJunts for this bulging action of the struts is presented in Fig. 1.8(b).
Design procedures have typically adopted a simpler assumption of straight compression struts in
combination with a minimum arnount of reinforcement uniforxniy distributed in the horizontal and
vertical directions as s h o w in Fig. 1.8(c). This uniformly distributed reinforcernent serves to
control cracking in disturbed regions (see Section 1.4).
In deep bearn design, unifonnly distributed reinforcement corresponding to geornetnc
ratios of 0.002 to 0.003 is usually provided in the horizonta1 and vertical directions. Marti
(1985) investigated the role of this reinforcement in controllhg cracks, perrnitting redistribution
of stresses after cracking and increasing the strength of the member. Figure 1.9 shows one-half
of a deep bearn which is subjected to a concentrated load applied on its top surface and with
simple supports at its ends. It is assumed that this beam has uni fody distributed reinforcemnt
in the verticai direction ody. Figure 1,9(a) illustrates the arching and fanning of the compressive
stresses in the member. The presence of the unifonnly distributed vertical reinforcement perniits
the main compression stmt to curve, thus forming an arcb, and also provides anchorage for the
fanning compression smts near the bottom of the beam. Figure 1.9(a) shows the variation of
the force in required in the main tension tie reinforcement. The main tension tie has a maximum
force at the centre-line of the beam (point d) corresponding to the tensile force, T. In the region
crack cantrol V V sted I I
(a) Flow of principal stresses
(b) Required tension ties
(c) Assumption of straight compressive stnits
Figure 1.8 Crack control reinforcement required with assumption of straight-line compressive stnits (adapted from Schlaich et al. 1987)
effective distnbuted V vertical reinforcement I
lie representing distributed V vertical reinforcement i
(a) Arch and fan action (b) Strut-and-tie model
Figure 1.9 lnvestigating the effect of distributed reinforcernent on deep beams (adapted from Marti 1985)
between points b and d, that is where uniformly distributed vertical reinforcement is present, the
force in the longitudinal reinforcement changes as shown in Fig. 1.9(a). in the regions between
points a and b and between d and e the force in the main tension tie remains constant. As
pointed out by Marti (1985), the vertical distributed reinforcement allows curtailment of some
of the longitudinal tension tie reinforcement. Figure 1.9(b) shows the idedized strut-and-tie
model for this deep beam containing uniformly distributed vertical reinforcement. The uniformiy
distributed vertical reinforcement has been idealized as a tension tie at the centre of zone
containing vertical reinforcement. This idealkition permit5 the compressive arch and
compressive fanning to be represented as shown in Fig. 1.9(b). Also shown is the variation of
force in the longitudinal reinforcement as predicted by this refined strut-and-tie model.
While uniformiy distributed vertical reinforcement reduces the demand on the main
tension tie reinforcement close to the support region, its presence does not result in increased
member strength. This is due to the fact that the strength is controlled by the conditions at
midspan. The presence of uniforxniy distributed horizontal reinforcement assists the main tension
tie reinforcement and resuIts in increased strength.
Although the simple strut-and-tie models are very useful in design and give conservative
strength predictions, for detailed analysis of the strength a more refmed stmt-and-tie model,
including both the vertical and horizontal distributeci reinforcement, gives more accurate strength
predictions.
As was mentioncd in Section 1.2, it is not appropriate to design disturbed regions with
the usual beam theory assumptions. Elastic finite element analysis may be used to determine the
stresses in a reinforced concrete member prior to cracking, however this type of analysis may not
be appropriate for predicting stresses in a cracked member as significant redistribution of stresses
occurs after cracking. In order to predict the full response (including post-cracking response) of
reinforced concrete members a computer program, FIELDS, was developed (Cook 1987, Cook
and Mitchell 1988) which combines two-dimensional non-linear finite etement analysis with the
compression field theory (Collins and Mitchell 1980, 1986, and Vecchio and Collins 1986).
Triangular and quadrilateral elements are used to mode1 the reinforced concrete member.
To account for significant non-linearities which may arise within a finite element, up to four-by-
four Gauss quadrature may be chosen for an element. Figure 1.10 filustrates the method used
to evaluate stresses correspondhg tcb a state of strain at each Gauss point (Cook and Mitchell
(a) Element with 4 x 4 quadrature
(b) State of strain at a single Gauss point
t t t - t
(c ) Deterrnining stresses at a Gauss point corresponding to a strain state
Figure 1 . I O Evaluating stresses at Gauss points in quadrilateral elernent (Cook and Mitchell 1988)
1988). n ie principal tensile strain, cl, the principal compressive strain. E,, the strain in the x-
direction, E - ~ , the strain in the y-direction, 5, and the principal compressive strain direction, B.
are inter-related by the requirements of strain compatibility (see Fig . 1.1 O@)).
The average steel stresses, f, and f,, at a Gauss point can easily be detennined by using
the stress-strain relationships of the reinforcing steel. However. the average stresses in the
cracked concrete, f,, and f,, are not as easy to determine. The average principal campressive
stress, f,, is not only a huiction of the principal compressive strain, q, but is also dependent on
the principal tensile strain, c l . As E , increases f, decreases; this effect is known as strain
softening. Combining the Iimiting compressive stress for cracked concrete developed by Vecchio
and Collins (1986) and a parabolic concrete stress-strain curve gives the compressive stress-strain
relationship for cracked concrete (see Fig. 1.4(a)) as:
where:
and c: = strain in the concrete at peak compressive stress.
After cracking, the principal tensile stress in the concrete varies from zero at a crack location to
a maximum between cracks. Figure 1.11 shows the average principal tensile stress. fcl, plotted
against the principal tensile strain, E , (Vecchio and Collins 1986) as:
where: E, = initial tangent modulus of the concrete,
E c ~ = strain in the concrete at cracking, and
Lr = concrete cracking stress = Ececr.
Figure 1.12 shows that the average principal tensile stress may be lirnited by yielding of
reinforcement or by sliding dong the crack interface (Vecchio and Collins 1986). Between the
Figure 1.11 Determining average concrete tensile stress,^, , from strain, E,
(Vecchio and Collins 1986)
(a) Cracked reinforced (b) Transrnitting shear concrete element across crack interface
(c) Average stresses (d) Stress condition at between cracks crack interface
Figure 1.12 Investigating stress condition at crack interface (Vecchio and Collins 1986)
cracks, the concrete and the steel are assumed to have average values of stress (see Fig . 1 .12(c)),
while at a crack the tensile stress in the concrete is zero, the steel stress is a maximum, and a
shear stress v, may exist at the crack interface (see Fig. l.l2(d)). An approximate expression
for the shear stress limit dong a crack has been developed (Vecchio and Collins 1986) based on
the interface shear transfer tests conducted by Walraven (1981). This expression can be
simplifieci as:
where: w = average crack width in mm,
a = maximum aggregate size in mm.
Note that this is an empirical expression and that stresses are expressed in MPa units. The
average crack width c m be assurneci to equal the average crack spacing tirnes e,. Since the stress
States shown in Fig. 1.12(c) and (d) are statically equivalent, it is possible to determine whether
yielding of the reinforcenent across the crack (Le. f,, or f,, equals 4) or sliding at the crack
interface (i.e. v, equals v,-) will result in a value off,, less than thac given by Eq. 1 -20.
Examples of the application of non-linear f ~ t e element analysis applied to deep beams.
corbels, dapped end beams and anchorage zones are given by Cook and Mitchell (1988) and
Collins and Mitchell (1991).
1.8.1 Compressive Strength
Advances in concrete technoIogy over the past two decades have resulted in the
availability of ready-mixed concrete with compressive strengths as high as 100 MPa in several
North American cities. There is a need to investigate whether the design proceciures, developed
for use with normal-strength concretes, are applicable to the full range of high-strength concrets
currently available (Collins et al. 1993).
The traditional parabolic stress-strain curve for normal-strength concrete recommended
by Hognestad (1957) can be expressed as:
This formula provides a reasonable approximation to the stress-strain curve for nomial-strength
concrete. However , as concrete strength increases , the compressive stress-strain cuve is near
linear over the rising branch, and exhibits greater initial stiffkess and decreased ductility (see Fig .
1-13). The parabota is too " rounded" to accurately represent this increased linearty and the more
bnttle post-peak response of very high-strength concrete.
Thorenfeldt er al. (1987) introduced a post-peak decay term, k, to the stress-strain
relationship developed by Popovics (1973) such that it could be applied to wide range of concrete
strengths. This resuited in the following expression:
where: fc = compressive stress,
fc' = maximum compressive stress,
Cc = compressive strain, I
c = compressive strain when fc reaches fCt,
n = cuve fitting factor, as n becomes higher. the rising portion of the curve
becomes more Iinear, and
k = post-peak decay term. taken as 1 when É& E: is Iess than 1, and taken greater
than 1 when eC E,' exceeds 1.
Equation 1.23 gives fc as a function of tc and involves four constants, namely. fct, rct, n
and k. While these four constants can al1 be determineci from actual cytinder stress-strain curves,
in rnany design situations, only the cylinder strength, f:, is laiown. Collins and Porasz (1989).
and Collins and Mitchell (1991) suggest that for € J e C r > 1 :
Figure i.13 Influence of concrete strength on shape of stress-strain curve
where Er = modulus of elasticity of concrete.
The 1994 CSA Standard gives an expression for E, (in m a ) , for concrete with y, between 1500
and 2500 kg/m3, as follows:
where y, = concrete density (in kg/m3)
From the value off,' the four constants in Eq. 1.24 through 1.27 can be used to develop
the stress-strain relationship given in Eq. 1.23.
1.8.2 Nexure and Axiai ha&
The new rectangular stress block factors, al and PI, of the 1994 CSA Standard are
suitable for a wide range of concrete compressive strengths. It is assurneci that a concrete stress
of al$cfc' is uniformiy distributed from the extreme compression fibre into the member a
distance of 8, c, where c is the distance of the neutrai axis from the extreme compression fibre.
These factors now depend on the concrete cylinder strength as follows:
The new factors are intended to account for both the signifiant shape change in the stress-strain
cuve as the concrete strength increases and the difference between the cylinder strength and the
in-situ concrete strength.
1.8.3 Minimum Reinforcement for FIexure and Shear
The 1994 CSA Standard requires a minimum arnount of fiexural reinforcement in order
to give adequate reserve of strength after cracking and hence provide a ductile response. The
1994 CSA Standard requires that one of the foiiowing three provisions be satisfied:
1. The factored moment resistance, M,, must be such that:
2. Except for slabs and footings, provide a minimum area of flexural reinforcement, A,,
as foIlows:
where: b, = width of tension zone of member.
3. The minimum reinforcement requirements given above may be waived provided that the
factored moment resistance, M,, is at least one-third greater than the factored moment,
Mr.
The 1994 CSA Standard also requires a minimum arnount of shear reinforcement which
is dependent on concrete strength. An increase in the concrete compressive strength leads to an
increase in the tensile strength, which in turn results in an increase in the cracking shear. This
increase in the cracking shear requires an increase in the minimum shear reinforcement in order
to ensure that the shear strength exceeds the cracking shear. The 1994 CSA Standard requires
a minimum area of shear reinforcement, A,, as follows:
where: b, = minimum effective web width,
s = spacing of shear reinforcement.
This requirement, together with the maximum spacing limits for shear reinforcement, is intendeci
to control inclineci cracking at service load levels.
