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EFFECT OF FIBRE-REINFORCED CONCRETE ON THE PERFORMANCE OF SLAB-COLUMN SPECIMENS
by
Peter J. McHarg
July 1997
Department of Civil Engineering and Applied Mechanics
McGill Universi@
Montréal, Canada
A thesis submitted to the Faculty of Graduate Studies
and Research in partial fulfilment of the requirements
for the degree of Master of Engineering
O Peter J. McHarg, 1997
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Effect of Fibre-Reinflorced Concrete on the Performance of Slab-Column Connections
Abstract
The behaviour of slab-column connections in flat plates is investigated. The first part of
this thesis discusses six two-way slab-column specimens which were designed such that they
would fail in punching shear. The parameters investigated were the placement of fibre-
reinforced concrete in the slab and the concentration of slab reinforcement around the column.
The effects of these parameters on the punching shear capacity, negative moment cracking, and
stifkess of the two-way slab specimens were investigated.
The second part of this thesis investigates the effects of the same parameters on six slab-
column specimens and six column specimens without the surrounding stab for their ability to
transmit axial loads from the high-strength concrete columns through the normal-strength
concrete slab.
Currently there is no beneficial effect in the CSA code for using fibre-reinforced
concrete or concentrated slab reinforcement near the column in the calculation for the punching
shear resistance or for the transmission of loads through slab-column connections. The
beneficial effects of concentrating the slab reinforcement near the column and of using fibre-
reinforced concrete are demonstrated.
L'effet du béton-fibre sur le comportement d'assemblages dalle-colonne
Résumé
Le comportement d'assemblages dalle-colonne est étudié. La première partie de cette
thèse décrit le comportement de six assemblages dalle-colonne dimmensionés pour une
défaillance par poinçonnement en cisaillement. Les paramètres étudiés comprennent
l'emplacement du béton-fibre dans ia dalle et la quantité d'armature dans la dalle à proximité de
la colonne. L'influence de ces paramètres sur la résistance a la contrainte de poinçonnement, la
fissuration en flexion négative et la rigidité des spécimens sont étudiés.
La deuxième partie de cette thèse discute de l'influence de ces mêmes paramètres sur la
transmission des charges axiales pour des colonnes en béton à haute résistance et une dalle en
béton normal. Les essais comprennent six assemblages dalle-colonne et six colonnes non-
confinées par une dalle.
Le Code Canadien, CSA A23.3-94, néglige la contribution du béton-fibre et de
l'armature de la dalle autour de la colonne pour le calcul de La resistance au poinçonnement et
pour la transmission des charges à travers l'assamblage dalle-colonne. Les bénéfices de l'usage
du béton-fibre et de Ia concentration de l'armature de la dalle autour de la colonne sont
démontrés.
Acknowledgements
The author would like to express his deepest gratitude to Professor Denis Mitchell for his
continued encouragement and knowledgeable advise throughout this research programme.
Furthemore, the author would Iike to thank Dr. William Cook for his guidance and support.
The research was carried out in the Jarnieson Structures Laboratory at McGiIl
University. The author wishes to thank Ron Sheppard, John Bartczak, Darnon Kiperchuk and
Marek Pnykorski for their assistance in laboratory. Special thanks is extended to Glenn Marquis
and Stuart Bristowe for al1 their time and helpfül suggestions. The author would also tike to
thank Pierre Koch, Bryce Tupper, Johnathan Vise, Hanaa Issa, Arshad Khan, Kent Harries,
David Dunwoodie, and Gavin MacLeod for their assistance.
The completion of this project would not have been possible without the patience and
valuable help of the secretanes of the Civil Engineering Deparment, particularly LilIy Nardini,
Ann Bless, and Donna Sears.
Finally, the author would like to thank his friends, family and Jen for their constant
support, patience and understanding over his years at McGill.
Peter J. McHarg July, 1997
Table of Contents
...................................................... Abstract ......................................................... ... i
. . Resumé ................................................................................................................................ 11
... Acknowledgements ............................................................................................................. I L I
Table of Contents ...................... .... .................................................................................. iv
List of Figures ..................................................................................................................... vi
... List of Tables ....................................................................................................................... vu1
List of Symbols ................................................................................................................... ix
1 Xntroduction and Literature Review ........................................................................... 1
Introduction ............................................................. 1 Punching Shear Resistance of Two-Way Slabs ........................................... 1
............................................................................ 1.2.1 Previous Research 1 .................................................................. 1.2. I Current Code Provisions 5
............................ Transmission of Loads through Slab-Column Connections 6 ............................................................................ 1.3.1 Previous Research 7
............................................................................... Fibre-Reinforced Concrete 10 ............................................................................ 1.4.1 Previous Research 11
................................................................ Objectives of Research Programme 13
.................................... 2 Experimental Programme .... ............................................. 1 4
2.1 Description of Prototype Structure .................. ... ........................................ 14 2.2 Details of Test Specimens ................................................................................ 15
..... .................. 2.2.1 Design and Details of Two-Way Slab Specimens .... 15 2.2.2 Description o f Column Specimens .................................................. 20
.......................................................................................... 2.3 MateriaI Properties -23 ............................................................................ 2.3.1 Reinforcing Steel 23
........................................................................................... 2.3.2 Concrete 24 ............................................................. 2.3.3 Fibre-Reinforced Concrete 27 ............................................................ 2.4 Testing Procedure for Slab Specimens 29
2.4.1 Test Setup and Loading Apparatus .................................................. 29 ......................... ............... 2.4.2 Instrumentation of Slab Specimens ... 31
....................................................... 2.5 Testing Procedure for Column Specimens 32 .................................................. 2.5.1 Test Setup and Loading Apparatus 32
2.5.2 Instrumentation .................... ....... .............................................. 33
............... Response and Cornparison of Test Results of Two-Way Slab Specimens 35
Response of Two-Way Slab Specimens ......................................................... 35 3.1.1 Specimen NSCU .............................................................................. 36 3 . L -2 Specimen NSCB ............................................................................... 37 3.1.3 Specimen FRSU ............................................................................... 43 3.1.4 Specirnen FRSB ............................................................................ 44 3- 1 -5 Specimen FRCU ............................................................................... 50 3.1.6 Specirnen FRCB ................... ... ................................................... 50
Cornparison of Two-Way Slab Test Resuks .................................................... 57 3 .2.1 Load-Deflection Responses ............................................................. 57 3.2.2 Strain Distribution of Reinforcing Steel .......................................... 63 3.2.3 Maximum Crack Width ................................................................... 63 3.2.4 Cornparison FaiIure Loads to Code Predictions .............................. 70
4 Cornparison of Column Specimen Results .................................................................. 71
5 Conclusions ............................... ,. ............................................................................... 80
References
Two-Way Slab Specimens .................... .. ..................................................... 80 Column Specimens ........................................................................................... 81
..................................................................................... Significance of Results 81
Appendix A-Design of Test Specimens ............................................................................. 85
List of Figures
Chapter 1 1-1 Non-dimensional shear stress versus fibre content ........................................... 12
Chapter 2 2-1 Prototype flat plat structure ................................................................................. 14 2-2 Slab-column test specimen ................................................................................ 15
.......................................................................... 2 3 Distribution of top No. 15 bars 16 2.4 LayoutofbottornNo . 10bars ............................................................................ 17 2.5 SIab reinforcement ............................................................................................. 17
.................................................................................... 2.6 Two-way slab test series 18 ..................................................................... 2.7 Construction of Specirnen FRS-B 19 ..................................................................... 2.8 Construction of Specimen FRC-U 20
.............................................................................................. 2.9 Column test series 1 2.1 O Typical tensile stress-strain curves for reinforcing steel ................................... 23 2.1 1 TypicaI compressive stress-strain curves for concrete ...................................... 25
............................................ 2.12 Shrinkage readings for concretes ................... .. 25 2.13 Flexural toughness pedorrnance ievels for fibre-reinforced concrete ............. ..28
.................. 2.14 Test setup for two-way slab specimens ................................. ..,.. 29 ....................................... 2.15 Photoagaph of test setup for two-way slab specimens 30
............................................ 2 16 Strain gauge locations on top mat reinforcernent 31 2.17 Target locations on concrete surface of two-way slabs ..................................... 32 2.18 Axial compression testing of stab-coiumn specimen .............................. .. ...... 33 2.19 Instrumentation of coiumn and slab-column specimens .................................... 34
Chapter 3 3.1 Total Ioad versus average deflection responses of normal-strength concrete
specimens (NSC Series) ...................................................................................... 38 3.2 Strains in top mat reinforcing bars at full service and peak load for
......................................................................................................... NSC Series -29
Load versus maximum crack width for normal-strength concrete specirnens (NSC Series) ..................... .... ......................................................................... 40 Crack pattern of NSC Series at fiiI1 service Ioad ................................................ 41 NSC Series at failure ........................................................................................... 42 Total load versus average deflection responses of fibre-reinforced concrete slab specimens (FRS Series) ................................................................ 45 Strains in top mat reinforcing bars at full service and peak Ioad for FRS Series ........................................................................................................... 46 Load versus maximum crack width for fibre-reinforced concrete slab specimens (FRS Series) ...................................................................................... 47 Crack pattern of FRS Series at fidl service toad ................................................ 48 FRS Series at failure ............................................................................................ 49 Tot4 Ioad versus average defiection responses of fibre-reinforced concrete cover specimens (FRC Series) .................................... .. ...,.... 52
Strains in top mat reinforcing bars at full service and peak load for FRC Series ......................................................................................................... 53 Load versus maximum crack width for fibre-reinforced concrete cover
...................................................................................... specimens (FRC Series) 54 ................................................ Crack pattern of FRC Series at f i I I service foad 55
FRC Series at failure ......................................................................................... 56 Influence of fibre-reinforced concrete on the load-deflection responses .......... 58 Influence of concentrating reinforcernent near coIumn on loâd-deflection responses ......m........ ....... ................................................................................ ..59
...................................... Strains in top mat reinforcing bars at full service Ioad 65 ......... ...........*. Load versus maximum crack width for uniform specimens .., 66 .............................. Load versus mzcxirnum crack width for banded specimens .67
Load versus average tensile strain around coIumn of slab-colurnn specimens ............................................................................................................ 68 Influence of fibre-reinforced concrete on the load versus average tensile sû-ain around column ........................................................................................... 69
........................................... Cornparison of shear strength to predicted strength 70
Chapter 4 ...................... 4.1 Compressive load versus average column strain for NSC Series 72 ................... 4.2 Compressive load versus average column strain for ERS Series -73 ...................... 4.3 Compressive load versus average column strain for FRC Series 74
.................................................. ...................... 4.4 Column specimens at faiture .... 75
List of Tables
Chapter 1 1-1 Cornparison of Code Provisions for Nominal Shear Strength ........................... 6
Chapter 2 2.1 Reinforcing steel properties ................................................................................ 23 2.2 Concrete mix designs ..................... ,. ............................................................... 24
....................... 2.3 Concrete properties for NSC Series ............................... ,...... 26 .................................................................... 2.4 Concrete properties for FRS Series 26
2.5 Concrete properties for FRC Series .................................................................... 27
Chapter 3 ....................... 3.1 Summary of load-deflection curves for slab-column specimens 57
3.2 Maximum crack width at full service load for slsb-column specimens ............ 64
Chapter 4 .................................. 4.1 Summary of experimental resu1ts for column specimens 76
....... 4.2 Cornparison of experirnental and predicted results for column specimens 77 4.3 Effect of fibre-reinforced concrete on axia1 compressive strength in
slab-column specimens ....................................................................................... 79
List of Symbols
depth of equivalent rectangular stress block area of concrete
ratio of tension steel through Ioaded area to tota1 area of tension steeI in slab calculated ultimate load of colurnn spacing of tension reinforcernent nominal shear strength factored shear stress resistance provided by concrete factored shear stress factored shear stress resistance shear force factored shear force resistance attributed to the concrete factored shear force at section nominal shear force resistance shear transmitted to column due to specified Ioads, not Iess than twice self-weight of slab factored load per unit area of slab percent of fibres by weight resistance factor for concrete resistance factor for reinforcement ratio of ultimate load to the load at which flexural failure should occur partial safety factor factor to account for concrete density ratio of tension reinforcement 1 +(200/d)IR
area of reinforcement perimeter of loaded area perimeter of critical section for shear size of rectangutar or equivalent rectangular coiumn distance from extrerne compression fibre to centroid of tension reinforcement nominal bar diameter specified compressive strength of concrete
foc compressive strength of the cotumn concrete effective strength of the column compressive strength of the slab concrete modulus of rupture of concrete specified yield strength of reinforcernent overall thickness of slab effective depth of sIab length of clear span measured face- to-face of supports factored moment factored moment resisance
Chapter 1
Introduction and Literature Review
1.1 Introduction
This report investigates the behaviour of slab-column connections in flat plates. Two
experimental programmes were conducted. The first programme investigates the punching shear
resistance of six two-way slab specimens. The second investigates the transmission of axial loads
through slab-coiumn connections with six slab-column specimens and six "sandwich" colurnn
specimens without the surrounding slab. Al1 of the specirnens tested for this report were fiil1 scale.