1.8.4 SW-and-Tie Provisions
The provisions for strut-and-tie models in the 1994 CSA Standard are the same as those
in the 1984 CSA Standard. The stress limit for a concrete strut. 0.85+,fc'. remains a linear
function of the concrete cylinder strength. MacGregor (1997) has introduced a factor. v,, to
account for the infiuence of high-strength concrete (see Tables 1.1 and 1.2).
The 1994 CSA Standard and the 1997 CHBDC provisions for suut-and-tie models require
minimum arnounts of uni forrnly distributeci reinforcement which are independent of concrete
strength (see Section 1.4).
1.9 Crack Widths and Crack Spacing
Concrete cm only withstand srnall tensile strains before it cracks. As these cracks do not
form at equai spacings, crack widths may Vary in size. and it is therefore appropriate to define
the mean crack width, w,,,, as:
where: s,,, = mean crack spacïng , and
€cf = strain in the concrete caused by stress.
The characteristic crack width (the width which only 5% of the cracks will exceed), w,, is
approximated by the CEB-FIP Model Code (CEB 1990) as w, = 1.7 w,. The CEB-FIP Model
Code (CEB 1990) gives the following expression for the mean crack spacing:
where: c
S
Pd
As
4.4
= clear concrete cover,
= maximum spacing between longitudinal reinforcing bars, but shall not be taken
as greater tiian 15d, (where d, is the diameter of the reinforcing bar),
= Ai*c,g = area of steel considered to be effectively bonded to the concrete,
= area of the effective embedment zone of the concrete where the reinforcing
bars c m influence crack widths (see Fig. 1.14(a)),
7
15 d,
4 = shaded area
(a) CEB-FIP expression
neutral axis /
shaded area
\- tension face
(b) Gergely-Lutz expression
Figure 1 .i4 Crack width parameters
neutral axis
skin reinforcernent
cross-section elevation
Figure 1.1 5 Side-face cracks controlled by skin reinforcement
ki = coefficient that characterizes bond properties of reinforcing bars,
= 0.4 for defonned b a s
= 0.8 for plain bars
k2 = coefficient to account for the strain gradient.
= 0.25 (t, + c3 /2 e,. where e, and c2 are the largest and srnallest ten
in the effective embedment zone, respectively .
The Gergely-Lutz expression (Gergely and Lutz 1968) estirnates the maximum crack
width as:
where: 6 = factor accounting for strain gradient,
= 1.0 for unifom strains
= h2/h, for varying strains, where h, is the distance of the main tension
reinforcement from the neutral axis and 4 is the distance of the extreme tension
fibre from the neutral axis
€S. cr = strain in a reinforcing bar at a crack Iocation,
4 = distance frorn the extreme tension fibre to the centre of the closest bar, and
A = effective area of concrete surrounding each bar, taken as the total concrete
area in tension, which has the sarne centroid as the tension reinforcement,
divided by the number of reinforcing bars (see Fig. 1.14(b)).
In the Gergely-Lutz expression, the strain in the reinforcement at a crack is taken as:
where: N = applied axial tension, and
ES = modulus of elasticity of steel.
The CEB-FIP Mode1 Code, (CEB 1990) lirnits crack widths to 0.30 mm for structures
exposed to both frost and de-king conditions. The 1995 AC1 Code and the 1994 CSA Standard
require the calculation of a crack width parameter, z , to detennine if the crack widths would be
within acceptable limits. This crack width parameter is based on the Gergely-Lutz expression
(see Eq. 1.35) and is given as:
where: f, = calculated stress in reinforcement at specified loads, may be taken as 0.64.
The 2-factor is lirnited to 30,000 Nlrnrn for interior exposure and 25,000 Nlmm for exterior
exposure. These limits correspond to maximum crack widths of 0.40 and 0.33 mm, respectively.
If epoxy-coated reinforcement is used the CSA Standard requires multipIication of the limiting
crack width parameter, z , by a factor of 1.2, based on the research of Abrishami et al (1995).
Figure 1.15 illustrates the requirement for skin reinforcement in the 1995 AC1 Code and
the 1994 CSA Standard for members with an overall depth, h, exceeding 750 mm. The required
longitudinal skui reinforcement shall be unifonniy distributed dong the exposed side faces of the
member over a depth of O S h - 2(h -6) fiom the principal reinforcement (see Fig. 1.15). The total
area of such reinforcement shall be p&, where A, is the sum of the area of concrete in suips
dong each exposed side face, each strip having a height of 0.5h - 2(h -4 and a width of twice the
distance from the side face to the centre of the skin reinforcernent but not more than hdf the web
width. The minimum amount of skin reinforcement shall be such that p, equals 0.008 or 0.0 10
for interior or exterior exposure, respectively. The maximum spacing of this skin reinforcement
is 200 mm.
Research Objectives
The objectives of this research programme are:
to study the complete behaviour of full-scale reinforced concrete cantilever cap
bearns ,
to investigate the suitability of current design approaches for these disturbed
regions,
to compare the predicted responses using simple strut-and-tie models, refined
strut-and-tie models arid non-linear finite element analyses,
to investigate the influence of concrete strength on the behaviour of large
cantilever cap beams, and
to study the amount of uniformly distributed reinforcement required for crack
control at service load Ievels.
Cl3APTER2
EXPERIMENTAL PROGRAMME
Two full-scaie cantilever cap beams were constructeci and tested in order to study their
complete responses. These test specimens are representative of the cantilever portions of
continuous cap beams and of cantilever cap beams as shown in Fig. 2.1. These cantilever cap
bearns were designed using the strut-and-tie approach of current codes (CSA 1994, CHBDC 1996
and AASHTO LFRD L994). The arnounts of uniformly distributed horizontal and vertical
reinforcement were varied in order to study their influence on crack conîrol at service load levels.
The geometry of the cantilever cap beams was chosen after snidying a number of
drawings of typical cap beams (see Fig. 1.1). The loads at each bearing location for the
prototype bridge investigated were a service dead load of 460 kN and a service dead plus Iive
plus impact Ioad of 1140 kN.
2.1 Details of Specimens
Cap beam specimen CAPN was cast with normal strength concrete (design fc' = 35 W a ) ,
while specimen CAPH was constmcted with high-performance concrete (design fc' = 70 MPa).
Both specimens have identicd geometries. As shown in Fig. 2.2, each cap beam is 3350 mm
long, 750 mm wide and has cantilevers which extend 1300 mm from the faces of the 750 mm
square columri. The depth of each cantilever is 900 mm at its end, increasing to 1100 mm over
a distance of 625 mm from the end.
The reinforcement for both specimens was identicai, with epoxy-coated bars used
throughout to conform to the requirements of the Canadian Highway Bridge Design Code
(CHBDC 1996) for corrosive environrnents. The main tension tie reinforcement was provided
by two layers of reinforcement, each containing 5 No.25 bars, with a clear vertical spacing of
35 mm. One layer of 5 No.25 bars served as the compression steel. The square colurnn was
reinforceci with 12 No.25 bars and confued by sets of 3 No.10 colurnn ties spaced at 300 mm
(see Fig. 2.2). The specimens had crack control reinforcement ratios of 0.18% and 0.30% in
cantilever ends A and B, respectively (see Sections A-A and B-B). In end A, this reinforcement
(a) Prototype continuous cap beam
(b) Prototype cantilever cap bearn (c) Test setup
Figure 2.1 Test simulation of cantilever cap beams
7 4 - No. 10 /double stirrups
L I
Section A-A
(vertical distributed
reinforcement) s = 300
'2 - NO. 15 U-shaped bars
(horizontal distnbuted
reinforcement) s = 295
double stirrups (vertical
distributed reinforcement)
s = l ? S
4 - No. 15- U-shaped bars
(horizontal distributed
reinforcemen t) s =lï?
Section B-B
10 -No. 25 (tension
reinforcement) 3 -NO. I O 12 - No. 25 (colurnn ties)
(column bars) s = 3G0
Notes: dimensions in mm
minimum cover = 50 mm
Figure 2.2 Specimen details
was provided by 4 double No.10 stirrups spaced at 300 mm in the vertical direction, and 2
U-shaped No. 15 bars spaced at 295 mm in the horizontal direction. These spacings were reduced
to 175 mn for the 7 vertical double stirnrps and 177 mm for the 4 horizontal crack control bars
in end B. A minimum cover of 50 mm was maintained &oughout the specimens.
Ninety-degree end anchorages with free end extensions of 300 mm beyond the bend were
provided on al1 the No. 25 bars used for the main tension tie reinforcement. In order to fully
develop the reinforcement (fy = 400 m a ) , the code (CHBDC 1996) requires straight embedment
lengths, l&, of 430 mm and 304 mm beyond the hooks for specirnens CAPN and CAPH,
respectively. The tension development length, ld, of the No. 25 bars in CAPN is determined as:
where: k, = bar location factor, taken as 1 .O.
k2 = coating factor, taken as 1.2 due to the epoxy-coated bars.
k, = bar size factor, taken as 1.0 because bars are larger than No. 20.
Likewise, ld = 782 mm for the No. 25 bars of CAPH. The stress in the bar that can be
developed by the hook is [(Il06 - 430)/1106] * 400 MPa = 244 MPa for specimen CAPN and
[(782 - 304)/782] * 400 MPa = 244 MPa for CAPH. Knowing the geometry of the bend and
the placement of the bearing pads (see Fig. 2.2). the avaiIable straight bar embedment length to
the inner edge of the bearing plate is 286 mm for the bottom Iayer and 226 mm for the bottom
layer of bars for CAPN. Therefore, the bottom Iayer of bars in CAPN is capable of developing
a stress of 244 MPa + 286/1106 * 400 MPa = 348 MPa, while the top bars can develop 326
MPa. SimiIarly the bottom and top bar layers of CAPH can develop 371 MPa and 340 MPa,
respectively. These calculations assume that the bond stress is uniform over the development
tength, which results in a linear build-up of stress aiong l& A1thoug.h stresses greater than 400
MPa are expected during testing, these smaller embedment lengths were provided to investigate
the beneficial effects of the compressive bearing stress on the bond strength.
The horizontal distributed steel was lap spliced in the central regions of the specirnens
where additiod confinement is provided by the column ties which are typically continued into
the cap bearn. Without considering the beneficial effects of the confinement provided by these
column ties, the required lap splice length is calculateci as 1.3 1, (CHBDC 1996). where:
Hence the required lap splice Iength for specimen CAFN is 1.3 x 531 mm = 690 mm.
Sirnilarly, the required lap length for specimen CAPH, having a design compressive strength of
70 MPa is 488 mm. Full development of the horizontal bars was therefore achieved in the
central region of the cap beam. Over the constantdepth porüons of the cap beam the vertical
uniformiy disuibuted reinforcement was provided by No. 10 double closed stimps (see Fig. 2.2).
Because of the changing depth of the cap beam near its ends, it was necessary to use double U-
shaped spliced stimps over the tapered portions of the specimem. The required lapsplice length
for these U-shaped stimps, using Eq. 1.1, is 460 mm for CAPN and 340 mm for CAPH. A
conservative value of 460 mm was used for both specimens.
2.2 Material Properties
2.2.1 Concrete
Both specimens were cast with ready-mix concrete. The specified concrete strength for
CAPN was 35 MPa with a water to cernent ratio (wlc) of 0.40 and a maximum aggregate size
of 14 mm. The high performance concrete of CAFH had a specified strength of 70 MPa, a wlc
of 0.28, and a 10 mm maximum aggregate size. Mix designs are presented in Tables 2.1 and
2.2, and the slump and air content measurernents taken upon delivery are shown in Table 2.3.
The test specimens, together with the controI cylinders and flexural beams, were covered with
wet burlap and plastic sheeting a few hours after casting, and were kept moist. The test
specimens and the control specimens were stripped of their formwork 4 days after casting and
kept in the sarne air-cured conditions of the laboratory. The compressive strengths were
detennined fiom the resuits of testing 3 standard, 150 mm diameter by 300 mm long, concrete
cylinders, and the splitting tensile strengths were taken as the average fiom 3 Brazilian tests on
150 mm 4 by 3 0 mm cylinders. in addition, 3 flexural beam tests were used to determine the
average modulus of rupture. These flexural beam specimens measured 150 x 150 x 600 mm and
were subjected to third-point loadùrg over a span of 450 mm. A sumrnary of the results of the
cylinder and beam tests are presented in Table 2.3. Representative compressive stress-strain
curves for the 35 MPa and 70 MPa concretes are shown in Fig . 2.3(a). In addition, shrinkage
strains were determinecl from externaily applied strain targets on concrete beam specimens
measuring 100 x 100 x 400 mm. The strain targets were placed on these shrinkage specimens
24 hours after casting. The shrinkage strains determineci From these measurements are shown
Ir fine aggregate 1 Lafarge St.-Gabriel 1 757 kg/m3
cernent
II water reducer 1 Pozzolith 2ON 1 1346 mL
10
coarse aggregate
water (fotal)
total density
II air-entraining agent 1 Micro- Air 1 330 mL
415 kg/m3
II superplasticizer 1 Rheobuild 1 0 0 1 2.7 L
10-14 mm limestone
II retarder 1 pozzolith 1 0 0 ~ ~ 1 375 mL
1003 kg/m3
167 kg/m3
2342 kg/m3
Table 2.1 Mix design for 35 MPa concrete
11 fine aggregate ( Lafarge St.-Gabriel ( 850 kg/m3 IL
II coarse aggregate 1 10 mm lirnestone 1 10 15 kg/m3
- --
cernent lOSF
1 II water reducer 1 Pozzolith 2ûON 1 1630 mL
480 kg/m3
1 totai density
II superplasticirer 1 Rheobuild 1 0 0 1 L3.0 L
water (total)
2480 kg/m3
II retarder 1 Pozzolith lûûXR 1 780 rnL
135 kg/m3
Table 2.2 Mix design for 70 MPa concrete
in Fig . 2.3(b). It is interesthg to note that the 70 MPa concrete exhibited considerably higher
shrinkage strains in the first few days after casting than the 35 MPa concrete.
microstrain
(a) representative stress-strain curves
35 MPa
A--
O 50 100 150 200 250
tirne (days)
(b) average shrinkage strains
Figure 2.3 Concrete Properties
II air content (% ) 1 6.5 1 2.3
- - - -- Ir average 28-day sumgth @Pa) 1 36.1 1 72.8
age at testing (days) --
secant modulus (GPa)
II characteristic peak suain ( d m ) 1 2.18 1 3.08
compressive strength at testing
(MW
splitting tensile strength at testing
(MW
modulus of rupture at testing
(MW
1 average 1 37.6 1 79.2
- - 1 average 1 3.2 1 5.2
1 average 1 4.6 1 6.7
1 std. dev. 1 0.3 1 0.3 - -. - . .
Table 2.3 Concrete properties
2.2.2 Reinforcing Steel
Steel reinforcement consisted of No. 10, No. 15 and No.25 epoxy-coated deforrned bars
with a specified grade of 400 MPa. A minimum of 3 tensile samples were testeci for each bar
size to determine their mechanical properties. Table 2.4 summarizes the average values and the
standard deviation of the yield and ultimate stresses and strains at strain hardening, strains at the
dtimate stress and the rupture strains. Figure 2.4 shows typical stress-strain curves for the three
different bar sizes. The modulus of elasticity for d l reinforcing steel has been taken as 200 GPa
for the purpose of both design and anaiysis.
O 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
strain (mm/mrn)
(a) No. 10 bars
strain (mm/mrn)
(b) No. 15 bars
I UY --
1 . 1 I O 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
strain (mm/mm)
(c) No. 25 bars
Figure 2.4 Typical stress-strain responses of reinforcing bars
R O P ~ 1 No. 10 1 No. 15 1 No. 25
1 average 1 441.0 1 419.0 1 468.5
1 std. dev. 1 2.7 1 1.0 1 7.1
1 std. dev. 1 2.2 1 2.9 ( L.2
strain at strain
hardenhg ( %)
ultimate stress
average
std. dev.
average
strain at ultimate stress
( w ) rupture strain,
Table 2.4 Reinforcing steel properties
2.3 Test Setup and Instrumentation
average
I 1 1
The pier caps were installeci upsidedown under the 11,000 kN capacity MTS universai
testing machine (see Fig. 2.5). Figure 2.6 shows the loading arrangement at the top of the stub
column for each specimen. Load was transferred through the 559 mm diameter bottom platen
of the MTS's spherical seat, which in turn loaded two plates. These plates had a total thickness
of 127 mm in order to ensure sufficient spreading of the load. The 51 mm thick bottom plate
rneasured 660 x 660 mm, and was seated with plaster to the top of the 750 x 750 mm stub
column. The size of this bouom plate was chosen such that the load wodd be transrnitted to the
vertical column bars without loading the concrete cover.
OS4
0.06
768.6
0.77 1 1.12
std. dev.
average
over 200 mm ( % ) std. dev. 1 0.6 1 1.1
The cap beams were simply supported on the laboratory strong floor. Figure 2.6 shows
the bearing details used for specimens CAPN and CAPH. Two 20 mm thick by 152 mm wide
by 600 mm long bearing plates were seated with a plaster mortar compound on the bottorn of
CAPN. The bearing plates for specimen CAPH had a width of 76 mm, that is, one-half that
provided for CAPN due to the higher concrete compressive strength of specimzn CAPH. These
600 mm long bearing plates were centred across the 750 mm wide cap beams such that they did
not bear on the cover concrete. The centre of the bearings was Iocated 375 mm from the end
faces of the cap beams (see Fig . 2.6). The bearing plates rested on a rocker, with a radius of
0.04
707.5
13.4
0.6
0.02
688 -4
0.2
14.1
12.0 10.2
0.5
16.0
O. 1
13.5
Figure 2.5 Specirnen CAPN under the MTS testing machine
Notes; dimensions in mm
I, = 152 mm for CAPN I, = 76 mm for CAPH
Figure 2.6 Different bearing details of specimens CAPN and CAPH
250 mm, which in tum rested on two 152 mm diamerer rollers sandwiched between two 76 mm
thick steel plates.
Three Linear Voltage Differential Transducers (LVDT's) or extensometers were installecl
to m u r e vertical displacements of the specimen at the supports and at mid-span (see Fig. 2.7).
The centre deflection reporteci is taken as the deflection from the LVDT at midspan (CV), minus
the average of the LVDT's at ends A and B (AV and BV), in order to remove rnovements at the
supports. In addition, extensometers were used to determine average strains in the test
specimens. These LVDT's were attached to threaded rods which, in turn, were glued in holes
drilled 50 mm into the concrete. Ten extensometers were positioned, as shown in Fig. 2.7, at
the level of the centroid of the tension steel, between the centres of the bearhgs. A second Iine
of eight extensometers was located at nid-height of the cap beam. Additional extensometers were
positioned, as shown if Fig. 2.7, to fonn 260 mm rosettes within the shear spans of the cap
beam. The purpose of these rosettes was to determine principal strains and their directions in the
diagonal compressive stnits.
Figure 2.8 shows the locations of the twenty-two electricd resistance strain gauges which
were glued to the reinforcing bars prior to casting. Twelve gauges were Iocated on the bonom
layer of the main tension reinforcement, 6 on the centre and 6 on the outerrnost bar. These
gauges were positioned at the start of the hooks, at the inner edges of the bearing plates, and at
locations aligned with the colurnn faces (see Fig. 2.8). An additional ten gauges were glued to
the h o ~ o n t a i and vertical distributed bars in the shear spans of the cap beams as shown.
2.4 Testing Procedure
The loading was displacement controlled at a rate of approximateiy 0.004 mrnkec.
Throughout the testing, load, displacement and strain readings were recorded at intervals of 25
khi or 0.1 mm, whichever came first. During the early stages of a test, load application was
haited, to create major load stages, at increments of approximately 500 kN. At these load stages,
widths of cracks crossing the horizontal lines shown in Fig. 2.8 were measured using a crack
comparator, and the crack patterns were sketched and photographed. Afier yielding of the main
tension reinforcement, load stages were taken at increments of 1 to 2 mm of the mid-span vertical
deflection. The loading of the specimens continueci until a significant decrease in load-carrying
capacity was observed.
Note: dimensions in mm
Figure 2.7 LVDT locations
crack widths measured on
figure 2.8 Strain gauge locations and crack width lines of measurernent
CHAPTER 3
EXPERIMENTAL RESULTS
This chapter describes the experimentai results of each specimen. Appendix A gives
more details of the rneasurements taken.
3.1 Load-Deflection Responses
The response is described in terms of the applied shear on each shear span, which is
taken as one-haif of the total load applied to the top of the column. Figures 3.l(a) and (b) show
the shear vs. centre deflection responses for specirnens CAPN and CAPH, respectively.
3.1.1 Specimen CAPN
First cracking of CAPN occurred in ends A and B simultaneousiy at a shear of 430 W.
These flexural cracks which occurred on the bottom face of the cap barn, in line with the colurnn
faces, resulted in a slight decrease in member stiffness (see Fig. 3.l(a)). At a shear of 870 kN,
a major diagonal crack fonned on each end, causing a slight drop in load and a reduction of the
stif-fhess. First yielding of the tension tie occurred at a shear of less than 2310 IcN near the
location of the first flexural crack of end A. First yielding of the crack control reinforcement
occurred at a shear of 1350 kN for end A and 1740 kN for end B. Generai yielding of the
specimen occurred at a shear of 25 10 kN and a centre deflection of 4.33 mm. A maximum shear
of 2920 kN (that is, a total applied load of 5840 kN) was reached at a deflection of 14.78 mm.
FaiIure occurred by diagonal cnishing of the concrete at the re-entrant corner between the column
and end A of the cap beam followed by slippage dong the diagonal crack which f o d between
the re-entrant corner and the support of end A. This resulted in a drop of about 30% of the load-
carrying capacity as shown in Fig. 3.l(a)
first blding of end B +tributed steel 1 1 lding of end A distibuted steel 7-
ig and shear slip
centre deflection (mm)
(a) Specimen CAPN
first diagon l cracking i I
' first ffexural citacking
5 10 15 20
centre deflection (mm)
(b) Specimen CAPH
Figure 3.1 Load-deflection responses of specimens
First cracking of CAPH occurred in end A at a shear of 490 W, and resuIted in a
signifiant decrease in rnember stiffness (see Fig. 3.l(b)). The first crack in end B did not
develop until a shear of 570 IcN was reached. These f i e d cracks were aligned with the
colurnn faces and propagated from the bottom face of the cap beam. At a shear of 890 k.N, a
major diagonal crack formed on end A which caused considerable Ioad dropoff and a reduction
in stiffness. First yielding of the tension tie occurred at a shear of 2120 kN near the Iocation of
the first flexural cracks of end A. First yielding of the crack conuol reinforcement occurred at
a shear of 1360 kN for end A and 1910 kN for end B. Generai yielding of the specirnen took
place at a shear of 2620 kN and a centre deflection of 4.06 mm. A maximum shear of 3000 kN,
or a total applied Ioad of 6 0 kN, was reached at a deflection of 9.36 mm. Failure occurred
by shear slippage dong the diagonal crack which formed between the re-entrant corner and the
support of end A, with only rninor signs of crushing near the re-entrant corner. This resulted
in a drop of approxirnately 38% of the load-carrying capacity as show in Fig. 3.l(b)
LVDT's were used to deterrnine the average strains over the gauge lengths provided. and
the main gauges, glued to the reinforcing bars, were used to determine local strains in the bars.