The variables for both progammes were the concentration of the flexural reinforcernent near the
column and strategically placed fibre-reinforced concrete in the slab.
This chapter will outline the previous research on punching shear resistance of two-way
slabs, transmission of axial Ioads through slab-column connections and the effects of fibre-
reinforced concrete on shear resistance. The objectives of this report will also be discussed.
1.2 Punching Shear Resistance of Two-Way Slabs
It has been long debated whether or not the concentration of flexural reinforcement near the
column is beneficiai to the performance of the slab. Previous research has presented conflicting
results conceming the shear strength of the slab with respect to the effects of concentrating the
flexural reinforcement near the column.
1.2.1 Previous Research
In the early 1900's, E. M6rsch of Gemany made significant contributions to the field of
reinforced concrete with his work on shear. In 1906 and 1907 his papers (Morsch l906,1907)
presented an expIanation of diagonal tension and proposed the foliowing equation for the
nominal shearing stress, v:
where V is the applied shear force, b is the perimeter of the loaded are& and, jd is the effective depth.
The shear stress calculated from this equation was taken along the perirneter, b, of the
ioaded area. Hence for a uniformly loaded slab, b is equal to the perimeter of the column.
Extensive research was done on the sliear strength of slabs by Talbot in 19 13. He
published a report of 114 walI footings and 83 colurnn footings tested to failure. Twenty of the
column footings faiIed in shear. He proposed the following formula for the nominai shearing
stress, v, which was similar to Morsch's, except the criticat section was moved from the column
face to a distance d f?om the face. Therefore b was now equal to 4(c+2d), giving:
where c is the lengîh of one face of a square column.
Talbot also recognised that increased percentages of tensile reinforcernent resulted in
increased shear stren,ath of the slabs. In 1924, the AC1 (1924) committee recommended the
shear stren,oth be lirnited to
v = 0.02fi(l+ n) < 0.03fi ( r .3)
where n equals the area of steel through the loaded area divided by the total area of steel
in the slab, and f,' is in MPa. The diagonal shear stress was now critical at a distance (h-1.5 in.)
from the periphery of the loaded area, where h is the slab thickness. Tt must be recognised that
this shear stress is a working stress Iirnit.
Graf (1933) studied the shear strength of slabs loaded by concentrated loads near the
supports. From these tests he suggested the following:
1 . Shear capacity decreases as the Ioads are moved away fiom the supports.
2. Shear strength increases with increasing concrete strength, but it was found that the
increase was not proportional to the increase in compressive strength.
3. Flexural cracking has some influence on shearing strength.
Graf also proposed a formula for calcutating the shearing stress:
where h is the thickness of the slab.
Richart (1948) presented an extensive report on reinforced concrete footings. From
experirnental results, he concluded that high tensile stresses in the reinforcement and extensive
cracking in the footings reduced the shear strength.
EIstner and Hognestad (1956) reported on tests of thirty-nine 6 foot square siabs, of
which 34 displayed a punching shear failure. They concluded that a concentration of the fiexural
reinforcement placed directly over the column did not increase the shearing strength of the slabs.
They also revised an earlier formula first proposed by Hognestad in 1953, to predict the shearing
strength of slabs. Their revised expression is:
where O, is the ratio of the ultimate load to the Ioad at which flexural failure should
occur.
Whitney (1957) reviewed the results of Richart, EIstner and Hognestad and proposed an
ultirnate shear strength theory. He believed the slabs frorn previous tests that had high
percentages of reinforcing bars probably failed due to bond faiture and not shear. Whitney
concluded that the shear strength is primarily a function of the "pyrarnid of rupture", which is a
pyrarnid with surfaces sloping out fiom the colurnn with angles of 45'.
The 1956 AC1 Building Code had two different limits for shear stresses in slabs at a
distance d from the periphery of the loaded area:
0.034 0.69 MPa,
if more than 50% of the flexuraI reinforcement passes through the periphery; or
when only 25% of the flexural reinforcement passes through the periphery.
Moe (1961) reported tests of forty-three 6 foot square slab specimens. In the analysis of
the results he ais0 included results from 260 slab and footings tested by earlier investigators.
Some of Moe's concIusions are:
1. The shear strength of slabs is to some extent dependent upon the flexural strength.
2. Concentration of the flexural reinforcement in narrow bands across the column does not
increase the shearing strength, but does increase the stiffness of the load-deflection
response and increases the toad at which first yielding occurs.
3. The ultimate shear strength of slabs can be predicted with the following forrnuIa:
Hawkins, Mitchell, and Hanna (1975) tested the effects of concentration of flexural
reinforcement in the immediate column region. They concluded that the behaviour of the
connection, especially for low reinforcement ratios, will be improved if there is a concentration
of reinforcement in the column vicinity.
Hawkins and Mitchell (1979) repofied that the shear strength of a slab decreases if there
has been significant yielding of the flexural reinforcement.
Alexander and Simmonds (1988) note that the CSA Standard (1984) ensures that a large
portion of the flexural reinforcement should pass through the column vicinity, but also believe
that there should be a beneficial effect for this distribution in the calculations for shear stren,gth
capacity.
Alexander and Simmonds (1992) studied the effects of concentrating the reinforcement
near the column on the shear strength of slab specimens. They concluded that al1 of the tests
appeared to have the classic punching shear pyramid shaped failure, but several tests actually had
Ioss of anchorage. The loss of anchorage can not be determined unless the variation in the bar
force is monitored during the test. They suggest that many of the punching shear failures
reported in previous tests were actualIy bond failures. They believed investigators such as Moe,
Elstner and Hognestad wrongly diagnosed the modes of failure in many of their tests, and
therefore did not observe an improvement in the shear capacity of the slab column connection
with the concentration of the top mat bars near the column.
In 1996, Gardner and Shao reported on the resuIts of a hvo-bay by two-bay reinforced
concrete slab structure. They reviewed the standards of the AC1 3 18-89, BS 8 i 10-85, and CEB-
FiP 1990 Codes, and compared these predicted values to previous experimental research from
various investigators. They concluded that equations that inchded size effects and
reinforcement ratios (such as BS 8110-85 and CEB-FIP 1990 mode1 code) have smaller
coefficients of variation than the AC1 equations. They also cautioned that increasing the
reinforcement ratio increases the punching shear capacity, but also results in a more brittle
behaviour.
Shenf and Dilger (1996) wrote a critical review of the CSA A23.3-94 punching shear
strength provisions for interior columns. They also compared the results of experiments from
previous literature. They suggested the following changes to the existing CSA Standard:
1. The
2. The
The
shear resistance ofconcrete slabs should be a function of 6 instead of JfC. strength should be a fûnction of the reinforcement ratio, p, especially for p < 1% .
following equation is recomrnended:
1.2.2 Current Code Provisions for Punching Shear Resistance of Two-Way Slabs
Due to the differences in the previous research there is significant variation in the
approaches in the calculation of shear resistance for slab-column connections in the concrete codes
of North America, Europe and Britain. The AC1 code (1995) does not include the flexural
reinforcernent concentration in the shear resistance calculations. The current CSA Standard (1994)
requires that half of the flexural reinforcernent needed in the colurnn strip be placed within 1.5h of
the colurnn face, but does not give beneficial effects for this distribution in the calculations for
shear strength capacity. The CEB-FIP code (1990) and the BS Standard (1985) include the flexural
reinforcement concentration in the caIcuIations for the shear resistance of the connection. The
equations used to determine the noniinal shear strength in the CSA, ACI, BS Standard and CEB-
FIP provisions are compared in Table 1.1.
Table 1.1 Cornparison of Code Provisions for Nominal Shear Strength
Code Critical periphery Nominal shear strength -- - 1 CSA A23.1-94 b, =4(c + d) v = 0.083(4&)
BS 8 1 10-85 b, =4(c + 3d) v = 0_79(1 00p) ' j 3 (400 / d) 1/4
where: p = ratio of steel within 1.5d of column face
where: 5 = 1 + (200 / d) 1/2
y, = partial safety factor = 15
1.3 Transmission of Loads through SIab-Column Connections
The columns of multi-storey reinforced concrete buildings rnay be constructed with high-
strength concrete while the slabs are built with normal strength concrete. The most cost effective
method of this forrn of construction is to continue the slab concrete through the colurnn, creating a
weaker sandwich region in the high-strength column. With improvements in the fieid of high-
strength concrete, the difference in the coIumn and stab strengths is continuously getting larger.
Since the 1960's much research has been done on the determination of the strength of this
connection.
According to the current CSA Standard (1994) the design of high-rise buildings witfi high-
strength concrete columns rnust include a check on the capability of the column load to be
transrnitted through the normal strength floor slabs. The çtrength of this critical region can be
increased by:
1) accounting for the confinement effect of the slab surrounding this critical region,
2) "puddling" hi& strength concrete in the slab in the column vicinity, and
3) adding vertical dowek through this critical region to enhance the column strength.
1.3.1 Previous Research
Due to the relatively short history of the use of hi&-strength concrete there has not been
a significant arnount of research regarding the transmission of Ioads €rom high-strength coIurnns
througli a normal-strength floor slab- Some of the first research in tliis field was done by
Bianchini, Woods and Kesler (1960). Ttiey tested 45 specimens representing corner, edge and
interior dab-column connections. The coIumns were 279.4 mm square with concrete
compressive strengths ranging from 15.8 to 56 MPa. The slabs of the specimens were 177.8 mm
thick with concrete compressive strengths varying from 8.8 to 24.8 MPa. These dimensions
result in an aspect ratio o f slab thickness to coIumn , WC, of 0.64-
They conctuded that when a high-strength column is intersected by a normal-strength
floor, the strena@ of the column is a function of both the column and floor concrete compressive
strength. Ttley also concluded that the strength of the column is irnproved with increasing
num ber of restrained edges. Bianchin i et al suggested the following ultimate load formula:
where: Pal, is ultimate load,
A, is area of steel,
f, is the yield strength of steel,
Ac is the area of concrete,
and:
for a sandwich column, f&
I
I fcc = 15fc. if - 5 15
fcs
for a interior slab-column connection, f&
fcc = 0.40f& + 0.74fiC if 7 1 15 fcs
where fi! is the effective strength of the colurnn, and f,'! and fi, are the concrete compressive
strengths of the slab and the column, respectively.
The AC1 later based their code requirements on the paper by Bianchini et al (1960),
where the effective concrete strength of the column was equal to 35% of the floor concrete
strength plus 75% of the strength of the column concrete strength, provided that the column
strength is 1.4 times greater than the sIab strength. These provisions have not changed in
subsequent editions of the AC1 code. The AC1 code also allowed the option of "puddting" the
higher strength concrete in the slab with an area four times the colurnn area about the column.
This puddled concrete also has to be wel1 integrated into the slab concrete. The 1995 AC1 code
requires the area of puddled concrete be extended a distance of 600 mm fiom the colurnn faces.
Garnble and Klinar (1991) reported on 13 slab-column connections to study the efFects
of s i x , strength and confinement properties on the effective z ~ i a l strength of the column. One
of the specimens was a sandwich column (without the slab) and six were interior connections.
The columns were 254 mm square and had concrete strengths ranging from 69 to 96 MPa. The
slabs were 127 to 177 mm thick with concrete compressive strengths between 15.9 to 45.5 MPa.
Therefore the aspect ratio, Mc, varied from 0.5 to 0.7.
They compared their results to the 1989 AC1 code, which is the same as the 1995 AC1
version with respect to the transmission of loads through sIab-column connections. Garnble and
KIinar (1991) agreed with the ultimate load formula up to a column concrete strength/sIab
concrete strength ratio of 1.4. When there is a higher ratio than this, they reported that the code
was unsafe, and suggested defining the column effective strength as:
Shu and Hawkins (1992) tested 54 sandwich column specimens with no restraint to study
the effects of the higher strength columns above and below the weaker sandwich region. The
slab concrete compressive strength ranged iiom 6.9 to 39.2 MPa, and the ratio of coIumn
concrete strength to slab concrete strengtb, f:c/ f&, varied from 1.00 to 5.60. The columns were
152.4 mm square, with the sandwich region between 25.4 and 457.2 mm high. The aspect ratio,
h/c, was therefore from 0.17 to 3 .O.