3.2.1 Specimen CAPN
Figure 3.2 shows the variation of shear vs. horizontal strains rneasured in the bottom bars
of the main tension tie. The development of strains is shown at different Iocations of the main
tension tie for both ends A and B. with solid lines used to identify readings from gauges placed
on the outermost bar and dashed lines used to identifjr those readings from the innennost bar.
From gauges A5 and A6, as well as B3 and B4, it is ckar that the outermost bars are strained
approxirnately the sarne amount as the uinermost bars. Gauge B5 did not work during testing.
Gauges A5 and A6, as well as gauge 86 (see Fig. 3.2(e) and (f)), located close to where the first
flexural cracks f o d , clearly indicate the change from pre-cracking to post-cracking stiffness
at a shear of 430 kN, corresponding to first flexural cracking. A11 of the strain measurements
on end A were Iost after a shear of 1590 khi was reached due to a rnalfunction in the data
acquisition system. Up to this shear level of 1590 kN, end A experienced slightly greater strains
than end B. Gauge B6 indicates that first yielding of the tension tie in end B occurs at a shear
A1 (outer bar) - A2 (inner bar) - - -
vield
A3 (outer bar) - A4 (inner bar) - - -
micmstrain
yield
2.000 4,000 6.000
microstrain
B l (outer bar) 82 (inner bar)
O 2.000 4,000 6,000 8.
micmstrain
rnicmsttain
vield
500 s' --- 86 (inner bar) I
1
1 I
O 2,000 4,000 6.000 8,
microstrain
Figure 3.2 Strains in bottom bar of CAPN tension tie. determined from strain gauges
of 23 10 kN, that is, somewhat less than the shear corresponding to general yielding of 25 10 W.
Extrapolation of readings from gauges AS and A6 indicates that first yielding of the tension tie
in end A occwed at a shear of about 2260 W. The readings from gauges B3 and B4 (see Fig.
3.2(d)), located at the imer edge of the bearing in end B, indicate that the strains at this location
were close to the yield strain at maximum shear level. At general yield of the specimen (2510
kN), these strains had only reached about 65% of their yield suain. Strains in the bars at the
start of the main tension tie hook (BI and B2) remained well below yield throughout the loading
(see Fig. 3.2(b)).
Figure 3.3 shows the applied shear vs. the measured strains in the distributed
reinforcement. Gauges located on the distributed reinforcement in end A were Iost after a shear
of 1590 kN. Gauges A10 and Al 1, as well as BI0 and Bl 1, glued to the vertical legs of the
closed hoops, experienced significant tende strains afier the first major diagonal cracking at a
shear of 870 kN. As can be seen from Fig. 3.3(a) and (b), gauges A10 and B10, which were
glued to the outer hoop legs, experienced larger suains than gauges Al 1 and B 1 1, attached to the
inner hoop legs. Gauges A7 through Ag, and B7 and B8 were placed outside the region where
major diagonal cracks formed, and therefore experienced very Iittle straining (see Fig. 3.3(c) and
(W.
Figure 3.4 shows the strains determined from the sets of LVDT's placed dong a line
corresponding to the mid-height of the cap beam, and at the level of the centroid of the tension
tie. The average strains determined from these LVDT readings are plotted for four different load
stages: at a loading corresponding to Ml-service plus impact, at general yielding, at maximum
shear, and after failure. Also shown in Fig. 3.4 are the yield strains of the uniformly distributed
steel and the tension tie reinforcement. Figure 3.4(a) shows that some regions of the tension tie
had reached yield at a load corresponding to full-service plus impact, while the uniformiy
distributed crack control reinforcement had a maximum suain of 76% of its yield strain. At
generai yield (see Fig. 3.4(b)), the average strains exceeded the strain-hardening strain of 5.4
millistrain in three regions of the main tension tie steel. in addition, yielding of the distributed
reinforcernent at mid-height of the section occurred. At maximum shear (see Fig . 3.4(c)) there
is a noticeable difference between ends A and B, with strains in end A reaching a maximum
strain of 2.83% in the main tension tie reinforcement in linc with the c o l m face (this average
strain corresponds to a steel stress of about 600 ma). The maximum strain achieved in the
stronger end (end B) was 1.46%- As can be obsewed in Fig. 3.4(d), the strains generally
decreased due to the d r o p f f in load after failure, with the exception of the regions where a
major diagonal crack formed between the re-entrant corner and the support in end A.
microstrain
(a) horizontal strain, E, (b) vertical strain,
microstrain micmstrain
(c) maximum principal strain, E, (d) minimum principal strain, E,
micmstrain
O 10 20 30 40 50 60 70 80 90 deg rees
(e) shear strain, y, (f) principal angle, 8,
Figure 3.5 Responses of CAPN-A rosettes A6 and A7
microstrain
(a) horizontal strain, E,
O 5,000 10,000 15.000 20,000
microstrain
(c) maximum principal strain, E,
(e) shear strain, y,
500
(b) vertical strain, 5
(d) minimum principal strain, E~
O I
5.000 10.000 15,000 20.000
mianstrain
1 .
(f) principal angle, 8,
I
Figure 3.6 Responses of CAPN-6 rosettes B6 and 87
Figures 3 -5 and 3 -6 show the shear vs. horizontal strain, vertical strain, principd strains,
shear strain and angle of minimum principal strain detennined fiom the rosettes in ends A and
B, respectively. The strains detennined from the rosettes were very small until a crack formed
within the gauge lengths of the LVDT's. The first diagonal cracks, which fonned in ends A and
B at a shear of 870 kN, resulted in the development of significant principal tende strains and
shear strains. These are the same cracks that caused the slight drop off in load as shown in Fig.
3.1(a). The shear vs. horizontal suain, E,, and the shear vs. vertical strain, responses are
described in Fig. 3.5(a) and (b), and Fig. 3.6(a) and (b), for ends A and B, respectively, Both
the horizontal and vertical strains in the region of the cap beam close to the column face
experienced a sudden increase in strains upon first diagonal cracking. In end A, the horizontal
strains are slightly larger than the vert id strains, with yielding of the uni fody distributed steel
in the horizontal and vertical directions taking place at a shear of 1350 kN and 1500 kN,
respectively. In end B, the strains were Iower than in end A due to the larger arnount of
uniformiy distributed reinforcement in end B. This reinforcement, in end B, yielded in the
horizontal and vertical directions at shears of 1740 kN and 1780 kN, respectively. Both the
principal tensile strain, and the shear strain, y,, plots indicate that significant yielding took
place, resulting in very Iarge principal tensile strains and shear strains, particularly in end A.
The principal tensile strain was greater than 2%. resulting in very large cracks, and hence slip
dong the crack interface occurred at shears greater than 2700 W. In end B, the strains were
somewhat lower than those experienced in end A, with a maximum tende strain of 1.28% and
a maximum shear strain of 0.78%. For both ends A and B, the angle, Oz, corresponding to the
minimum principal strain was close to 45" from the horizontal until significant yielding took
place, which resulted in the angle becoming steeper.
Figure 3.7 shows the variation of shear vs . horizontal strains rneasured in the bottom bars
of the main tension tie. Solid lines are used to identiQ readings from gauges placed on the
outermost bar and dashed lines are used to identiQ those readings from the innermost bar. It can
be seen fiom gauges A3 through A6, and B3 through B6, that the strains in the outermost bars
are approxirnately the sarne as those in the imemost bars. Gauges A5 and A6, Iocated close to
where the first flexural crack fonned, clearly indicate the change from pre-cracking to post-
cracking stifiess at a shear of 490 kN, corresponding to first flexurai cracking (see Fig. 3.7(e)).
Readings fiom gauges B5 and B6 indicate that the first flexural crack in end B did not forrn until
a shear of 570 kN was reached (see Fig. 3.7(9). Strains in the tension tie in cantilever end A
vield
soo 1- A? (outer bar) - A2 (inner bar) - - -
500 k-; -t- 1 ~ i ( o u t e r bar) - A4 (inner bar) - - -
O 2.000 4,000 6,000 8,000
microstrain
yieid 3,500
3,000 -
1,500 .-
A6 ( m e r bar) - - -
O 2.000 4,000 6.000 8,000
microstrain
- 85 (outer bar) - - - 86 (inner bar)
500
Figure 3.7 Strains in bottom bar of CAPH tension tie, detenined from strain gauges
. , - 81 (outer bar) - - - 82 (inner bar)
I t l
O 2,000 4,000 6,000 8.
micros train
were slightly greater than those in end B. Gauges A5 and A6 indicate that first yielding of the
tension tie occurred at a shear of about 2120 kN, chat is, somewhat less than the shear
corresponding to general yielding (2620 W. At general yielding. the strains fiom gauges A3
and A4, located at the inner edge of the bearing in end A, were at 85% of their yield strain.
while strauis from gauges 83 and 84 had only reached 76% of their yield strain (see Fig. 3.7(c)
and (d)). The readings from gauges A3 and A4 indicate that, at the maximum shear, the strains
at this location were slightly greater than the yield suain, while strains from gauges B3 and B4
remained just below yield. Strains in the bars at the start of the main tension tie hooks (Al, A2,
B1 and B2) remained well below yield throughout the loading (see Fig. 3.7(a) and (b)).
Figure 3.8 exhibits the applied shear vs. the measured strains in the distributed
reinforcement. Gauges A10 and A l 1, expenenced significant vertical tensile strains after the first
major diagonal cracking occurred at a shear of 890 W. As can be seen fiorn Fig. 3.8(a), gauge
A10 which was glued to the outer hoop leg, expenenced large; strains than gauge A l 1, located
on the inner hoop leg. Gauges B 10 and B 1 1, experienced significant tensile strains at a shear of
L625 kN when a major inclined crack propagated up towards the re-entrant corner of end B (see
Fig. 3.8(b)). Gauges A8, and B7 through B9 experienced very small strains as they were
positioned outside the region where major diagonal cracks formed (see Fig. 3,8(c) and (d)).
Figure 3.9 shows the strains determincd fiom the lines of LVDT's positioned at mid-
height of the cap beam, and at the level of the centroid of the tension tie. The LVDT readings
indicate that the tension tie reinforcement in end A had reached yield at a location in line with
the colurnn face at full service loading plus impact (see Fig. 3.9(a)). At this load level, the crack
control reinforcement rernained below yield. Figure 3.9(b) shows that strain hardening of the
tension tie occurred at the same location where first yielding was measured and yielding of the
distributeci reinforcement at rnid-height of the section was measured at generai yield of the
specimen. Strains in end A are considerably greater than those of end B at this stage. At the
extremities of the rnid-height Iine of measurernent, the strains were close to zero throughout
loading until a diagonal crack formed through the outer gauge length at failure. At maximum
shear, mid-height strains in end A are roughly twice those in end B (see Fig. 3.9(c)). Strains at
the level of the tension tie are largest at the locations of the major flexural cracks. The maximum
strains in ends A and B at the maximum shear were 2.62%. and 1.9496, respectively. The post-
failure strains decreased due to the drop in load, with the exception of the extreme left reading
at mid-height due to the formation of the diagonai crack which caused failure (see Fig. 3.9(d)).
Figures 3.10 and 3.1 1 show the shear vs. horizontal strain. vertical strain. p ~ c i p a l
strains, shear strain and angle of minimum principal strain detennined from the rosettes in ends
w O 5,000 10,000 15.000
micmstrain
(a) horizontal strain, E,
O 5,000 10,000 15,000
microstrain
(c) maximum principal strain, E,
" O 5.000 10.000 15.000
micmstrain
(e) shear strain, y,
(b) vertical strain. E,
" O 5,000 10,000 15,000
microstrain
(d) minimum principal strain, E,
O 10 20 30 40 50 60 70 80 90 deg rees
(f) principal angle, 8,
Figure 3.1 0 Responses of CAPH-A rosettes A6 and A7
(a) horizontal strain, E,
microstrain
(c) maximum principal strain, E,
Y
O 5,000 10,000 15.000
microstrain
(e) shear strain, y,
O 5,000 10.000 15,000
microstrain
(b) vertical strain, E,
(d) minimum principal strain, E,
deg rees
(f) principal angle, 8,
Figure 3.11 Responses of CAPH-B rosettes B6 and B7
A and B, respectively. The strains detennined from each rosette were very srnall until a crack
f o d within the rosette. Significant principal tensile strains and shear strains developed at a
shear of 890 W, which corresponds to the formation of the first diagonal crack in end A. This
is the same crack that caused the slight drop-off in load as shown in Fig . 3.l(b). The rosettes
in end B did not register significant strains until the formation of the first diagonal crack in that
end at a shear of 1040 W. The shear vs. horizontal strain and the shear vs. vertical strain
responses are described in Fig. 3.10(a) and (b), and Fig . 3.1 1(a) and @), for ends A and B,
respectively. Both the horizontal and vertical strains in the cantilever ends near the colurnn face
experienced sudden increases upon first diagonal cracking. In end A, the horizontal strains were
somewhat larger than the vertical strains, with yielding of the uniformly distnbuted steel in the
horizontal and vertical directions taking place at shears of 1360 kN and 16 10 kN, respectively.
In end B, the strains were lower than in end A due to the larger arnount of uniformly distributeci
reinforcement in end B. The horizontal distributed reinforcement in end B yielded at a shear of
1910 kN, while the vertical distributed reinforcement did not yield until a shear of 2730 W.
Both the principai tensile strain and the shear strain plots show that significant yielding had taken
piace resulting in very large principal tensile strains and shear strains, particularly in end A.
As can be seen from Fig. 3.10, significant strains were rneasured in CAPH-A rosette A7
when the shear reached the diagonal cracking shear of 890 kN. A maximum tensile strain of
1.4% and a maximum shear strain of 0.7% were reached during the test. Afier this maximum
strain was reached, failure occurred by shear slippage as shown in Fig. 3.15. Significant strains
developed in rosette B7 of CAPH-B at shears greater than 1040 kN (see Fig. 3.1 1). This
corresponds to the formation of diagonal cracks through this rosette. A maximum [ensile strain
of 0.65% and a maximum shear strain of 0.69% were reached in end B.
The angles of minimum principal strain for both ends were considerably steeper (see Fig.
3.10(9 and 3.1 l(f)) than those reached in specimen CAPN (see Fig. 3.5(f) and 3.6(f)).
3.3 Development of Cracking
Since one of the main objectives of this research programme is to examine the influence
of different arnounts of uniformly distributed reinforcement on crack control at service load
levels, particular care was taken to measure crack widths at al1 load stages. In order to have a
consistent means of measuring crack widths, they were rneasured at locations where the cracks
crossed two horizontal lines, one at middepth of the cap beam and the other at the level of the
cenuoid of the tension tie (see Fig. 2.8).
3.3.1 Specimen CAPN
Figures 3.12(a) and (b) illustrate the change in cracking pattern and crack widths which
were measured over the full service load range for the cap beam. First cracking of specimen
CAPN occurred at a shear of 430 kN with the formation of two short flexurai cracks, near the
bottom of the specimen, in Iine with the column faces (see Fig. 3.12(a)). As the shear was
increased to 460 kN, the load corresponding to the self-weight of the superstructure, the cracks
extended slightly but their widths had not changed significantly. Figure 3.12(b) shows the crack
pattern at a shear of 1120 kN, which corresponds closely to NI service plus impact loading on
the superstructure. This crack pattern had essentially developed at a shear of 870 kN, and as the
load was increased to 1 120 kN, the cracks grew in width alone. It can be seen from Fig . 3.12(b)
that ends A and B had maximum diagonal crack widths of 0.20 and 0-25 mm, respectively, even
though end B had a larger amount of unifonnly disuibmed reinforcement (p = 0.003). than end
A (p = 0.00 18). At this load Ievel the maximum flexural crack width was 0.20 mm. It is noted
that the maximum diagonal crack width and the maximum flexural crack width were about the
same, and both are within acceptable limits for this member containhg epoxy-coated bars
As the shear was increased beyond 1120 kN, it was observed that cracks had formed at
nearly every hoop location dong the bottom of the bearn. Figure 3.12(c) shows the crack pattern
at a shear of 25 10 kN, corresponding to general yietding. The diagonal cracks had a maximum
width of 1.00 and 0.60 mm in ends A and B, respectively. For this loading case, well above the
service load range, the higher percentage of uniformly distributed reinforcement in end B
provided better crack control. Minor cnishing at both re-entrant corners was observed at load
levels slightly higher than general yield.
The crack pattern at maximum shear is shown in Fig. 3.12(d). In end A, a new major
diagonal crack formed with a width of 2.20 mm, white two existing diagonai cracks, also had
widths greater than 2.00 mm. Two of these cracks delineate the "bulging" of the newly formed
strut in end A (see Fig. 3.12(d)).
At failure, a new 3 .O mm wide diagonal crack opened suddeniy, delineating the strut
between the re-entrant corner and the bearing in end A, as shown in Fig. 3.13. This was
followed immediately by major crushing near the re-entrant corner of end A (see Fig. 3.13).
Figure 3.13 CAPN after failure
Figures 3.14(a) and (b) illusuate the change in cracking pattern and crack w i d h which
were rneasured for the HPC specimen CAPH over its MI service load range. First cracking of
specimen CAPH occurred in end A at a shear of 490 kN, slightly higher than 460 W, the load
corresponding to the superstructure dead load. This flexural crack propagated from the bottom
of the specimen, in line with the column face, over a distance of approximately one-half metre
(see Fig. 3.14(a)). This behaviour is typical of HPC as large amounts of energy are released
upon initial cracking due to the elevated tensile strength of the concrete. At a shear of 570 kN,
the first flexural crack in end B had fonned in line with the column face. Figure 3.14(b) shows
the crack pattern at a shear of 1120 kN, which corresponds closely to full service load plus
impact Ioading on the superstructure. This crack pattern had essentially developed at a shear of
890 kN, with the only change taking place, as the Ioad was increased to 1120 kN, being the
widening of the cracks. It can be seen from Fig. 3.14(b) that end A had a maximum diagonal
crack width of 0.45 mm, which is greater than permissible Iimïts. The maximum diagonal crack
width in end B was only 0.25 mm, indicating that the higher percentage of unifonnly distributed
reinforcement in this end provided sufficient crack control. The maximum flexurai crack width
was 0.25 mm at this load levei, and splitting cracks could be observed dong the main tension tie.
As the shear was increased beyond 1 120 kN, nearly every hoop location dong the bottom
of the beam had attracted a crack. Figure 3.14(c) shows the crack pattern at a shear of 2620 kN,
the load corresponding to general yielding. The diagonal cracks had a maximum width of 1.25
and 0.60 mm in ends A and B, respectively.
The crack pattern at maximum shear is s h o w in Fig. 3.14(d). In end A, a new major
diagonal crack forrned with a width of 1.25 mm between the re-entrant corner and the support
of end A. Just before failure occurred, minor cnishing at both re-entrant corners was observed,
and a horizontal crack at the top of tile cap beam directly under the column formed.
Figure 3-15 shows the crack pattern of specimen CAPH after failure. Failure was causeci
by relative shear slip of 8.0 mm dong the newly formed diagonal crack in end A. A minor
arnount of crushing aiso occurred near the top of this crack.
Figure 3.15 CAPH after failure
CHAPTER 4
COMPARISONS AND ANALYSES OF RESULTS
4.1 Cornparison of Responses of Normal- and High-Strength Concrete
Specimens
Loaddeformation responses of the two specimens are compared in Fig. 4.1. First
flexurd cracking occurred at a shear of 430 kN for the normal-strength concrete specimen,
CAPN, and 490 kN for the high-strength concrete specimen, CAPH. The first diagonal cracking
in CAPN occurred at a shear of 870 kN, while the first inclineci crack CAPH occurred at a shear
of 890 W. While the high-strength concrete had about twice the compressive strength of the
normal-strength concrete. it is somewhat surprishg that CAPH had only rnarginaily higher
cracking loads. It is important to realize that at the tirne of testing, the shrinkage strains in
specimens CAPN and CAPH were about 320 and 420 microsuain, respectively (see Fig .2.3@)).
The higher expected restrained shrinkage stresses in specimen CAPH would cause a larger
reduction in the cracking load than that of specimen CAPN.
Specimen CAPN reached general yield at a shear of 2510 kN and exhibited a
displacement ductility, defined as the ultimate deflection divided by the yield deflection (Au/$),
of 3.4. Specimen CAPH exhibited a slightly stiffer response than specimen CAPN and yielded
at a shear of 2630 W. However, this specimen was considerably less ductile than CAPN,
achieving an ultimate deflection of only 2.3 times 4. The failure of the nonnal-strength concrete
specimen was caused by cmhing at the re-entrant corner of end A, followed by shear slip (see
Fig. 3.13). The high-performance concrete pier cap failed by shear slip dong a diagonal crack
extending from the re-entrant corner to the support of end A (see Fig. 3.15).
Steel strains in cantilever ends A of both specimens were generally slightly greater than
those of ends B. The strains measured on the tension tie reinforcement at the inside edges of the
bearing pads were significantly lower than those measured in line with the column faces. This
curtaihnent of stresses in the main tension tie is described in section 1.7.1. The steel stresses
measured at the inner edge of the bearing in end A of each specimen was typically 69 % of those
measured in Lne with the column faces after signifiant cracking had occurred. In end B of each
specimen, the stresses at the inner edge of the bearing were approximately 63 96, representative
i _. .I shear slio CAPN
5 1 O 15 20 25
centre defiection (mm)
Figure 4.1 Cornparison of loaddeflection responses of specirnens
of the higher ratio of vertical distributed reinforcement. Most of the strain gauges located on the
distributed reinforcement did not register large strains as they were located just outside the region
of significant diagonal cracking.
By comparing the horizontal strains at mid-height for specimens CAPN and CAPH (see
Fig . 3.4(a) and Fig . 3.9(a)), at a load level correspondhg to full service plus impact loading, the
following observations can be made:
1. End A of each specimen, which contained a distributed reinforcement ratio of 0.0018,
had a maximum horizontal strain in the cantilever portion of 1.6 millistrain. 3 . End 0 of each specirnen, contaking a distributed reuiforcement ratio of 0.003, had a
maximum horizontal strain of 1.1 millistrain for CAPN and 1.2 millistrain for CAPH.
At higher load levels the differences between these horizontal strains at mid-height of
ends A and B for both specimens becarne more significant.