Shu and Hawkins (1992) concluded the amount of colurnn reinforcement did not effect
the effective concrete compressive strength of the columns tested. For certain h/c ratios, they
thought the AC1 code expression for uttirnate compressive strength of interior sIab-column
connecticns was not conservative enough for f,!J f& values less than or equal to 1.4, and thought
the code was unsafe when the f&/ fis ratio was geater tltan 1.4. They proposed the following
equation for the effective concrete strength for edge and corner sfab-column connections:
The CSA A23.3-94 Standard was radicalIy changed from the 1984 version. The new
code defined the effective concrete strength as:
With this equation, f& becomes f& if the ratio f&/ fk is less than L .4.
Ospina and Alexander (1997) reported on thirty slab-column connection specimens. The
effects of slab loading and aspect ratio were investigated.
Some of their conclusions involving interior slab-column connections include:
1. As the applied load on the slab increases, the effective compressive stren,ath of the
coIurnn decreases, therefore designs should consider this.
2. As h/c increases, the effective compressive strength of the colurnn decreases.
3. The 1995 AC1 code and CSA A23.3-84 give unsafe designs for high h/c ratios, while the
CSA A23.3-94 Standard gives designs that are too conservative for low Idc ratios.
4. The following equation should be used to determine the effective concrete compressive
strength for interior slab-column connections:
1.4 Fibre-Reinforced Concrete
In order to overcome the common deficiencies found in two-way slabs, such as excessive
cracking around columns, excessive deflections and low punching shear streno@h, it was proposed
to investigate the strategic use of steel fibre-reinforced hi&-performance concrete (SFR-WC).
This report will investigate if the very selective use of the SFR-WC would improve the response of
the slabs without significantly increasing construction costs. Currently there are no provisions in
any of the codes to account for any beneficial effect for the use of fibre-reinforced concrete in slab-
column connections.
1.4.1 Previous Research
R. N. Swamy et al (1979) reported on rnany tests invoIving fibre-reinforced concrete.
They observed the effects fibre-reinforced concrete had on strength, ductility, and crack control.
The foIlowing improvements due to the addition of steeI fibres to the concrete rnatrix were
found:
1. transforms unstable, uncontrolled tensile cracking into slow, controlled crack growtli.
2. achieves smaller and a more uniforrn distribution of tensile cracks.
3. enhances the stiffness considerably as failure approaches.
4. increases ultimate shear capacity of flat plate specimens.
5. reduces the suddenness of the uiireinforced concrete failure.
6. reduces strains in flexural reinforcement.
7. increases residual load capacity after failure.
R.N. Swamy and S. A. R. Ali (1982) investigated the effects of fibre-reinforced concrete
on the punching shear behaviour of slab-colurnn connections. Similar conclusions were made
fiom the slab-column tests as from their previous research. The results showed that with the
addition of 1% fibre by volume, the specimens showed:
1. an increase of punching shear Ioad by 40%.
2. a reduction of deflections by 30% at service load.
3 . a reduction of steel strains, concrete strains, and rotations by 40-50%.
4, an increase in residual load of 2OO-3OO%.
They also reported that placing fibre-reinforced concrete a distance I.5h from the
collrmn face is as effective as constnicting the entire slab of fibre-reinforced concrete. The fibre-
reinforced concrete seemed to push the failure surface away frorn the column faces, creating a
larger failure surface.
Alexander and Simrnonds (1992) reported on the effects of fibre-reinforced concrete on
the punching shear behaviour of 6 slab-column connection specimens. The variables of these
tests were the concrete clear cover (1 1 and 38 mm) and the fibre concentration (0, 0.4, and
0.8%). They found with the addition of 0.4% fibres to the concrete matrix increased the uttirnate
shear capacity of the flat plate slab by 20%. With 0.8% fibres added, there was a further
increase of 7% in the shear capacity. They also concluded there is an increase in ductility with
the use of fibre-reinforced concrete compared to plain concrete.
A. M. Shaaban and H. Gesund (1994) tested 13 slab-coiumn specimens to determine if
the use of fibre-reinforced concrete would significantly increase the punching shear capacity.
They varied the fibre content from O to 6.4% by weight of the concrete. They concluded fibre-
reinforced concrete does significantly increase the shear capacity of the slab, and from these tests
and previous research they derived a formula to calculate the shear capacity of a fibre-reinforced
two-way slab:
where Wf is the percent of fibres by weight.
Adebar el al (1997) surnmarised many of the shear strength tests involving fibre-
reinforced concrete over the last 25 years. They concluded that the increase in shear strength
was proportional to the fibre content at low fibre voIumes, but increasing high fibre percentages
has less beneficial effects.
The influence of hooked steel fibres on the shear strength of concrete bearns without
stinvps was investigated by Adebar et al (1997). These bearns were 150 mm wide and had an
effective depth of 557.5 mm. Two different lengths of hooked steel fibres (30 and 50 mm) and
different volumes of fibres (ranging fiom O to 1.5 percent) were investigated. Figure 1.1 shows the
variation of the non-dimensional shear stress as a function of the percentage volurne of fibres. For
these bearn tests, only the test data From specimens containing the 30 mm long fibres \vas used.
The "best-fit" curve through this data shows that the shear strength of these beams increases with
increasing volumes of fibres- Also shown in Fig- 1.1 are the experimental results from a series of
one-way slab tests carried out by Mindess el al (1997). The width of the slab test specimens was
610 mm and the effective depth was 184 mm. The slabs had varying amounts of 30 mm long
liooked steel fibres with the concrete strength varying considerabiy fiorn 24 MPa to 96 MPa. Since
the concrete strength played a very significant role, the data plotted in Fig. 1.1 has been separated
into different sets for the different ranges of concrete compressive strength- It is clear that the 96
MPa concrete is very sensitive and can give a low shear stren-gth for the one-way sfabs, even with a
significant amount of fibres.
There has been very little research on the effects of fibre-reinforced concrete on the axial
capacity of a sIab-column connection.
0.7 1
O 0.5 1 .O 1.5 2.0
fibre content in percentage by volume
Figure 1.1 Non-dimensional shear stress versus fibre content
1.5 Objectives of Research Programme
The specific objectives of this research program are:
1) To investigate the effects of concentrating the slab flexural reinforcement near the column
and the strategic use of fibre-reinforcement in the slab on the punching shear capacity,
negative moment cracking and stiffhess of interior two-way slab-column connections. The
use of "puddled" fibre-reinforced concrete around the column and the use of fibre-
reinforced concrete in the top cover of the slab wilI be investigated,
2) To investigate the influence of the following parameters on the transmission of loads from
high-strength concrete columns through normal-strength concrete slabs:
a) the confining effect of the slab surrounding the slab-coiumn comection.
b) the effects of concentrating the slab flexural reinforcement around the colurnn.
c) the effects of the use of the of fibre-reinforcement in the normal-strength slab on the
axial capacity of the high-strength columns.
Chapter 2
Experimental Programme
2.1 Description of Prototype Structure
In order to decide on the dimensions and loading details for the test specimens the
prototype structure, sliown in Fig. 2.1, was analysed. The prototype structure consists of a four
bay by four bay fiat plate structure with 4.75 m x 4.75 rn bays. This structure was designed for
assembly area use, with a superimposed dead load of 1.2 kPa and a specified live Load of 4.8 kPa
according to the National Building Code of Canada (NBCC, 1995). The siab thickness is 150
mm with a 25 mm clear concrete cover on the top and bottom reinforcement. The interior
columns are 225 mm square with a 30 mm clear concrete cover on the colurnn ties. This
prototype structure has relatively srnall columns and a relatively high live load in order to
produce high punching shear stresses in the slab around the columns.
Figure 2.1 Prototype flat plat structure (4-75m x 4.75 m bays)
2.2 Details of Test Specimens
2.2.1 Design and Details of Two-Way Slab Specimens
Six, full-scale hvo-way slab specimens representing 2.3 x 2.3 m regions around the
interior colurnns were tested in the Structures Laboratory in the Department of Civii Engineering
at McGill UniversiS. The slab test specimens, representing the column strip regions of the
prototype slab (see shaded region in Fig 2.1), were constructed with 300 mm high reinforced
concrete stub colurnns above and betow the slab (see Fig. 2.2). The slab has a design concrete
compressive strength of 30 MPa, while the columns have a design concrete stren,@h of &O MPa,
Figure 2.2 Slab-column test specimen (2.3 m x 2.3 m)
The slab design was carried out in conformance with the AC1 code (ACI, 1995) and the
CSA Standard (CSA, 1994) with a superimposed dead load of 1.2 kPa and a live load of 4.8 kPa.
The computer program ADOSS (CPCA 1991) was used to design the protowpe structure. In
order to investigate both the cracking performance at service load and the punching shear
strength, the slab was designed such that the there was sufficient flexural reinforcement to meet
the code requirernents, but a relatively small colurnn was chosen such that the specimen would
fail in punching shear. The final design resulted in a flexural capacity that was 9.5% greater than
that required by the AC1 code, while the punching shear strength was only 66% of the required
strength.
The reinforcement was distributed both uniformIy and banded. The uniform distribution
of reinforcement is representative of a design carried out using the 1995 AC1 Building Code
(ACI, 1995), whereas the banded distribution is representative of the distribution obtained by
designing according to the 1994 CSA Standard (CSA, 1994). Both the uniform and banded top
bar layouts contain fourteen (14) No. 15 reinforcing bars in each direction. The columns contain
four No. 15 vertical bars and two No. 10 hoops above and below the slab. Figure 2.3 shows the
Iayout of the reinforcement in the two-way slab specimens. The layout of the bottom
reinforcernent that was used in a11 the specimens is shown in Fig. 2.4. Three of the bottom No.
10 bars were continuous through the column in order to satisfy the structural integrity
requirements of the 1994 CSA Standard. Figure 2.5 shows the slab reinforcement for the slab-
coIumn specimens.
a) unifoim distribution b) banded distribution
Figure 2.3 Distribution of top No. 15 bars
Figure 2.4 Layout of bottom No. IO bars
Figure 2.5 SIab reinforcement
The testing program consisted of six test specimens having different methods of
construction of the slab and two different distributions for the top slab reinforcement. Steel
fibre-reinforced concrete with a compressive strength of 30 MPâ was used in four of the
specimens. The six specimens were divided into three series: NSC (Normal-Strength Concrete
slab), FRS (Fibre-Reinforced Concrete slab around column), and FRC (Fibre-Reinforced
Concrete in cover only), as summarised in Fig. 2.6.
Uniforrn Distribution Cu)
Pa with fibres
FRS Series
- -- - -
. ' Bandëd Distribution
FRC Series
Figure 2.6 Two-way sIab test series
The sIab specimens are described below:
NSC Series: Normal-strength concrete slabs (NSC). These tests are the benchmarks with
which to compare the responses of the steel fibre-reinforced concrete slab specimens (see Fig.
2.6).
i) Specimen NSC-U: A normal-strength concrete slab containing a uniform distribution
(U) of top reinforcing bars. The uniforrn distribution of top bars is consistent with
current US. practice (ACT, 1995).
ii) Specimen NSC-B: A normal-strength concrete slab, the sarne as Specimen NSC-U, but
with a greater concentration of top flexural steel in the immediate colurnn vicinity to
demonstrate the influence of a banded steel distribution (B). This banded distribution is
representative of recent changes to Canadian design practice (CSA, 1994)-
FRS Series: Specimen with fibre-reinforced concrete placed over the entire depth of the slabs
(FRS), but only in the irnmediate vicinity o f the column, to study the influence of strategically
placed steel-fibre reinforced concrete on crack control, stifiess and punching shear capacity
(see Fig. 2.6). One of the main advantages of using fibre-reinforced concrete within the region
500 mm from the column face is that the concrete is stiffer and hence much more able to
maintain its shape (see Fig. 2.7) while the normal-strength concrete is being placed around it.
The normal-strength concrete was then placed in the remaining area of the slab before
vibrating both concretes. By using a low sIump fibre-reinforced concrete mix, time consuming
mesures such as screens to obtain the 45 degree angle interface between the two types of
concrete were avoided.
iii) Specimen FRS-U: A specimen with fibre-reinforced concrete placed over the entire
depth of the slab in the irnmediate vicinity of the column, with a uniform distribution of
top steel.
iv) Specimen FRS-B: A specirnen identical to Specimen FRS-U, but with a banded
distribution of top steel.
FRC Series: Specimen with fibre-reinforced concrete placed only in the top cover concrete
(FRC) plus one bar diarneter to see the influence on the crack control. The fibre-reinforced
concrete was placed on top of the normaI-strength concrete forming the bottom portion of the
slab (see Fig. 2.6). The steel-fibre reinforced concrete was placed before the normal-strength
concrete fdly set and was vibrated at a number of Iocations to avoid the formation of a weak
plane or coId joint. Figure 2.8 shows Specimen FRCU just before the placement of the fibre-
reinforced concrete.
v) Specimen FRC-U: A specimen with fibre-reinforced concrete ptaced only in the top
cover concrete (FRC) that h a . a uniform distribution of top steel.
vi) Specimen F E - B : A specimen identical to Specimen FRC-U, but with a banded
distribution of top bars.