The rosettes of specirnen CAPN indicate that after cracking and up to a load of about
2700 kN the principal tensile and shear strains in ends A and B were virtudly the same (see Fig.
3.5 and 3.6). At loads higher than 2700 kN, general yielding of the reinforcement resulted in
very large principal tensile and shear strains in end A. The angle of minimum principal strain
deterrnined frorn rosettes A7 and B7 were roughly 45 O . Principal tensile strains determuied from
rosette A7 of the high-performance concrete specirnen, CAPH, were considerably greater than
those determined from rosette 87, while the shear strains were virtually the sarne in the two ends
(see Fig. 3.10 and 3.1 1). The angle of minimum principai strain detennined from rosette B7 was
slightly steeper than that of A7.
Figure 4.2 compares the flexural crack widths measured at the level of the tension tie in
the normai- and high-strength concrete pier cap specimens. Crack widths are slightly higher in
the high-strength concrete specirnen due in large part to the greater release of energy upon initial
cracking. Figure 4.3 compares the diagonal crack widths measured at mid-height of the norrnal-
and high-strength concrete specimens. It is clear that crack widths are considerably larger in end
A of the high-strength concrete specimen than in the normal-strength concrete specimen, while
the crack widths in end B of each specimen are roughly the same.
Figures 4.4(a) and (b) compare the maximum diagonal crack widths in ends A and B of
specimens CAPN and CAPH, respectively. There was nor a significant difference between the
crack widths of the two ends of CAPN under upper serviceability conditions (refer to Fig.
3.12(b)), and they were al1 smaller than required by code limits. However, at higher load levels,
the extra reinforcement in end B caused a moderate improvement in crack control over end A.
manimum crack width (mm) maximum crack width (mm)
(a) Maximum crack widths
3,500
3,000 N d -
,/ ---
CAPN-A 500 -
CAPH-A - - -
sum of crack widths (mm) sum of crack widths (mm)
(b) Surn of crack widths
Figure 4.3 Diagonal crack widths measured at mid-height of specimens
0.5 1 .O 1.5 2.0
maximum diagonal crack width (mm)
(a) Normal-strength concrete specirnen, CAPN
0.5 1 .O 1.5 2.0
maximum diagonal crack width (mm)
(b) High-strength concrete specimen, CAPH
Figure 4.4 Influence of distnbuted reinforcement ratio on crack control
Altematively, a significant difference in crack control performance of the two ends of CAPH
could be observed at full service plus impact Ioading. A diagonal crack in end A had already
opened up to 0.45 mm, while the cracks in end B were well controlled (refer to Fig. 3.14@)).
It is interesthg to note that the high-strength concrete specirnen has a post-cracking
stifmess which is only slightly higher than that of the normal-strength concrete specimen (see Fig.
4.1). This result is sornewhat surprishg since the tensile strength of the high-strength concrete
is about 1.6 times the tensile strength of the no&-strength concrete (see Table 2.3). The
reduced tension stiffening observed in the high-strength concrete specimen may be due to the
greater tendency for bond splitting cracks as c m be obsewed by comparing the crack patterns
of CAPN and CAPH (see Fig. 3.13 and 3.15). A ' ' ' et al. (1993) have postulated that
high-suength concrete, due to its higher compressive strength, develops higher , more localized
bond stresses. This, together with the fact that the bearing capacity of the concrete is related to
fcl whereas the tensile strength is related to K. results in bond splining of the concrete before
a uniform bond stress c m be achieved. Abrisharni et al. (1995) conciuded that the presence of
epoxy-coating on reinforcement results in fewer flexural cracks, larger crack widfhs, more
splitting cracks and decreased ductility. In addition, Abrisharni and Mitchell (1996) concluded
that bond splitting cracks reduce the tension stiffening in the concrete and that after significant
deformations in the postcracking range, the tension stiffening of hi&-strength concrete specimens
approaches that of normal-strength concrete specimens. The effects associated with the use of
high-strength concrete in combination with the use of epoxy-coated reinforcing bars has resulted
in a reduced tension stiffening, fewer flexural and diagonal cracks, bond splitting cracks and a
lower ductility.
A number of different types of predictions were carrieci out to determine the response of
the specimens tested.
Although pIane-sections analysis is not applicable for prdicting the responses of disturbed
regions, it is of interest to compare the predicted cracking loads, using this method, with the
rneasured cracking loads.
The predicted shears corresponding to first flexural cracking, at rnid-span of the
specimens, from plane-sections analyses were 462 kN and 661 kN for specimens CAPN and
CAPH. respectively. These values are significantly higher than those measured during testing,
that is, 430 kN for CAPN and 490 kN for CAPH. The key reasons why these predictions are
unconservative are that the strain distribution in disturbed regions is significantly non-linear and
that concrete shrinkage strains were not given any consideration. The cornputer prograrn
RESPONSE (Collins and Mitchell 1991) was used to cary out the sarne predictions including the
effect of concrete shrinkage strains. The shears corresponding to first flexural cracking including
shrinkage strains were predicted to be 304 kN and 476 kN for specimens CAPN and CAPH,
respectively, which are conservative predictions.
4.2.2 Simple Strut-and-Tie Models
Simple stnit-and-tie rnodels were developed to establish preliminary predictions of the pier
cap yield strengths (see Fig. 4.5 and 4.6). Both specimens were governed by yielding of the
main tende tie. The main tension tie, which consists of 10 No. 25 bars with a yield stress of
468 Mh, has a yield force of 2340 kN. It is assumed that the lines of action of the diagonal
stmts intersect the lines of action of the compressive resultants in the column (Le., at the quarter
points of the column). From equilibriurn, the shear which corresponds to yielding of the main
tension tie is 1995 kN for specirnen CAPN and 2050 kN for specimen CAPH (see Fig. 4.5 and
4.6). In these predictions, the materid reduction factors were taken as 1.0. These models are
simple and no consideration is given to any strength enhancement provided by the distributeci
reinforcement, particularly the horizontal bars. The predictions are therefore conservative.
Figure 4.5 Simple strut & tie modei for specimen CAPN
Figure 4.6 Simple strut 8 tie model for specirnen CAPH
4.2.3 Refined Sm-and-Tie Modeis
The r e f d strut-and-tie modeis s h o w in Fig. 4.7 and 4.8 account for the contribution
of the crack controI reinforcement to the strength of the specimens. In addition to the main
tensile tie at the bottom of the specimens, additional ties are provided to represent the horizontal
and vertical distributed steel. These secondary tension ties are positioned at the centroids of the
effective horizontal and vertical unifonnly distributed reinforcement. The refined strut-and-tie
models shown in Fig. 4.7(a) and 4.8(a) model the response of each specùnen as though they were
reinforced throughout with a reinforcement ratio of 0.0018 for the distributed steel. These
details, which were used in ends A of both test specimens, are rnodelled by a secondary
horizontal tension rie (4 legs of No. 15 bars) with a yield force of (800 mm2)(419 MPa) = N O kN
and vertical tension ties (3 sets of 4 legged No. 10 hoops) at each end with yieid forces of (1200
mrn2)(44 1 MPa) =Yi0 kN. The predictions obtained from Fig 4.7(a) and 4.8(a) are representative
of the weaker side of each specimen and hence should be used when comparing with the actual
strengths. The refined strut-and-tie models s h o w in Fig. 4.7(b) and 4.8@) model a distributed
reinforcement ratio of 0.003, which is the same reinforcement ratio contained in ends B of
specimens CAPN and CAPH. The yield forces of the horizontai and vertical tension ties in Fig.
4.7(b) and 4.8(b) were calculated to be 670 kN and 880 kN, respectively. The predictions
obtained frorn Fig. 4.7(b) and 4.8(b) are presented in order to demonstrate the how the strengths
would increase if the Iarger amount of uniformly distributed reinforcement (Le., a ratio of 0.003)
were present throughout the specimens.
The changing inclinations of the main diagonal struts in Fig. 4.7 and 4.8 are induced by
the presence of the vertical and horizontal distributed reinforcement. The tensile forces result
in discrete angular changes at the nodes where the secondary tension ties intersect the struts. The
resulting arching action provides steeper struts above the supports, ultirnately resul ting in higher
strengths. If more distributed steel were present, then the arching action would be even more
pronounceci (see Fig. 4.7(b) and 4.8 (b)).
This more detailed strut-and-tie model gives a better representation of the flow of
compressive stresses. The modelling of the flow of compressive stresses from the column into
the cap bearn results in higher localized compressive stresses near the re-entrant corners and
secondary struts which represent the fanning compressive stresses anchored by the vertical
uniformly distributeci reinforcement. A comparison of Fig. 4.7 with 4.8 illustrates that the struts
for the high-strength concrete specimen are considerably smaller than those in the normal-strength
concrete specimen. This effect gives a slight increase in the capacity for the high-strength
concrete specimen.
(a) End A details
V = 2540 kN (b) End B details
Figure 4.7 Refined strut & tie models for specimen CAPN
(a) End A details
(b) End R details
Figure 4.8 Refined strut & tie models for specirnen CAPH
Table 4.1 compares the predictions made with the simple strut-and-tie mode1 and the
refmed suut-and-tie mode1 with the measured values of total load applied to the pier caps at
general yield. in rnaking these predictions, it was assumed that both ends of the cap beam were
reinforced with the smaller amount of uniforiniy distributed reinforcement, that is consistent with
end A, since end A will give a lower predicted load. It is apparent that the refined strut-ad-tie
models give excellent predictions of the load at general yielding. Accounting for the uniformly
distributed reinforcement can significantly increase the predicted yield load. while giving slightly
conservative predictions. It m u t be pointed out that the acniai faiIure loads are somewhat higher
than the general yielding loads due to strain hardening in the reinforcement. The predictions
made with the stmt-and-tie models neglected the effects of strain hardening.
1 Measured 1 Simple Strut-and-Tie 1 Re- Struî-and-Tie
Table 4.1 Conparison of strut-and-tie predictions with measured loads at generai yielding
Specimen
CAPN
CAPH
4.2.4 Non-Linear Finite Element Analysis Using Program FIELDS
Figure 4.9 compares the measured loaddeflection responses with the predicted responses
obtained by using the non-linear finite element prograrn FIELDS (Cook 1987, Cook and Mitchell
1988) for specimens CAPN and CAPH. In predicting the responses the cracking stress was
Load at
Yield
Odv)
5020
5240
adjusted to account for the size effect of these NI-scaie specirnens. Using a cracking stress of
0.33 fi for these specirnens which experience signifiant diagonal cracking within the cantilever
portions of the cap beams, and assuming that the cracking stress is inversely proportional to the
I
fourth root of the size, then the cracking stress for these 1 1 0 mm deep members compared to
Predicted
Yield
0
3990
4100
the 150 mm deep control specirnens would be:
Measured
Predided
1.26
1.28
Predicted
Yield
OrN)
4820
5 120
Measured
1.04
1 .O2
5 10 15 20 25
centre deflection (mm)
(a) Specirnen CAPN
5 10 15 20 25
centre deflection (mm)
(b) Specimen CAPH
Figure 4.9 Predicted and measured loaddeflection responses of specimens
As can be seen from Fig. 4.9 the predicted responses for spechens CAPN and CAPH
agree very well with the rneasured responses up to loads of 2490 kN and 2670 kN, respectively.
At these load levels, the non-linear analysis predicts local crushing at the re-entrant corner. The
load deflection responses up to cracking and from cracking up to the points where local cnishing
is predicted, agree reasonably well with the measured response. As can be seen from comparing
Fig . 4.9(a) and (b), the predictions over-estimate the tension-stiffening , particularly for the high-
strength concrete specimen (see discussion in Section 4- 1).