Figure 2.8 Construction of Specimen FRC-U
2.2.2 Description of Column Specimens
Cornpanion column specimens were constmcted to enable a determination of the effect
of the Iayer of 30 MFa concrete over the slab thickness on the axial load response of the 80 MPa
column. The 700 mm high column specimens contain four No. 15 vertical reinforcing bars and
No. IO hoops spaced at 160 mm. The column specimens were divided into the same three series
as the two-way slab specimens: NSC, FRS, and FRC, Figure 2.9 shows the column specimens.
In addition to testing these isolated column specimens the slab column specimens
described in Section 2.2.1 were also tested by loading the colurnns in compression afier the slab
specimens failed in punching shear. Although the slabs were damaged in the column vicinity,
these specimens provided an indication of the beneficial effects of the slab and presence of the
sIab reinforcement on the ukimate strength of the column.
MPa Pa with fibres
a) Control specimen C b) Specimen C-NSC c) Specimen C-FRS d) Specirnen C-FRC
Figure 2.9 Column test series
The column test specimens are described below:
NSC Series
i)
ii)
iii)
iv)
Specimen Cl: A high-strength concrete column, constructed with 80 MPa
concrete, cast in two [ i h , with a construction joint at the mid-height of the coIumn. This
specimen is the control specimen to which the responses of the other column specimens
will be compared.
Specimen C-NSC: A high-strength concrete column with a 150 mm thick layer of 30
MPa sïab concrete at its mid-height. This specimen is a cornpanion to the NSC series of
the two-way slab specimens.
Specimen C-NSC-U: The column of the two-way slab specimen NSC-U.
Specimen C-NSC-B: The column of the two-way slab specimen NSC-B.
FRS Series
v) Specimen CS: A high-stren,oth concrete column similar to Cl. This specimen is the
control specimen to which the responses of the other FRS series specimens will be
compared.
vi) Specimen C-FRS: A high-strength concrete column with a 150 mm thick layer of fibre-
reinforced concrete at its mid-height. This specimen is a companion to the FRS series of
the two-way slab specimens.
vii) Specimen C-FRS-U: The column of the two-way sIab specimen FRS-U.
viii) Specimen C-FRS-B: The cotumn of the two-way slab specimen FRS-B.
Specimen C3: A high-strength concrete column similar to Cl and C2. This specimen is
the control specimen to which the responses of the other FRC series specimens will be
compared-
Specimen C-FRC: A high-strength concrete column with a 95 mm thick layer of 30
MPa slab concrete topped with a 40 mm layer of fibre-reinforced concrete at its mid-
height. This specirnen is a companion to the FRC series of the two-way slab specimens.
Specimen C-FRC-U: The colurnn of the two-way slab specimen FRC-U.
Specimen C-FRC-B: The column of the two-way slab specirnen FRC-B.
2.3 Material Properties
2.3.1 Reinforcing Steel
Table 2.1 summarises the material properties of the hot-rolled deformed reinforcement
used in constructing the test specimens. AI1 of the reinforcement used was Grade 400. The
values reported are the averages of material testing on samples taken from three random bars.
Figure 2.10 shows typicat stress-strain responses of the reinforcing bars.
Size Designation
No. 10
No. 15
Table 2.1
column hoops top flexurd
Reinforcing steel properties
0.24 1 1.95 1 596 1 reinforcement & coIumn bars
&Y
(%)
0.34
strain (mm/mm)
Figure 2.10 Typical tensile stress-strain curves for reinforcing steel
Esh
(%)
O .43
f"
( M m
676
Function
bottom flexural reinforcement &
2.3.2 Concrete
Table 2.2 surnmarises the mix designs of the concrete used to construct the specimens.
Tables 2.3, 2.4 and 2.5 sumrnarise the material pro~erties of the concrete used in Series NSC,
FRS, and FRC respectivety. Compression, split cylinder and third point loading flexurat beam
tests were conducted to deterrnine the mean values of the concrete compressive strength, fo the
splitting tensile strengtli, frp, and the modulus of rupture, f,. At least three tests were carried out
in order to determine the mean values of these properties. Figure 2.1 1 shows Spical compressive
stress main responses of the concretes. Figure 2.12 shows the shrinkage readings for the high-
strength, normal-strength and fibre-reinforced concrete.
Table 2.2 Concrete mix designs
30 MPa concrete
with fibres for puddling
Characteristics normal
strength concrete h cement (Type IO), k g h 3 355
concrete high
for cover concrete
fine aggregates, kg/m3
coarse aggregates, k g h 3 1 1040 1 1040 1 1040 1 960
790
total water**, kg/m3 1 178 1 178 1 190 1 143
(rnax size, mm)
superplasticizer, rnllrn3 1 - 1 - 1 - 1 11.97
(20)
water-cernent ratio
water-reducing agent
** Includes the water in admixtures
(20)
0.50
11 10
--
air-entaining agent, rn l/m3
slump, mm
air content, %
density, kg/m3
steel fibre content (0.5% by volume), kg/m3
(20)
0.50
1110
* Type 1 O blended cernent containing 8-9% silica fume
--
180
146
8.8
2130
-
(10)
O -54
11 10
180
75
8.8
2130
39.4
0.25
754
180
120
8.8
2130
39.4
-
200
1.5
2417
-
\
column concrete /
C / slab concrete
O 0.001 0.002 0.003 0.004
strain, E,
Figure 2.1 1 Typical compressive stress-strain curves of concrete
,--- fibre-reinforced ..-.-..-- + .......,...
' ' normal-strength 1
. .. hig h-strength 1
O ?
O 30 60 90 120 time (days)
Figure 2.12 Shrinkage readings for concretes
Table 2.3 Concrete properties for NSC Series - -
Specimen
C-NSC
1 slab Iayer 1 30.0 1 2620
top half std. deviation bottom I d f
std. deviation column top
std, deviation
column bottom std. deviation
1 std. deviation 1 0.9 1 152 1 0.24
NSC-U & NSC-B I coIumn top 87.4 2680 std, deviation 1 4.6 1 142
83.1 3 -7
80.7 O. 1
83.1 3 -7 80.7 O. 1
2600 125
2640 95
2600 125
2640 95
cotumn bottom std. deviation
slab layer std, deviation l 0.9
1 std. deviation 1 2.5 1 103 1 0.43
81.8 1 .O
30.0 152 1 0.24
Table 2.4 Concrete properties for FRS Series
bottom half std. deviation
2740 7 -24 56 0.62
2620 3 -26
f,
xlod WP)
2469 1 6.62
1 slab layer with fibres 1 43.3 1 2506 1 3.22
fc w a )
85.7
Specimen
C2
C-FRS
FRS-U & FRS-B
Batch
top half
colurnn top std. deviation
column bottom std. deviation
slab layer with fibres std. deviation
colurnn top std. deviation
column bottom std. deviation
slab layer std. deviation
I std. deviation
85.7 2 -5
85.9 7.0
43.3 1.8
1.8 75 1 0.36
2469 1 03
2586 132
2506 75
0.62 0.43
7.14 0.3 5
3.22 0.36
7.23 0.04
6.8 1 0.47
3.12 0.22
93 -9 12.7
89.5 1.2
39.0 O -3
2549 268
2673 65
243 6 69
Table 2.5 Concrete properties for FRC Series
Specimen
C3 std. deviation
bottom half
slab Iayer 3 7.5 1981 3.01 std. deviation 1 0.6 1 74 1 0.08
Batc h
top haIf
C-FRC
1 cover with fibres 1 33.4 1 2210 1 4.63
0.5
83 -6
fc' w a )
85.1
std. deviation colurnn top
std. deviation column bottom std. deviation
189 23 50
FRC-U & FRC-8
c X I O ~
2475 O. 17
6.59 0.3
85.1 0.5
83 -6 0.3
std. deviation
column bottom
fr
v a )
6.00
std. deviation column top
std. deviation slab Iayer
61 1
2475 189
23 50 611
O -4
83.6
std. deviation cover with fibres
2.3.3 Fibre-reinforced Concrete
0.28
6.00 0.17
6.59 0.28
0.6 84.3
O -4
3 7.5
std. deviation
The first stage in this project is to evaluate the influence of different dosages of steel fibres
in combination with high-performance concrete in order to choose a practical and cost effective
rnix design. The primary objective is to choose a mix which would provide improved post-
cracking performance, particularly the control of cracking in reinforced concrete flexural members.
it is cIear from the one-way shear tests in Fig. 1.1 that large volumes of fibres may not be
cost effective because above a fibre volume of about 0.7% the increase in shear strength is not as
sipificant. Hence a volume of 30 mm long hooked steel fibres of 0.5% was chosen for the two-
way slab specimens in this test series. SteeI fibres were chosen over carbon fibres because of the
excessively high cost of carbon fibres. Potypropylene fibres were not chosen because they do not
offer the sarne improvement in structural performance as steel fibres.
58 2524
0.6
33 -4
9 1 2393
0.02
6.87 330 1981
O -6
0.2 1 6 -45
0.04 3.01
74
2210
0.08
4.63 9 1 0.2 1
The steel fibres used in the slab-cohmn specimens were 30 mm long with a diameter of
0.5 mm. The sarne standard tests were conducted on the fibre-reinforced concrete as the
conventional noma1 and high-strength concretes. The Toughness Performance Level rnethod, or
Template Approach proposed by Morgan, Mindess, and Chen (1995) \vas used to quanti@ the
toughness of the fibre-reinforced concrete and the benefits of the steel fibre addition to the
concrete material properties. The mean vatues of the fibre-reinforced concrete properties are
surnmarised in Tables 2.4 and 2.5. Load defiection curves and the tougliness performance levels
for the fibre-reinforced concrete are shown in Fig. 2.13. The fibre-reinforced concrete used in
the slab specimens was found to have a toughness performance Level which is on the border
between Level II and LeveI III touglmess.
0.5 1 .O 1.5 2.0 net midspan defiection (mm)
Figure 2.13 FIexural toughness performance Ievels for fibre-reinforced concrete
2.4 Testing Procedure for Slab Specimens
2.4.1 Test Setup and Loading Apparatus
The lower coIumn stub of the slab-column specimen was placed on a steeI supporting
block and the slab was loaded with eight equal point loads around the perimeter (see Fig. 2.14).
From the slab analysis, the inflection points of the prototype stmcture were found to be
approximately 900 mm fiom the column face. Therefore, to obtain sirnilar moment-to-shear
ratios on the test specimen, pairs of Ioad points were located 887.5 mm from the face of the 225
mm square cofurnn. Four hydraulic jacks were used to Ioad steel distribution beams beIow the
slab that spanned the 750 mm between adjacent load points as shown in Fig. 2.14. ALI jacks
were connected to a single hydraulic pump. Figure 2.15 shows a photograph of the test setup for
two-way slab specimen.
The tests were performed monotonically. The loading was applied in srnaIl increments
with loads, deflections and strains being recorded at each increment. At key load stages, the
crack pattern and crack widtl-is were recorded.
two-way slab specimen I
hydraulic jack
Figure 2.14 Test setup for two-way slab specimens
Figure 2.15 Photograph of test setup for two-way slab specimens
2.4.2 Instrumentation of Slab Specimens
The load applied to the slab was measured with four load cells, one for each hydraulic
jack. The deflection of each loading point was monitored with an linear voltage differentiat
transformer (LVDT). Four additional LVDTs on the underside of the slab were used to monitor
the deflection of the slab relative to the colurnn, close to the column face. These four LVDT
readings were used to detect the start of a punching shear failure. Three LVDTs were also
placed on the column to measure the movement of the column relative to the reaction floor to
measure the rigid body rotation of the slab-column specimen.
Electrical resistance strain gauges were glued to reinforcement bars in the top mat in Iine
with the coIumn face in the two principal directions of the slab, as shown in Fig. 2.16.
Additional strain gauges were glued to the concrete on the bottom s u ~ a c e of the slab which were
directly below the strain gauges on the top bars. The concrete stain readings obtained from these
gauges together with the stains obtained from gauges on the steel bars enable the curvature to be
determined at a number of sections.
a) unifurm distribution b) banded distribution
Figure 2.16 Strain gauge Iocations on top mat reinforcement
Targets were glued to the top surface of the slab to enable the determination of strains
using a 203 mm gauge Iength mechanical extensorneter. The location of these targets correspond
to the sû-ain gauges in the top mat of reinforcing bars. Another set of targets was located around
the perirneter of the column to determine the average strain on this perimeter. Target locations
are s h o w in Fig. 2.17. Al1 Ioad, displacement and strain readings, except strains from the
mechanical targets on slab surface, were recorded with a computerised data acquisition system.
a) uniform distribution 6) banded distribution
Figure 2.17 Target locations on concrete surface of two-way slabs
2.5 Testing Procedure for Column Specimens
2.5.1 Test Setup and Loading Apparatus
The cornpanion column specimens were tested in axial compression in a computer
controlled t 1,000 kN capacity testing machine. The tests were performed rnonotonically and
loading was appfied in increments until failure occurred.
The columns of al1 of the slab-column specimens were also tested in axial compression
after the slabs had faiIed in punching shear to examine any beneficial effects of the severely
distressed surrounding slab. To accommodate the sIab specimens in the iest machine, two 300
mm wide strips were saw cut off opposing sides of the slab specimens. The specimens were then
installed under the head of the test fiame as shown in Fig. 3-18.
2.5.2 Instrumentation
For the isolated column test, four LVDTs, one at each corner, were used to measure the
average strain over a 550 mm gauge [en@ centred on the column. One additional LVDT
measured the strain over the middle 150 mm of the south face of the column to provide strain
readings over the 150 mm thickness of sIab concrete (see Fig.2.19a).
For the slab-column specimens, five srnaIl holes were drilled through the slab to permit
the attachrnent of the LVDTs to measirre average strains over heights of 150 and 550 mm to
compare these strain readings with the strain measured on the isolated colurnn specimens. The
load and displacement readings were recorded with the data acquisition system of the testing
machine (see Fig 2.19b).
Figure 2.18 Axial compression testing of slab-column specimen
a) Colurnn specimen 6) Slab-colurnn specimen
Figure 2.19 Instrumentation of column and slab-column specimens
Chapter 3
Response and Comparison of Test Results of Two-Way Slab Specimens
3.1 Response of Two-Way SIab Specirnens
This section presents the observed experimental behaviour of the six sIab-column
specimens. It is important to note that the total Ioad reported is the surn of the applied Ioads at
the 8 loading points, the self-weight of the slab outside of the critical shear periphery and the
weiglit of the loading apparatus. The self-weight of the sIab test specimen outside of the region
d/2 fiom the column faces, and the loading apparatus was 21.5 m. The corresponding self-
weight of the prototype structure causes a shear at the interior column of approxirnately 90 W.
The average defiection reported is the average of the measured deflections at the 8 loading
points.
The loading was applied in small increments with loads, deflections, and strains being
recorded at each increment. At key load stages, the crack pattern and crack widths were
recorded. Some of the key Ioad stages included first cracking, self-weight, full service Ioad and
first yielding. The fidl service Ioad was taken as the self-weight of the slab with a superimposed
dead load of 1.2 kPa and a live load of 4.8 kPa. This is equivaIent to a shear of 214 kN on the
critical shear periphery of the slab-column connection.
To determine the difference in the performance of the unifonn and banded distribution
of the top mat of reinforcing bars, the maximum crack widths were determined sepmtely for the
"banded" region, within 1.5h fiom the column face, and for the remainder of the sIab outside of
this region.
3.1.1 Specimen NSCU
The total Ioad versus deflection response of Specimen NSCU, with normal-strength
concrete and a unifonn distribution of top steel, is s h o w in Fig. 3.Ia. As shown, first cracking
occurred at a load of 81 kN and the load-deflection response was stiffer up to the point of first
cracking. First cracking occurred in the North-South direction, perpendicular to the weak
direction reinforcement and extended from the four corners of the column. First yielding
occurred in one of the bars in the weak direction at a total load of 21 8 kN and a corresponding
average defiection of 9-9 mm. This yielding occurred in îhe second reinforcing bar, 134 mm
fiorn the coIumn face. The maximum load reached was 306 kN with a corresponding deflection
of 17.2 mm, before failing abruptly in punching shear. The failure was instantaneous, with the
Ioad dropping to 164 kN and an increase in deflection to 20.2 mm. The shear failure surface
extended from the bottom slab-cohmn intersection to the top surface of the slab at an angle of
approximately 45 degrees.
Figure 3.2a shows the measured strains in the strain gauges in the top mat of
reinforcernent at full service load and at the peak load- The highest strains were recorded in the
weak direction in the fust reinforcing bar outside the coIumn face, and in the strong direction in
the second reinforcing bar outside the column face. The strains are higher in the weak direction
due to the 15 mm smaller flexural Iever am. As can be seen, the reinforcement in the weak
direction has reached 2140 micro-strain at fuIl service load, that is just below the yield level of
2 150 micro-strain.
The totai load versus maximum crack width, inside and outside the banded region, are
shown in Fig. 3.3a. From this figure it can be seen than the cracks are larger in the banded
region than the rest of the slab tItroughout the entire test. The larger cracks observed closer to
the column is due to the higher tensile strains observed in this region. The crack pattern at the
full service load for Specimen NSCU is shown in Fig. 3.4a. The maximum crack width at the
full service Ioad was 0.80 mm in the "banded" region around the column and 0.50 mm outside
this region. Figure 3.5a shows the appearance of the slab after failure.
3.1.2 Specimen NSCB
Figure 3.1 b shows the total load versus deflection response of Specimen NSCB having
normal-stren,@h and a banded steel distribution. As expected, the load-deflection response
shows a drop in stiffness at a load of 78 kN, when first cracking occurred. First cracking
occurred in the North-South direction, perpendicular to the weak direction reinforcement. The
cracks started from the edge o f the sIab and propagated towards the column corners. The top mat
of bars first yielded at a load of 273 kN and a corresponding average deflection of 10.7 mm. The
first bar to yield was the second reinforcing bar from the slab centre in the weak direction- This
bar was 14 mm from the column face. An uItimate Ioad o f 349 kN and a corresponding
deflection of 15.3 mm was reached, before the specimen failed abruptly in punching shear. The
failure was instantaneous, with an immediate drop in load to 193 kN and an increase in
deflection to 18.4 mm. The banded distribution of reinforcement seemed to push the failure
plane away from the column. The failure plane formed fiom the slab-column intersection on the
bottom surface to the top flexural mat a t an angle of approximately 45 degrees from the slab
surface. From the top mat to the top slab surface the failure plane was flatter, resulting in the
punching shear crack surfacing a t about 2d fiom the column face (see Fig. 3.5b).
The measured strains in the strain gauges in the top mat of reinforcement at full service
load and at the peak load are shown in Fig.3.2b. At full service load, none of the bars had
reached yield, and the strains generally decreased with distance from the column face. The first
bar outside the column face in the weak direction displayed the highest strain readings during the
test.
The total load versus maximum crack width for Specirnen NSCB is shown in Fig. 3.3 b.
From this figure it c m be seen than the crack widths are slightly srnaller in the "banded" region
than the rest of the slab. For this specimen with banded reinforcement, the crack widths are of
similar width across the entire surface of the slab. The crack pattern at the full service load for
Specimen NSCB is shown in Fig. 3.4b. The maximum crack width at full service load was 0.35
mm in the "banded" region and 0.4 mm outside this region.
A fint yield
first crack
30 40 50 deflection (mm)
a) Specimen NSC-U
A first yietd
fint crack
full service load -- - - - - - - - . - - . - -- - - -- - - -
, - /- self weight
30 40 50 deflection (mm)
b) Specimen NSC-6
Figure 3.1 TotaI load versus average deflection responses of nomal-strength concrete specimens (NSC Series)
ultimate load \ full service load, \
3000 €y O
a) Specirnen NSC-U
b) Specimen NSC-B
Figure 3.2 Strains in top mat reinforcing bars at full service and peak load for NSC Series
outside banded region
/' in banded _ _ _ _ _ _ _ _ _ _ - C - - - - - - - region
- - C e - - =
. - - 0 - full service load
1 banded region 1
self weight
0 -4 0.6 0.8 1 .O 1.2 maximum crack width (mm)
a) Specimen NSC-U
banded region
self weight
0.4 0.6 0.8 1 .O 1.2 maximum crack width (mm)
b) Specimen NSC-B
Figure 3.3 toad versus maximum crack width for normal-strength concrete specirnens (NSC Series)
maximum cmck width: inside banded region = 0.80 mm outside banded region = 0.50 mm
a) Specimen NSC-U
maximum crack width: inside banded region = 0.35 mm outside banded region = 0.40 mm
b) Specimen NSC-B
Figure 3.4 Crack pattern of NSC Series at fùll service load
a) Specimen NSC-U
b) Specimen NSC-B
Figure 3.5 NSC Series at failure
3.1.3 Specimen FRSU
The total Ioad versus deflection response of Specimen FRSU, with fibre-reinforced
concrete in the slab around the coIumn and with a unifom distribution of top steel, is shown in
Fig. 3.6a. First cracking occurred at a totaI load of 97 kN, with the load-deflection response
eshibiting a drop in stiffitess upon first cracking. The fust cracks occurred in the North-South
direction, perpendicular to the weak direction reinforcernent and extended fiom the corners of
the colurnn to the edge of the slab. The top mat of bars first yielded at a load of 227 kN and a
corresponding average deflection of 9-0 mm- The first bar to yield was one of the bars that
passed through the column region. The Specimen FRSU reached a peak load of 422 kN and a
corresponding deflection of 36.0 mm. Figure 3.6a shows the ductile behaviour of the specimen
as it failed. The total load versus average deflection curve shows the general yielding of the
specimen before the ultirnate load was reached. The test was stopped when the specimen
reached an average deflection of about 55 mm, at a load of 266 W. Figure 3.10a shows the
specimen after failure. The failure can be classified as a flexuravshear failure, since the
specimen first exhibited general flexural yielding, followed by a punching shear type failure
around the colurnn. The failure plane started at the intersection of the colurnn and bottom
surface of the slab and emerged on the slab top surface outside the area where the fibres were
added to the concrete sIab. Near the end of the test, crack widths were larger than 8.0 mm in the
vicinity of the column due to the excessive bending of the slab.
Figure 3.7a shows the measured strains in the strain gauges in the top mat of
reinforcernent at full service load and a t the peak load. The highest strains were recorded in the
reinforcing bars inside the column fôces in both directions. The strains were higher in the weak
direction due to the 15 mm srnaller flexural lever m. None of the bars had yielded at the full
service Ioad.
The totaI load versus maximum crack width, inside and outside the "banded" region, are
shown in Fig. 3.8a. From this figure it can be seen than the cracks are approximately twice as
large in the banded region than the rest of the slab for the entire test. The crack pattern at the full
service Ioad for Specimen FRSU is shown in Fig. 3.9a. The maximum crack width at the full
service load was 0.45 mm in the "banded" region around the column and 0.25 mm outside of this
region.
3.1.4 Specimen FRSB
Figure 3.6b shows the total load versus deflection response of the "puddled" fibre-
reinforced siab, banded steel distribution, Specimen FRSB. As shown, the load-deflection
response was linear up to a load of 93 kN when first cracking occurred. First cracking occurred
in the North-South direction, perpendicular to the weak direction reinforcement. The first crack
extended fiom the centre of the south column face to the south edge of the slab, The top mat of
bars f m t yielded at a Ioad of 320 kN and a corresponding average deflection of 12.6 mm. The
first reinforcing bar from the slab centre in the strong direction, and the third and fourth bars in
the weak direction al1 yielded at about the same load. Specimen FRSB withstood an ukirnate
Ioad of 438 kN and a corresponding deflection of 32.8 mm. At a total load o f approximately 3 75
kN the specimen started to display general yielding, with an increase in deflection without a
corresponding increase in load. Specimen FRSB showed signs of punching shear failure only at
the end of the test, when the average deflection was about 65 mm. Figure 3.10b shows the
specimen after failure. The failure of Specimen FRSB was due to excessive yielding of the
flexural reinforcement, which caused a large increase in the average deflection. The punching
shear failure did not cause a large drop in the Ioad carrying capaciv of the specimen, but aIlowed
for even larger deflections to take place.
The measured strains in the strain gauges in the top mat of reinforcement at full service
load and at the peak load are shown in Fig. 3.7b. The highest strains were recorded in the first
four reinforcing bars From the slab centre in the weak direction. The strains are slightly higher in
the "banded" region of the slab at fu l l service load conditions. There is also very Iittle difference
in the strain values in the weak and strong directions at this Ioad level. At the peak load level,
the strains are much larger in the weak direction and are also larger in the "banded" region.
The total load versus ma.-ximum crack widths for Specimen FRSB is shown in Fig. 3.8b.
From this figure it can be seen that the crack widths are slightly smaller in the "banded" region
than the rest of the slab. The crack widths are of similar width across the surface of the slab
which corresponds to the strain distribution measured in the steel reinforcing bars at the full
service load. The crack pattern at the full service Ioad for Specimen FRSB is shown in Fig. 3.9b.
The maximum crack width at the at the fidl service load was 0.35 mm in the "banded" region
and 0.40 mm outside this region.