In order to reduce the sensitivity due to local cnishing, the elements at the re-entrant
corner were softened by specifying a compressive stress-strain curve having a peak strain equal
to 1.5 times the cylinder peak strain. The frnite element analysis gives an accurate prediction of
yielding, however since the analysis relies on a tangent stiffness model, it was unable to converge
after local crushing was predicted.
Figure 4.10 shows the deflected s~hapes of specimens CAPN and CAPH at the predicted
maximum load levels. It is apparent from this figure that the deformations are not symmetrical
about the centrelines of the pier caps due to the fact that end B of each specimen contains a
greater arnount of uniformly distributed horizontal and vertical reinforcement.
Figures 4.11 through 4.16 show the predicted strains and concrete stresses for specimens
CAPN and CAPH at three different load levels. At the lower service load level, that is a total
applied load of 920 kN, for both the normal-strength and high-strength concrete specimens the
stresses are nearly elastic with only minor cracking predicted for specimen CAPN. in addition,
no distinct compressive strut action is apparent at this load level (see Fig. 4.11 and 4.12).
Figures 4.13 and 4.14 show the predicted strains and stresses at the upper service load level
corresponding to a total applied load of 2280 kN. Significant principal tensile strains are
predicted in both spec'mens at this load level. It is apparent that Iarger principal tensile strains
occur in end A than in end B due to the smaller amount of uniformiy distributed reinforcement.
Figures 4.15 and 4.16 show the predicted strains and stresses at the maximum predicted
load IeveIs. It is apparent that the principal tensile strains are Iarger for the diagonal cracks than
for the flexural cracks. By observing the flow of compressive stresses it is apparent that more
direct compressive strut action is taking place close to failure. Some bulging of the compressive
stmts between the coIumn and the reaction bearhgs is apparent. The high-strength coricrete
specimen CAPH exhibits struts having smaller widths and higher compressive stresses. The non-
linear finite-element analysis predicts a 7% higher ultirnate strength for CAPH than for CAPN.
The predicted strains in the tension tie for the high-strength concrete specimen are higher than
those predicted for the normal-strength concrete specimen-
0 0 ) 1 displacement scale: , I I 5.00 mm I -
1 6 0 :
: - ----
- - ---.-
V = 2490 kN
(a) Specimen CAPN
V = 2670 kN
(b) Specimen CAPH
< 1
I
I I
! ! !
Figure 4.1 0 Predictions of deflected shapes of specirnens at maximum predicted loads
displacernent scale: 5.00 mm
(a) Principal strains
stress scale: 5 MPa
(b) Stresses in concrete
Figure 4.11 Predicted strains and stresses in specimen CAPN at a load of 920 kN
(a) Principal strains
stress scale: 5 MPa -
(b) Stresses in concrete
Figure 4.12 Predicted strains and stresses in specimen CAPH at a load of 920 kN
(a) Principal strains
stress scale: 5 MPa -
(b) Stresses in concrete
Figure 4.1 3 Predicted strains and stresses in specimen CAPN at a load of 2280 kN
stress scale: 5 MPa
(a) Principal strains
(b) Stresses in concrete
Figure 4.14 Predicted strains and stresses in specimer! CAPH at a load of 2280 kN
(a) Principal strains
(b) Stresses in concrete
stress scale: 20 MPa
Figure 4.1 5 f redicted strains and stresses in specimen CAPN at a load of 4980 kN
strain scaie:
-
(a) Principal strains
(b) Stresses in concrete
stress scale: 20 MPa
Figure 4.1 6 Predicted strains and stresses in specirnen CAPH at a Ioad of 5340 kN
Figure 4.17 shows the development of stress in the main tension ties of specimens CAPN
and CAPH. Stresses are plotted at applied shears of 460 kN and 1 140 k;N (the service load range
bounds), 2000 kN and at the maximum load predicted by the finite element analyses, The
predictions for both specimens indicate a significant stress drop-off within the region containhg
the confinement reinforcement provided by the column ties. The measured strains are typically
somewhat higher than the predicted strains. It m u t be pointed out that the predicted strains
shown in the figure are "average" strains and therefore would be Iess than the strains measured
at or near cracks. The non-linear finite element anaiyses provided excellent predictions of the
strains in the main tension tie at the inner edge of the bearing. The presence of uniformly
distributed reinforcement results in a drop-off in stress from the location of maximum moment
towards the inner edge of the bearing . As can be seen from the measured and predicted stresses
the tension tie force decreases for locations close to the bearing due to the contribution of the
vertical uni forml y dis tributed steel. The larger arnount of vertical reinforcement in end B results
in reduced force dernands on the tension tie at the imer edge of the bearings. (see Fig . 4-17).
Figure 4.18 compares the predicted stresses in the main tension tie using finite element
analysis and refined strut-and-tie modelling with the stress computed from the measured steel
strains at maximum predicted loads. It can be seen that the refined strut-and-tie model gives
reasonable predictions for these stresses.
Table 4.2 compares the predictions made using the r e f d strut-and-tie model and the
predictions from the non-linear fuiite-element analysis with the measured values of total load
applied to the pier caps at general yield. Although the non-linear finite element analysis gives
slightly better predictions, the refined strut-and-tie mode1 compares exceptionally well with this
more sophisticated approach. It mus: be pointed out however that the non-linear finite element
analysis is capable of predicting strains and crack widths at service load 1eveIs.
Yield s-u I CAPN 1 5020
Predided 1 Me& 1 Predicted 1 M e d
Table 4.2 Cornparison of refmed strut-and-tie predictions and non-linear finite element predictions with measured loads at generai yielding
(a) Specimen CAPN
rneasured -
(b) Specirnen CAPH
Figure 4.17 Predictions of stress development in main tension ties
I measu red
1 1 refined sM-and-tie
(a) Specirnen CAPN
measured + + finite element - - - - - - -
refined stnit-and-tie - - - - - - - - - -
(b) Specimen CAPH
Figure 4.d8 Predictions of stress development in main tension ties at general yield
4.3 Estimates of Crack Widths
Tables 4.3 and 4.4 compare the measured principal tensile strains and crack widths with
those predicted using the results from the non-linear f i t e element analyses. The crack width
predictions were made for both flexural and diagonal cracks. The expecteâ flexural crack widths,
w , were determined fiom:
where: td = maximum predicted principal tensile strain at the level of the niain tension tie,
Sm = average crack spacing predicted fkom CEB expression (see Section 1.9).
The expected diagonal crack widths were determineci h m :
where: e# = maximum predicted principal tensiie strain at mid-height of pier cap.
The predicted average spacing, s,, of the diagonal cracks is deterrnined from (Collins and
Mitchell 199 1):
where s, and s,, are the crack spacings indicative of the crack control characteristics of the
horizontal and vertical distributed reinforcement. respectively. For simplicity sm and s,. were
taken as the spacings of reinforcement in the two directions and the angle of principal
compression, 8, was assumed to be 45 O. In addition, the predicted crack widths were multiplied
by a factor of 1.2 to account for the influence of epoxy coating on the reinforcement (Abrishami
et al. 1995).
As can be seen fkom Table 4.3, the flexural crack widths predicted using non-linear finite
element analyses compare very well with the measured maximum crack widths.
The predicted widths of diagonal cracks can Vary considerably frorn the crack widths
observed (see Table 4.4). One concern is that when applying normal procedures to the high
strength concrete specimen, the principal tensile strain and the crack width rnay be
underestimated. This rnay be due to the larger energy released when cracks forrn in high-strength
concrete members, which can Iead to the formation of longer and larger cracks. In addition this
Specimen Load E P ~ %~mmi Wpndiacd %e=Wtd
OrN) cm (id, (mm) (mm)
CAPN-A 920 O. 169 0.29 1 0.05 0.05
s, = X8mm 2280 0.805 1.134 0.24 0.20
CAPN-B 920 O. 107 O. 144 0.03 0.05
s, = 2 4 8 m 2280 0.704 1.000 0.2 1 O. 15
CAPH-A 920 0.037 0.064 - -
s, =248mm 2280 0.704 1 .O87 0.2 1 0.25
CAPH-B 920 0.037 0.067 -
1 2280 1 0.562 1 1.068 1 0.17 1 0.20
Table 4.3 Comparison of predicted and measwed crack widths and principai tensile strains in the main tension tie
Table 4.4 Comparison O € predicted and measured diagonal crack widths and principal tens ile strains at rnid-height
Specime~~
CAPN-A
S ~ = ~ ~ O I I - I I I I
CAPN-B
sd=124mm
CAPH-A
sme = 2 10mm
CAPH-B
phenomenon may be due to the fact that the tension stiffening in high-strength concrete members
tends to approach that of normal-strength concrete members after signifiant cracking has
developed (see Section 4.1).
124mm 1 2280 1 0.585 1 1.096 1 0.09 1 0.25
Load
m 920
2280
920
2280
920
2280
920
E P r e t i î ~
(lm
O .O25
2.174
0.030
O. 985
0.019
1.638
0.019
'marumi
(107
O
2 -459
O
1.953
O
2.203
O
wprcdicttd
(-1
-
0.55
-
0.15
-
0.4 1
-
w m e a s ~ t ~
(mm)
-
0.30
-
0.25
-
0.45
-
CONCLUSIONS
The conclus ions arising from this research project are surnmarized as follows :
1. A reinforcement ratio for the unifomily distributeci steel of 0.002 was sufficient to control
cracking over the depth of the normal-strength concrete pier cap specimen. This amount
of reinforcement is required in the 1994 CSA Standard for controiling cracking in
disturbed regions. Side A of the normal-strength concrete specimen contained a
reinforcement ratio of 0.00 18. and exhibited adequate crack control at service load Ievels.
2, A unifonnly distributed steel reinforcement ratio of 0.003 was necessary to adequately
control cracking over the depth of the high-strength concrete pier cap specimen at service
load levels. Fcr the high-strength concrete specirnen, initial cracks tended to be longer
and wider than those observed in the normd-strength concrete specirnen.
3. The high-strength concrete specirnen had a slightly higher strength dian the normai-
strength concrete specimen due to the sinaller compressive struts in the high-strength
concrete pier cap, leading to a slightty larger effective depth. The high-strength concrete
pier cap specimen exhibited a 32% Iower ductility than the normal-strength concrete
specimen.
4. Both the normai- and high-strength concrete specimen exhibited cracking Ioads which
were influenced by the large size of the specimens and by the restrained shrinkage
stresses. The cracking load of the high-strength concrete specimen was only slightly
higher than that of the normal-strength concrete specirnen due to the higher shnnkage
strains experienced in the high-strength concrete.
5 . Simple strut-and-tie models provided conservative estimates of the strength of the pier cap
specimens .
6 . Refined strut-and-tie models which simulate the effect of the horizontal and vertical
distributed reinforcement, provided better estimates of the general yielding load of the
specimens than the simple strut-and-tie model. In the refined strut-and-tie model, the
inclusion of the horizontai tension tie representing the unifonnly distributed horizontal
reinforcement significantiy increases the strength prediction. The vertical tension ties
representing the uniformly distributeci vertical reinforcement reduces the required force
in the main tension tie near the support bearings.
7. The predictions using non-linear fiaite elernent analyses gave accurate predictions of the
variation of stress in the main tension tie and provideci a means of assessing the principal
tensile strains and crack widths at service Ioad levels.
8. Reasonably accurate predictions of flexural crack widths were made by applying the usual
crack spacing assurnp tions to the principal tensile strains obtained from the non-linear
finite elernent analyses.
9. More research is requireci to accurately predict the inclined crack widths in very large
disturbed regions and to properly account for the influence of high-strength concrete on
inclined crack w idths .
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3 18-95)", American Concrete Institute, Detroit, 1995.
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Reinforcement on Response of Normal and H igh-S trength Concrete Beams " , ACI Smctural
Journal, Vol. 92, No. 2, March-April 1995, pp. 157-166.
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Stiffening", ACI Structural Journal, Vol. 93, No. 6, Nov.-Dec. 1996, pp. 703-7 10.
Al-Soufi, S. (1990), "The Response of Reinforced Concrete Bndge Pier Caps", Masters
thesis, McGill University, MontreaI, 1990. 134 pp.
Azizinamini, A., Stark, M., Roller, J. J . and Ghosh, S. K. (1993), "Bond Performance
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Collins, M. P. and Mitchell, D. (1980), "Shear and Torsion Design of Prestressed and
Non-Pres tressed Concrete Beams " , Journal of the Prestressed Concrete ht i tu te , Vol. 25, No.
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Collins, M. P. and Mitchell, D. (1985), "EvaIuating Existing Bridge Structures using the
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of Msting Concrete Bridges, Amencan Concrete Institute, Detroit, 1985, pp. lC9- 14 1.
Collins, M. P. and Mitchell, D. (1986). "A Rational Approach to Shear Design - The
1984 Canadian Code Provisions", ACI Journal, Vol, 83, No. 6, Nov.-Dec. 1986, pp. 925-933.
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Inc., EngIewood Cliffs, NJ, 199 1, 766 pp.
Collins, M. P., Mitchell, D. and MacGregor, J. G. (1993), "Structural Design
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Bul!drin d'lnfonnation, No. 193, Dec. 1989, pp. 77-83.
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Telford Services Ltd., London, 1993.
Cook, W. D. (1987)- "Smdies of Reinforced Concrete Regions Near Discontinuities",
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Cook, W. D. and Mitchell, D. (1988). "Studies of Disturbed Regions near Discontinuities
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APPENDIX
EXPERIMENTAL DATA
This appendix presents a surnmary of the experirnental data recorded for the two pier cap
specimens. The data presented includes applied shear, LVDT readings, and strains from the
electrical resistance strain gauges. Refet to Fig. 2.7 and 2.8 for descriptions of the
instrumentation.
Table A.l Readings h m vertical LVDTs used to determine the deflection of specimen CAPN
Table A.2 Readings from LVDTs located at the level of the main tension tie in specimen CAPN-A
Table A.3 Readings from LVDTs located at the level of the main tension tie in specimen CAPN-B
Table A.4 Readings from LVDTs Iocated at rnid-height of specimen CAPN-A
Table A S Readings from LVDTs located at mid-height of specimen CAPN-B
TabIe A.6 Readings from LVDT rosettes located in end A of specimen CAPN
Table A.7 Readings frorn LVDT rosettes located in end B of specimen CAPN
Shear
W v
O
246 .O
427.5
615.5
864.5
1123.0
1502.5
1753.5
1998.5
225 1.5
2505 .O
2665.5
272 1.5
2786 .O
2833 .O
2895.5
29 12.5
2104.0
Table
A l
(106,
O
-2
-2
-2
-4
10
44
NIA
NIA
N/ A
NIA
NIA
A2
(109
O
-4
-6
-8
-6
6
26
NIA
NIA
N/ A
NIA
NIA
A3
(109
O
O
2
6
36
382
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
N/A
NIA
NIA
NIA
NIA
gauges located
NIA
NIA
NIA
NIA
NIA
NIA
A4
(103
O
4
8
14
66
540
986
NIA
NIA
N/ A
NIA
N/A
A.8 Strains from strain
N/ A
NIA
N/A
NIA
NIA
NIA
in end A of
AS
(109
O
44
210
496
8 12
1052
1446
NIA
NIA
NIA
NIA
NIA
A6
(103
O
46
254
520
834
Il06
1526
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
N/A
specirnen
NIA
NIA
NIA
NIA
NIA
NIA L
CAPN
Table A.8 (Cont 'd) Strains from strain gauges located in end A o f specimen CAPN
Shear
(kW
O
246 .O
427.5
615.5
864.5
1 123.0
1502.5
1753.5
1998.5
225 1.5
2505.0
2665 -5
272 1.5
2786 .O
2833 .O
2895.5
2912.5
2104.0
A7
(106,
O
- 14
-24
-34
-34
-60
-80
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
AS
(106,
O
- 12
-20
-32
-2 8
-38
-46
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
N/A
NIA
A9
t 103
O
8
18
32
20
14
22
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
A10
(109
O
4
1 O
-2
14
2 12
338
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
A l 1
(106,
O
4
8
-2 - -
18
58
124
NIA
NIA
N/ A
N/A
NIA
NIA
NIA
NIA
N/A
N/A
NIA
Shear
O
O
246.0
427 -5
615.5
864.5
1123.0
1502.5
1753 -5
1998.5
225 1.5
2505 .O
2665 -5
272 1.5
2786.0
2833.0
2895. 5
29 12.5
2 104.0
Table
B1
(10~)
O
-2
-4
-4
-8
- 10
10
24
48
110
1 64
232
274
302
388
446
466
454
A.9 Strains
B2
(10'3
O
-4
-6
- 10
-10
-8
8
14
B3
(10~)
O
4
4
6
24
186
642
872
B4
(106,
O
6
10
14
42
178
554
758
22
38
52
72
90
100
108
122
128
130
from strain
B5
(10'9
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
M
(106,
O
42
100
440
722
970
1368
1620
1140
1462
1612
1828
1882
1950
2168
2220
2266
1802
Nt A
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
specimen CAPN
968
1234
1476
1664
!734
1794
1902
1992
2054
1774
1878
2 180
2506
2740
2776
3 138
5698
3054
2998
2638
gauges located in end B of
Table A.9 (Cont 'd) Strains from strain gauges located in end B o f specimen CAPN
Shear
OrN)
O
246.0
427.5
6 15.5
864.5
1 123.0
1502.5
1753.5
1998.5
225 1.5
2505 .O
2665.5
272 1 -5
2786 .O
2833 .O
2895. 5
2912.5
2104.0
B7
(109
O
-12
-20
-28 -
-22
-34
-64
-82
-100
-1 12
-1 14
-94
-82
-70
340
6 12
668
636
Ba
(109
O
- 12
-24
-36
-40
-54
-80
- 100
-120
- 142
-164
-180
-192
-200
-24
54
80
106
B9
(106,
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
BI0
(109
O
4
- 10
-28
12
410
7 10
882
1080
1376
1564
1730
1818
1802
1378
1304
1244
1060
BI1
W6)
O
-6
-14
-32
26
148
338
458
598
796
956
1138
1268
1292
1230
1260
1 162
1016
Table A.10 Readings from vertical LVDTs used to detennine the deflection of specimen CAPH
Table A.11 Readings from LVDTs located at the level of the main tension tie in specirnen CAPH-A
Table A.12 Readings from LVDTs located at the level of the main tension tie in specimen CAPH-B
Shear
O
O
250.0
495.5
571 -5
745.5
890.5
1124.0
1326 -5
16 1 1 .O
1870.5
2122.0
2391 .O
2618.0
277 1 -5
2844.0
2902.5
2960 -5
2996 .O
2792. O
2910.0
1 842 .O
B4
(mm)
O
O
O
O
0.3 15
0.419
0.45 1
0.498
0.582
0.655
O. 745
0.855
0.960
1 .O59
1 -405
1.783
2.402
2.763
2.763
2.800
2.501
B5
(mm)
O
-0.003
-0.003
-0.003
-0.014
0.028
0.087
O. 140
O. 189
0.217
0.24 1
0.259
0.280
0.297
0.304
0.304
0.217
O. 185
O. 157
O- 154
0.080
B3
(mm)
O
O
O
0.003
0.013
0.333
0.499
0.552
0.600
0.743
0.852
0.982
1.134
1.426
1.871
2.525
3.760
4.500
4.528
4.665
4.123
B2
(-1
O
O
-0.007
0.020
0.013
-0.034
0.1 15
0-21 1
O. 027
0.286
0.3 13
0.320
0.333
0.299
4.055
-0.34 1
-1 .O63
- 1 -539
-1 -676
-1,717
- 1 -676
B1
(mm)
O
-0.006
O
0.006
0.003
0.000
-0.0 12
-0.009
O. 166
0.29 1
0.350
0.423
0.500
0.555
0.61 1
0.65 1
0.688
0.718
0.72 1
0.728
0.632
Table A.13 Readings From LVDTs located at mid-height of specimen CAPH-A
Table A.14 Readings fiom LVDTs located at mid-height of spechen CAPH-B
Table A.15 Readings frorn LVDT rosettes located in end A of specimen CAPH
Table A.16 Readings fiom LVDT rosettes located in end B of specimen CAPH
Table A.17 Strains from strain gauges Iocated in end A of specimen CAPH
890.5
1124.0
1326.5
161 1 .O
1870.5
2 122.0
239 1 .O
2618.0
277 1.5
2844 .O
2902 -5
2960.5
2996.0
2792 .O
2910.0
1842.0 i
Table A.17 (Cont'd) Strains From main gauges Iocated in end A of specimen CAPH
Shear
O
O
250.0
495 -5
57 1.5
745.5
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
- - - 3
- rn
- - -
1
3
- -
A7
(106,
NIA
NIA
NIA
NIA
NIA
-6
- 16
-26
-38
-46
-54
-54
-56
-64
-66
-74
-66
-60
34
148
272
A8 1 A9
(106, (106, l
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
NIA
A10 1 Al!
O
-6
-20
-16
-24
(104
O
4
-2
-2
-26
NIA
NIA
NIA
NIA
NIA
50
224
340
460
628
744
1050
12 16
1332
1418
1464
1512
1608
48
-26
O
(104
O
2
-4
-6
-26
8
80
140
220
308
376
4 14
444
494
568
744
1010
1088
-1 180
- 12
206
Shear
O
O
250.0
495 -5
571.5
745.5 h
890.5
1124.0
1326.5
161 f .O
1870.5 - -
2 122.0
239 1 .O
26 18.0
277 1.5
2844.0
2902.5
2960.5
2996. O
2792 .O
2910.0
1 1842.0 i
Table
BI
(106,
O
O
-2
-2
-2
-2
-2
-2
16
34
46
52
72
58
116
132
144
158
160
168
154
A.18 Strains
B2
(10~)
O
-4
-6
-8
- 12
-6
-8
-6
O
8
12
12
18
22
24
26
28
28
30
30
30
from strain
B3
(106,
O
2
6
6
6
12
60
f 44
806
1164
1340
1554
1748
1892
1976
2046
2122
2190
2162
2170
1714
gauges located
B4
(107
O
4
8
10
14
32
72
200
702
1132
1362
1630
1846
1982
2040
2092
2 140
2172
2146
2154
1674
in end B of
B5
(m O
30
56
70
688
874
1090
1282
1556
1832
2170
2536
2884
3248
4316
6818
6196
3794
3680
2846
2348
spechen
Bd
(103
O
34
64
82
644
782
988
1152
1510
1820
2098
2394
2606
2670
2762
2976
3554
5204
5 174
4458
3806
CAPH
Table A.18 (Cont'd) Strains fiom strain gauges located in end B of specirnen CAPH
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