500 - i
A firçt yield
first crack
full service load
self weight - - - - -- .. .-
O ! I O I O 20 30 40 50 60 70 80
deflection (mm)
a) Specirnen FRS-U
A first yield
f--7 a first cradc
30 40 50 deflection (mm)
b) Specirnen FRS-B
Figure 3.6 Totai load versus average deflection responses of fibre-reinforced concrete slab specimens (FRS Series)
ultimate load full service load.
a) Specirnen FRS-U
5000 €y O
b) Specirnen FRS-B
Figure 3.7 Strains in top mat reinforcing bars at fiill service and peak load for FRS Series
outside banded region in banded region 400 - ----- _---
__---- __---- ___------
full service load
banded region
self weight
1 .O 1.5 2.0 2.5 3.0 maximum crack width (mm)
a) Specimen FRS-U
----- - - - - -____
full service load --
banded resion
self weislht
1 .O 1 -5 2.0 2.5 3.0 maximum crack width (mm)
b) Specimen FRS-8
Figure 3.8 Load versus maximum crack width for fibre-reinforced concrete slab specimens (FRS Series)
maximum crack width: inside banded region = 0.45 mm outside banded region = 0.25 mm
a) Specimen FRS-U
maximum crack width: inside banded region = 0.35 mm outside banded region = 0.40 mm
b) Specimen FRS-B
Figure 3.9 Crack pattern of FRS Senes at full service load
a) Specirnen FRS-U
b) Specirnen FRS-B
Figure 3.10 FRS Series at failure
3.1.5 Specimen FRCU
The total load versus deflection response of Specirnen FRCU, with fibre-reinforced
concrete in the cover and a uniform distribution of top steel, is shown in Fig. 3.1 la. The drop of
stiffness upon first cracking, at a load of 93 kN, is apparent from this figure. First cracking
occurred in the North-South direction, perpendicular to the weak direction reinforcement and
extended from ail four corners of the column to the edge o f the siab. The top mat of bars first
yielded at a load of 242 kN and a corresponding average deflection of 10.6 mm, with yielding
occurring in the first two reinforcing bars from the slab centre in the weak direction. The load-
deflection response was relatively Iinear from first cracking up to about the peak load level. The
specimen reached an ultimate load of 329 kN and a corresponding deflection of 18.2 mm.
Specimen FRCU failed abmptiy in punching shear, with a sudden decrease in load to 219 kN
with a corresponding smaIl increase in average deflection. The specimen was hrther deflected
from 20 mm to over 40 mm with little change in total load. Figure 3.1 Sa shows the specimen
after failure.
Figure 3.12a shows the measured strains in the strain gauges in the top mat of
reinforcement at full service load and at the peak load. At the f i l 1 service load the strains are
[arger in the region closer to the centre of the slab, but were sorne what less than yield, The
strains were generally higher in the weak direction, with the highest strains being recorded in the
three reinforcing bars closest to the slab centre.
The total ioad versus maximum crack width, inside and outside the "banded" region, are
shown in Fig. 3.13a. This figure shows that the cracks were almost twice as large in the banded
region than the rest of the slab for the entire test. The crack pattern at the hl1 service load for
Specimen FRCU is shown in Fig. 3.14a. The maximum crack width at the hl1 service load was
0.60 mm in the "banded" region around the colurnn and 0.40 mm outside this region.
3.1.6 Specimen FRSB
Figure 3.1 1 b shows the total load versus average deflection response of specimen FRSB.
As shown, the load-deflection response was linear up to a Ioad of 84 kN when first cracking
occurred. First cracking occurred in the North-South direction, perpendicular to the weak
direction reinforcement. One crack was from the centre of the north column face to the edge of
the slab, and the other crack extended from the eastem corners of the coIurnn to the edge of the
"banded" region. The top mat of bars first yielded at a toad of 258 kN and a corresponding
average deflection of 10.1 mm. The first reinforcing bar from the slab centre in the weak
direction k v a s the first to yield. This bar was 71 mm inside the south column face. Specimen
FRCB reached an ultimate Ioad of 361 kN and a corresponding deflection of 16.3 mm. The Ioad-
deflection curve for Specimen FRCB in Fig.3.l l b shows a constant dope from first cracking to
the peak load. The load-deflection response of the specimen showed no degradation before
failure occurred. The abrupt punching shear failure resulted in an instantaneous drop in Ioad to
235 kN. The specimen was then further Ioaded to a total deflection of 78 mm. Specimen FRCB
reached a post failure maximum of 336 kN at a average deflection of 65.6 mm. The shear faiIure
plane extended from the bottom surface of the slab-column intersection to the perimeter of the
slab at the level of the top mat. This resulted in horizontal cracking at the level of the flexural
reinforcernent on the exposed side faces of the slab specimen. The fibre-reinforced concrete
cover did not allow the failure to protrude to the top surface of the slab, and forced the failure
along the longitudinal bars to the edge of the specimen. Figure 3.15b shows the specimen at the
end of the test.
The measured strains in the strain gauges in the top mat of reinforcement at full service
load and at the peak Ioad are shown in Fig. 3.12b. The first bar fiom the slab centre in the weak
direction showed the highest strains throughout the test. At fi111 service load none of the top
reinforcement had reached yield, the reinforcing bars within the "banded" region experienced
slightly higher strains than the rest of the bars and there was very Iittle difference in the strain
values in the weak and strong directions.
The totaI Ioad versus maximum crack widths for specimen FRCB is shown in Fig. 3.13b.
From this figure it can be seen than the crack widths across the entire slab surface are practically
the same width up to full service load. At higher Ioads the cracks within the "banded' region
were larger than the cracks outside tliis region. The crack pattern at the full service load for
specimen FRCB is shown in Fig. 3.14b. The maximum crack width at the at the full service Ioad
was 0.40 mm in and outside the "banded" region.
A first yield
first crack
full service load
-- - self weight
30 40 50 deflection (mm)
a) Specimen FRC-U
f 300 - 25 u m full service Io 0 200-
IO0 -
O 1
O 1 O 20 30 40 50 60 70
500
deflection (mm)
400 -
b) Specimen FRC-B
A first yield
first crack
Figure 3.11 Total load versus average deflection responses of fibre-reinforced concrete cover specimens (FRC Series)
Figure 3.12
ultimate load full service load,
4000 &y O
a) Specimen FRC-U
b) Specimen FRC-B
Strains in top mat reinforcing bars at fùll service and peak load for FRC Series
--" banded regioc-..----; -_-- b
_--- outside banded region ___--* L . ,
___--- --- full service'4,oad - - .. - C -
banded region _/--
4' self weight
0.4 0.6 0.8 1 .O maximum crack width (mm)
a) Specimen FRC-U
C--"c--,_ in banded region
- _ *-* - full service load
banded regian
self weight
0.4 0.6 0.8 1 .O 1 -2 maximum crack width (mm)
b) Specimen FRC-B
Figure 3.13 Load versus maximum crack width for fibre-reinforced concrete cover specimens (FRC Series)
maximum crack width: inside banded region = 0.60 mm outside banded region = 0.40 mm
a) Specimen FRC-U
-- pp - - - - - -
maximum crack width: inside banded region = 0.40 mm outside banded region = 0.40 mm
b) Specirnen FRC-B
Figure 3-14 Crack pattern of FRC Series at fidl service load
a) Specimen FRC-U
6) Specimen FRC-B
Figure 3.15 FRC Series at failure
3.2 Comparison of Two-Way Slab Test Results
This section compares the observed experimentat behaviour of the slab-column
specimens. The [oad versus defiection responses, the load versus strain distribution in the
reinforcing steel and the load versus crack widths are al1 compared.
3.2.1 Load-Deflection Responses
Figure 3.16 compares the total load versus average deflection responses for the six slab-
column specimens. Table 3.1 sumrnarises the measured total load and average deflections at
first cracking, first yielding, full service load and the peak load for al1 of the slab-column test
specimens.
A first yield
first crack
full service load
self weight - , - . .- - -. - - . - - . - . - - -A- .
- O 10 20 30 40 50 60 70 80
deflection (mm)
a) uniform specimens
500 A first yield
deflection (mm)
b) banded specimens
Figure 3.16 Influence of fibre-reinforced concrete on the load-deflection responses
NSC Series
FRS Senes
FRC Series
400 1 fint crack
full service load
self weight - - -
deflection (mm)
500 A first yield
deflection (mm)
500 -I A first yield
400 - a first crack
O ! O 1 O 20 30 40 50 60 70 E
deflection (mm)
Figure 3.17 Influence of concentrating reinforcement near column on load-deflection responses
From Fig. 3.16 and Table 3.1, it c m be seen that the load and deflection values when the
slab-column specimens exhibited first cracking were similar. When comparing companion
specimens witli and without banded reinforcement, the cracking loads were slightly higher in the
specimens with uniformly distributed top reinforcement. It is interesting to note that the banded
reinforcement exhibited initial cracks which formed near the edges of the specimens where the
reinforcernent ratio was lower. Although the uniformly distributed steel had slightly higher
cracking loads, they exhibited higher deflections at first cracking due to the smaller percentage
of reinforcernent in the regions of maximum moment.
The NSC Series displayed the Iowest Ioads at first cracking, with the FRS Series having
the largest cracking loads. The addition of fibres to the top cover concrete in the FRC Specimens
improved the cracking strength by 8% and 16% in the banded and uniform specimens,
respectively. With fibres placed through the entire slab thickness, as in the FRS specimens, the
cracking load was increased by 17% and 21% in the banded and uniform specimens,
respectively, over the normal-strength concrete specimens.
The stiîfness of the specimens at full service load was a function of both the flexural
reinforcement distribution and the depth of fibre-reinforced concrete. At full service load, the
banded specimens showed a decrease in deflection of 21%, 12% and 13% compared to the
companion uniforrn specimens for the NSC, FRS and FRC series, respectively (see Fig.3.17).
Moe (1961) also found that concentration of the flexural reinforcement near the column
increased the stiffness of the load deflection response.
From Fig. 3.16 and Table 3.1, it can be seen that the FRS Series was the stiffest,
followed by the FRC Series, with the NSC Series being the Ieast stiff. Swamy et al. (1979),
Alexander and Sirnmonds (1992) and A. M. Sliaaban and H. Gesund (1994) also reported that
using fibre-reinforced concrete increased the stiffiiess of the slabs.
The flexural reinforcement yielded in the uniform specimens at lower loads than in the
banded specimens. In the banded specimens, the area of steel is better distributed to resist the
applied moments, resulting in Iower, more uniform strains in the slab reinforcement. The use of
a banded distribution rather than a uniforrn distribution of steel resulted in increases in load at
first yielding corresponding to 25% for the NSC Series, 40% for the FRS Series, and 7% for the
FRC Series. Moe (1961) and Hawkins et al. (1975) also reported increased loads at which first
yielding occurs wlien the reinforcement is banded.
The peak toads of the slab-coIurnn specirnens ranged from 306 kN for Specimen NSCU
to 438 kN for Specirnen FRSB. The banded specimens of each series reached a higher peak
Ioad. The increase was 4% for the FRS Series, 10% for the FRC Series, and 14% for the NSC
Series.
Elsner and Hognestad (1956) and Moe (1961) found that banding the reinforcement did
not increase the ultirnate capacity of their two-way slab specimens, while Whitney (1957) and
Alexander and Simmonds (1992) reported that banding increases the punching shear capacity of
slabs. Whitney (1957) and Alexander and Simrnonds (1992) believed that the slabs fkorn the
previous tests that had high percentages of reinforcing bars probably failed due to bond failure
and not shear. Therefore there is a limit to the amount of flexural reinforcement that can be
placed in the column region. Sherif and Dilger (1996) suggested that the shear strength of
concrete slabs should be a function of the cubed root of the flexurat reinforcement ratio.
The uItimate strength of the slab was influenced more by the addition of fibres than the
distribution of the reinforcing steeI. The addition of fibres to the concrete cover stightly
increased the load canying capacity of the FRC slab-column specirnens, with peak loads 23 kN
and 12 kN higher than the NSC series for the uniform and banded specimens, respectively. In
the FRS series, Sie placement fibres though the entire thickness of the slab, resulted in increases
in peak loads corresponding to 116 kN and 89 kN compared to the normal-strength concrete
specimens, for the uniforrn and banded specirnens, respectively.
Adebar et al. reported on research carried out over the last 25 years on the shear strength
of fibre-reinforced concrete. This body of research indicated that the shear stren-oth of two-way
slabs increases with increasing volumes of fibres, up to 0.7% fibres by volume.
The most visible improvement in the behaviour of the specimens due to the addition of
the fibres to the concrete was the mode of failure. The fibres provided the concrete with
additional tensiIe strength, and therefore increased the punching shear capacity. The NSC
specimens Iost about one-half of their Ioad carrying capacities when punching shear failure
occurred. The FRC specimens displayed similar characteristics after reaching their peak loads.
Specimen FRCB however, was able to increase its post-failure load canying capacity as the
deflection was increased. The FRS specimens dernonstrated considerably greater ductility ?han
the specimens fiorn the NSC Series and FRC Series. Specirnens FRSU and FRSB did not fail
suddenly, but instead showed a very ductile behaviour. The specimens displayed general
yielding, with a gradua1 decrease in the slope of the load-deflection curve until it was practically
horizontal. As the deflection was increased, the load applied to Specimen FRSB rernained
basically constant, while the Ioad dropped in Specimen FRSU. When the shear failure surface
was finaliy visible on the top surface of the slab, the tests were stopped.
Swamy et al. (1979) also obsewed a reduction in the suddenness of the failure, and an
increase in the residual Ioad, due to the use of fibre-reinforced concrete.
The addition of fibres as well as the banded distribution of the reinforcing bars increased
the size of the shear failure surface. The failure surface of Specirnen NSCU was at an angle of
approximately 45 degrees fiom the bottom slab surface and the column intersection. The failure
plane therefore came through the top slab surface at about a distance d fiom the coIurnn face.
Specimen NSCB had the failure plane exit the top slab surface about 250 mm fiom the face of
the column as the banded reinforcement forced the failure plane away from the column. The
specimens with fibres through the entire slab thickness had failure surfaces that extended to
approximately 500 mm fkom the column face. This was the perimeter of the region where the
fibre-reinforced concrete was placed. The surfacing of the failure plane for the fibre-reinforced
concrete cover (FRC) specimens occurred at the edge of the slab in the strong direction. The
steeI fibres in the concrete cover did not allow the failure plane to penetrate through the cover,
but instead resulted in the formation of horizontal cracks along the plane of the top mat of
reinforcement.
3.2.2 Strain Distribution of Reinforcing Steel
Figure 3-18 shows the strain distributions measured in the steel reinforcement at full
service load for the uniform and banded specimens. The reinforcement of the specimens with
the uniformly spaced steei distribution had higher strains near the coIumn than the reinforcing
bars in the banded specimens. Due to the two-way action in the slab, the applied moment in the
slab is a maximum at the column face. The specimens with unifonn steel distributions witl have
higher steel strains near the colurnn (see Fig. 3.18) due to the larger stifmess of this region. In
the banded specimens, the steel is more closely distributed according to the applied moments,
resulting in more uniform steel strains across the siab width.
Figure 3.18a shows the improved service-load behaviour of the specimens with a
uniform distribution of steel when fibres are added to the concrete. When comparing the
specimens of uniformty distributed flexuraI reinforcement, it is apparent that Specimen FRCU
had lower strains than Specimen NSCU. But the lowest steel strains were recorded in the fibre-
reinforced slab specimen (FRSU), The effect of the fibre-reinforced concrete on the strains in
the stee! reinforcement at fidi service load w u not as evident in the banded specimens. The
three banded specimens shown in Fig. 3.18b have very similar strain distributions despite the use
of strategicaIly placed fibre-reinforced concrete.
3.2.3 Maximum Crack Widths
Table 3.2 shows the maximum crack widths at fuII service load for the slab-column
specimens. The crack widths both inside and outside the "banded" region for al1 three of the
banded specimens at fulI service load were 0.35 k 0.05 mm. Hence it is concluded that the crack
widths in the banded specimens were not strongly influenced by the presence of fibres for total
loads up to and including the full service Ioad of 214 kN. The crack widths in the specimens
with uniformly distributed top reinforcement were very much affected by the presence of the
fibre-reinforced concrete (see Fig. 3.19). The fibre-reinforced concrete cover reduced the crack
widths by 0.20 mm in the banded region and 0.10 mm outside this region. In the specimens with
full-depth "puddled" fibre-reinforced concrete (FRS series) the crack widths were further
reduced by 0.15 mm across the entire slab surface (see Fig. 3.20). The maximum crack widths at
full service load for Specimen FRSU were half the width of the maximum crack widths of
Specimen NSCU outside the banded region, and 56% of the width in the banded region.
Swarny et al. (1979) also reported that the addition of steel fibres to the normal-strength
concrete transformed the unstable, uncontrolled tensile cracking into slower, controlled crack
growth.
Table 3.2 Maximum crack width at h l l service load for slab-colurnn specimens
Specimen
r FRCB 0.40 0.40
Max crack tvidth at full service load (mm)
1
The crack patterns for the slab-column specimens at full service load presented in Fig.
3.4, Fig. 3.8, and Fig 3.14 show how the banded specimens have more cracks in the "banded"
region, compared to the uniform specimens of the same series. Although there are more cracks
in the column vicinity of the banded specimens compared to the uniform specimens, the crack
widths were smaller and the average tensile strains on the surface of the slab around the colurnn
were always less for the banded specirnens (see Fig. 3.21). The average tensile strain on the
surface of the slab around the column versus total load for the uniform specimens are shown in
Fig. 3.22a, and for the banded specimens in Fig. 3.22b. The FRS specimens have dightly lower
average strains around the coiumn, but the curves are very similar for the different series of
specimens. These results show a similar trend to the maximum crack width values shown in
Table 3.2.
The steel fibres in the concrete rnatrix do not increase the load at first cracking strength,
but bridge the cracks that form and Iimit their growth as loading is increased. Hence it is
expected that slabs with fibres would have a greater durability than those without fibres.
NSCU
in "banded" region
0.80
outside "banded" region
0.50
3000 €y O
a) uniform specimens
b) banded specimens
Figure 3.18 Strains in top mat reinforcing bars at full service load
1 FRS-L
maximum crack width (mm)
a) within banded region 1.51 from column face
self weight
0.25 0.5 0.75 1 .O 1.25 1.5 maximum crack width (mm)
6) outside banded region 1.5h from column face
Figure 3.19' Load versus maximum crack width for uniform specimens
l FRS-B __________C__________________c______________L____________.__________c______________L____________.__________c______________L____________.__________c______________L____________.~--------------__________c______________L____________.
__--- _---- ,
full senrice load
banded region c-1 t'., - -. t::[3:!i .A . ~ 2 2 self weight w
0.25 0.5 0.75 1 .O 1.25 1.5 1 -75 maximum crack width (mm)
a) within banded region 1.5h from column face
full service load
banded reqion
self weight I O 0.25 0.5 0.75 1 .O 1.25 1.5 1.75 2.0
maximum crack width (mm)
b) outside banded region 1 S R from column face
Figure 3.20 Load versus maximum crack width for banded specimens
b) FRS Series
c) FRC Series
average tensile strain around colurnn, microstrain (pn)
average tensile strain around column, microstrain ( p ~ )
average tensile strain around column, microstrain (pm)
Figure 3.21 Load versus average tensile striain around column of sIab-column specimens
strain perirneter 1 i E j -J 1 O 2000 4000 6000 8000 10000 12000 14000 16000
average tensile strain around column, microstrain (pm)
a) uniform specimens
strain penrneter
---.J a; I+-Y
406 mm
O 2000 4000 6000 8000 10000 12000 14000 16000 average tensile strain around column, microstrain (pm)
6) banded specimens
Figure 3.22 Influence of fibre-reinforced concrete on the load versus average tensile strain around column
3.2.4 Comparison of Failure Loads to Code Predictions
Figure 3.23 compares the non-dimensionalised shear stresses at failure for the NSC
Series and the FRS Series. For the case of the nomal-strength concrete two-way slab specimens
both specimens resulted in shear stresses greater t h a . the nominal two-way shear strength of the
1995 AC1 Code and the 1994 CSA Standard (0 .334~ ' ) . This figure also shows the benefit of
concentrating the flexural reinforcernent in the column region. The presence of fibres increases
the punching shear resistance considerably. The increase above the code values is 36% for the
uniforrn distribution and 4 1% for the banded distribution.
- - 1995 AC[ Code
1994 CSA Standard
O o i
O 0-1 0.2 0.3 O -4 0.5 0.6 0.7
fibre % by volume
Figure 3.23 Comparison of shear strength to predicted strength
Chapter 4
Cornparison of Column Specimen Results
This section presents the observed experimental behaviour of the twelve column
specimens described in Cliapter 2.
Figures 4.1, 4.2 and 4.3 show the compressive load versus average column strain for the
NSC Series, FRS Series, and FRC Series, respectively. From these figures it may be concluded
that:
1) The control specimen, IabelIed C for eacli series, contained high-strength concrete over
its fiil1 height. These specimens al1 failed in a brittle manner displaying an immediate
drop in load to approximately one-third o f the peak load, after the peak load had been
reached.
2) The companion column specimens, with a ccsandwich" of normal-strength concrete
representing the slab, showed the Iowest strength of each series, with slightly more
ductility than the control specimens but with considerably lower strength.
3) The slab-colurnn specimens tested by applying an axial compressive load to the column
stubs above and below the slabs, sliowed the rnost ductile behaviour. The maximum
capacity of each of the slab-column specimens exceeded the companion colurnn with the
normal-strength concrete layer. The residual, post-peak strength of the slab-column
specimens \vas always greater than that of the control column and the companion column
specimen with the normal-strength concrete "sandwich".
Figure 4.4 shows the column specimens afler failure.
O 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
average column strain (mmlmrn)
Figure 4.1 Compressive load versus average colurnn strain for NSC Series
O 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 average column strain (mmlmrn)
Figure 4.2 Compressive load versus average column strain for FRS Series
t . . . , -= .-. C-FRGB
O 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0-040 average column strain (rnmlrnm)
Figure 4.3 Compressive load versus average column strain for FRC Series
a) Specirnen Ci
b) Specirnen C-NSC
Figure 4.4 CoIumn specimens at faifwe
Table 4.1 shows a summary of the observed experimental results from the column tests.
The f,' ,nvaIue is the effective strength of the concrete in the colurnn specimens calculated from
the recorded peak load values, subtracting the force in the vertical reinforcing bars, and dividing
by 0.85. In a11 cases the strains rneasured in the columns in the vertical bars indicated that these
would yield in compression. The effective concrete compressive strength of the slab and the
column are represented by f,' and f,-, respectively.
As shown in the table, the colurnns of the slab-column specimens were stronger than the
companion columns of the same series which had a normal-strength concrete "sandwich". The
companion columns did not have the additional confinement provided by the slab in the slab-
column specimens. The strength was further increased by concentrating the top bars around the
column in a banded distribution. The columns of the uniform slab-column specirnens were 24%,
37% and 27% stronger than the companion cotumns for the NSC Series, FRS Series and FRC
Series, respectively. The banded specimens were 9%, 17% and 6% stronger than the uniform
specimens in the NSC Series, FRS Series and FRC Series, respectively.
Table 4.1 Summary of experimental results for column specimens
C-NSCU 1 3008 1 0.0052 1 62.8 1 30.0 1 81.8
Column Specimen
Cl
CNSC
C-NSCB 1 3254 1 0.0051 1 68.6 1 30.0 1 81.8
. . - . -
C-FRSU 1 3 5 1 3 1 0.0042 1 74.8 - 1 4.3 1 89.5
Peak Load
(W 3850
2493
E,'
(mm/mm)
0.0023
0.0025
CFRC
C-FRCU
C-FRCB
f&rr
82.7
50.7
2908
361 1
3804
fdslab
0.0024
0.003 8
0.0043
f,,'column
(MPa)
60.5
77.1
81.6
80.7
30.0
80.7
80.7
3 5.5
35.5
35.5
83 -6
83.6
83 -6
The effectiveness of the columns to transmit the maximum possible load through the
weaker slab layer is evaluated by comparing the strengths of the slab-co!umn and cornpanion
specimens with the weaker slab zone to the control specimen within the sarne series. Table 4.2
shows the comparison of the measured effective concrete compressive strength of the specimens
with the effective concrete compressive strengths of the "sandwich" region, the high-strength
coIumn and the expected strength. The fierr is the effective concrete strength determined from the
experimental program and f,, is the expected effective strength frorn the Canadian Standard
(CSA 1994).
Table 4.2 Comparison of experimental and predicted results for colurnn specimens
I 1 - - - - - - - - - - - II C-NSCU 1 62.8 I 52.0 1 2.09 1 0.77 1 1.20 11
. . 1 C-NSCB 1 68.6 j 52.0 j 2.29 1 0.84 1 1.32 1
I l -- - - -- II C-FRSU 1 74.8 I 67.8 I 1.73 1 0.84 1 1.10 11
II C-FRSB 1 87.2 ; 67.8 1 2.01 1 0.97 / 1-29 11
The column Iabelled fkrr Ifci in Table 4.2 compares the effective concrete compressive
C3
CFRC
C-FRCU
C-FRCB
strength of the specimen to the effective compressive concrete strength of the stub column above
and below the slab. These values indicate the ratio of the maximum possible Ioad the column
1 I
91.2 I 83.6 I 1.09 I I
60.5 1 37.5 1 1.61 I I
77.1 1 56.0 2.06 I J
81.6 1 56.0 1 2.18
can transmit tiirough the "sandwich" region compared to the strength of the high-strength
concrete. The controt specimens obviously have a high ratio because they do not have a weaker
1 .O9
0.72
0.92
0.98
"sandwich" region of concrete. The companion specimens were able to reach 63%, 64% and
1.09
1.6 1
1.32
1 -40
72% of the capacity of the higli-strength stub colurnns above and below the weaker concrete
middle region. The columns of the slab-column specirnens were much more effective in
transmitting the load through the colurnn than the coIumns with the weaker slab concrete, but
without the presence of the slab, The slab-column specimens, with a uniform steel distribution,
carried 77%, 84%, and 92% of the capacity of their high-strength stub columns. The most
effective axial Ioad carrying specimens were the banded slab-colurnn specimens, that reached
84%, 97%, and 98% of the maximum possible loading of the column. The confining effect of
the fibre-reinforced concrete sIab and the closely spaced reinforcing bars around the coIurnn
irnproved the axial compressive capaciv of the sIab-column specimens so much that the
presence of the weaker "sandwich" region was alrnost undetectable. The normal-strength fibre-
reinforced concrete of the slab effectively had the sarne strength as the high-strength stub
columns above and below the slab.
The Iast coturnn of Table 4.2 compares the effective compressive concrete strength of
the specimens to the predicted compressive strengths for these columns fiom the Canadian
Standard (CSA 1994). The strength of the specimens surpassed the predicted strength in every
case except the control specirnen fiom the FRS Series. It is interesting to note that the slabs were
subjected to punching shear failure before loading the columns. The prediction is therefore a
safe estimate.
The slab concrete strengths are the same within each series, but are different between the
different series. To compare the results of the coIumn specimens between different series, the
effective strengths of the columns were non-dimensionalised by dividing the catculated effective
concrete strength by the effective concrete strength of the companion column of the same series
(see Table 4.3).
The columns of the normal-strength slab-colurnn specimens were 24% and 35% stronger
than the normal-strength concrete companion colurnn, for the uniform and banded specirnens,
respectively. The strength of the columns of the slab-column specimens in the FRS Series were
37% and 60% greater than the companion coIumn, for the uniform and banded specimens,
respect ively.
Table 4.3 Effect of fibre-reinforced concrete on axiaI compressive strength in slab-cotumn specimens
11 1 Banded 1 1.35 li
Uniforrn 1 / Banded
Uniform / / FRC / Buidcd
NSC Uniforrn 1 -24
Chapter 5
Conclusions
5.1 Two-Way Slab Specimens
The following conclusions were drawn fiom the results of the experirnental programme
on the two-way slab specimens:
1) Concentration of the top mat of flexural reinforcement (banded distribution) as required by
the 1994 CSA Standard results in a higher punching shear resistance, higher post cracking
stiffness, a more uniform distribution of strains in the top bars and smaller cracks at al1
levels of loading. The increase in punching shear resistance due to the banded distribution
of top reinforcement was 4% for the FRS Series, 10% for the FRC Series and 14% for the
NSC Series.
2) Providing "puddled" fibre-reinforced concrete, having 0.5% by volume of steel fibres, in
the slab around the column for the distance of at Ieast 500 mm fiom the column face
results in a sipificant improvement in the performance. This includes an increase in the
punching shear resistance, a significant increase in the ductility, greater post-cracking
stiffness and smaller crack widths. The strains in the top bars were also smaller due to the
fibre-reinforced concrete slab. The increase in punching shear resistance due to the
addition of a fibre-reinforced concrete slab was 38% and 26% for the uniform and banded
specimens, respectively.
3) Providing fibre-reinforced concrete cover results in an increase in punching shear
resistance, and better crack control. The crack widths of the unifom specirnens were 25%
and 20% smaller inside and outside the banded region, respectively, due to the fibre-
reinforced concrete cover.
4) The CSA code gives a conservative design for the punching shear of hvo-way slabs.
5.2 Column Specimens
The foliowing conclusions were drawn from the results of the experimental programme
on the column specimens:
The confining effects o f the slab around the column of the slab-column specimens
increased the axial compressive strength and ductiIity of the columns. The columns of the
slab-column specimens were 24%, 38%, and 27% stronger than the cornpanion colurnns
for the NSC Series, FRS Series, and FRC Series, respectively.
Concentrating the reinforcing bars near the column of the slab-column specimens resulted
in a higher effective strength of the slab concrete in the "sandwich" region. The banded
specimens were 9%, 17%, and 6% stronger than the uniform specimens in the NSC Series,
FRS Series and FRC Series, respectivefy.
The addition of fibre-reinforced concrete to the slab-column specimens increased the
strength and stifmess o f the specimens. The strength of the columns o f the slab-column
specimens in the FRS Series were 1 1% and 19% stronger than the columns of the NSC
Series for the uniform and the banded specimens, respectively.
The beneticial effects o f the fibre-reinforced concrete and the closely spaced reinforcing
bars around the column improved the axial compressive capacity of the slab-column
specimens to the extent that the presence o f the weaker "sandwich" region was almost
undetectable.
The CSA code gives a safe design for transmission of axial loads through sIab column
connections even when the sIabs were subjected to punching shear failures before loading
the columns.
Significance of Results
It has been demonstrated that using a banded distribution of flexural reinforcement
concentrated in the column resion, together with the use of fibre-reinforced concrete in the slab
around the column gives superior performance in the slab and superior performance for the axial
load response of the column. The addition of fibres to the "puddkd" concrete around the colurnn
also gave a simpler construction procedure without the need to contain the stiffer "puddled"
fibre-reinforced concrete.
References
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Alexander, S. D. B., Sirnmonds, H. S. 1988. "Shear-Moment Interaction of Slab-Colurnn Connections", Cam J. Civ. Eng. V. 15, pp.828-833
Alexander, S. D. B., Sirnmonds, S . H. 1992 "Punching Shear Tests of Concrete SIab-Column Joints Containing Fiber Reinforcement", AC1 Structural Journal, V. 89, No. 4, July-Aug, pp. 425-432.
Alexander, S. D. B., Simmonds, H. S. 1992. "Tests of Column-FIat Plate Connections", AC1 Structural Journal, V. 89, No. 5, Sept-Oct. pp. 495-502.
American Concrete Institute (AC[) 1973. Manual of Concrete Practice, Part 2, Detroit, Michigan.
American Concrete Institute (ACI) 1995. Building Code Requirements for Reinforced Concrete and Cornmentary (AC1 3 t 8-95 and AC1 3 18R-95). Detroit, Michigan, 369 pp.
Associate Cornmittee on the National Building Code O\IBC) 1995. National BuiIding Code of Canada 1995 (NBCC), National Research Council of Canada, Ottawa, 571 pp.
Bianchini, A. C., Woods, R. E., Kesler, C. E. 1960. "Effect of Floor Concrete Strength on Column Strength", AC1 Journal, Proceedings, V. 3 1, No. 1 1, pp. 1 149- 1 169.
British Standards Institution (BSI) 1985. Structural Use of Concrete (Standard BS-8 110). London, United Kingdom.
Canadian Portland Cernent Association (CPCA) 199 1. "Analysis and Design of Slab Systems" (ADOSS), Ottawa.
Canadian Standards Association (CSA) 1994, CSA A23.3-94, Design of Concrete Structures. CSA, Rexdale, Ont., 220 pp.
Comité Euro-International du Béton et Féderation International de la Précontrainte (CEB-FIP) 1990. Mode1 Code for Concrete Structures (MC90 mode1 code). Lausanne, Switzerland.
Elstner, R. C., Hognestad, E. 1956. "Shearing Strength of Reinforced Concrete Slabs", AC1 Journal Proceedings, V. 53, No. 1, July, pp. 29-58.
Gamble, W. L., Klinar, J. D. 1991. "Tests of High-Strength Concrete Columns with Intervening Floor Slabs", Journal of Structural Engineering, ASCE, V. 117, No. 5, pp. 1462-1476.
Gardner, N. J., Shao, X. 1996. "Punching Shear of Continuous Flat Reinforced Concrete Slabs", AC1 Structural Journal, V. 93, No. 2, Mar.-Apr., pp 2 18-228.
Graf, 0. 1933. "Tests of Reinforced Concrete Slabs under Concentrated Load Applied Near One Support", Deutscher Ausschuss fur Eisenbeton, Berlin, No. 73,28 pp. (in Geman)
Hawkins, N. M., Mitchell, D., Hanna, S. N. 1975. "The Effects of Shear Reinforcement on the Reversed Cyclic Loading Behaviour of Flat Plate Structures", Can. J. Civ. Eng. V. 2, pp.572-582
Hawkins, N. M., Mitchell, D. 1979. "Progressive Collapse of Flat PIate Structures", AC1 Structural Journal, 76(7), No. 7, July, pp. 775-808.
Moe, J. 196 1. "Shearïng Strength of Reinforced Concrete Slabs and Footings Under Concentrated Loads'', Portland Cernent Association Developrnent Department BuIIetin D47, Apr., 230
PP-
Morgan, D.R., Mindess, S., and Chen, L. 1995. "Testing and Speci&ing Toughness for Fiber Reinforced Concrete and Shotcrete", Proc. Second University-lndustry Workshop on Fiber Reinforced Concrete and Other Advanced Composites, Fiber Reinforced Concrete - Modem Developments, Eds. N. Banthia and S. Mindess, Toronto, pp. 29-50.
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Appendix A
Design of Test Specimens
This appendix describes the design of the interior region of the fiat plate structure described in Chapter 2. Figure 2.1 shows the structure, which has 4.75 m square panels. The slab is designed for a specified superirnposed dead load of 1.2 k ~ / m ~ and a specified Iive load of 4.8 kN/rn2. The specified 28-day compressive strength of the concrete is 30 MPa and the steel has a yidd stress of 400 MPa.
Note that a small column size (225 x 225 mm) was chosen to make the punching shear more criticaI.
The key steps in the design are given below:
a) Choice of Slab llickness (Clause 13.3.3)
Use h, = 150 mm.
b) Design for Shear for Slabs Wirhoui Beams (Clause 13.4)
Critical Shear Section (Clause 13 -4.3)
c) Mmrimum Shear Stress Resistance (Clause 1 3 -4.4)
Nominai Shear Stress Resistance, V,,
Factored Shear Stress Resistance, V,
d) Sheur Stress (Clause 13.4.5)
Factored Shear Stress, Vf,
where: T.A. is the tributary area, calculated as:
T.A.= (4.75 - 0.225 - 0.1 1 0 ) ~ = 195 mm2
The self weight of the slab, S. W., is:
superimposed dead load = 1.2 kPa Iive Ioad = 4.8 kPa
e ) Determinafion of factored moments
The detemination of the total negative factored moment was done with the computer programme ADOSS:
Matetai) = 94.0 kNm
Factored Moments in Column Strips (Clause 13.12.2)
Multiply by factor within 0.6 and 1 .O for negative moment at interior column
Choose 0.75, therefore: Mmw1 (75%) = 70.5 kNm, for column strip, and,
Mx,,, (25%) = 23.5 kNm, for middle strip.
f) Facored Moment Resistance (Clause 8.4)
for column strip, where M, = Mr = 70.5 kNm, gives As(rquird) = 2254.3 mm'
Try As = 2800 mm2 (14-No.15 bars)
2 for middle strip, where M, = Mr = 23 -5 kNm, gives As(iquiKd) = 696.4 mm
Try A, = 800 mm2 (4-No. 15 bars)
minimum flexural steel, As(minl = (200) x 2500/450 = 11 12 mm2
Therefore use A, = 1200 mm2 for middle strip (6-No. 15 bars)
g ) Reinforcernent for Interior Columns (Clause 13.12.2.1)
At least one-third of the reinforcement for total factored negative moment at interior columns shall be located in a band with a width extending a distance 1 Sh, fkom the side faces of the column.
Band width, b.w. is: b.w.=3.h+c
=3.150+225 = 675 mm
One-third of the total steel must be in the band width, that is:
Use As = 1600 mm2 @-No. 15 bars)
Spacing, s = 675/8 = 84.4 mm
h) Curtailment ofrieinforcernent (Clause 13.12.5.1)
Without drop panels (fiom Figure 13-1)
I 1 into slab from column face: I
top bars: minimum % of As
maximum length available in specimen is OS(2300-225) = 1037.5 mm therefore weld steel plates to the end of half of the bars.
minimum distance bar must extend
remainder
i) Minimum Reinforcernent for Structural Inlegriiy (Clause 13.1 1.5)
0.201, = 0.20(4525) = 905 mm
The surnmation of the area of bottorn reinforcernent connecting the slab to the column on al1 faces of the periphery of the column shall be:
where: V,, = shear transmitted to column due to specified loads, but not less than the shear corresponding to twice the self-weight of the slab.
ASb one face = 1 170/4 = 292.5 mm
Therefore use 3-No. 10 bars in each direction.
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