Shear strength of stud connectors in lightweight and normal weight concrete, AISC Eng'g Jr., April

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Lehigh University
Lehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1971
Shear strength of stud connectors in lightweight
and normal weight concrete, AISC Eng'g Jr., April
1971 (71-10)
J. G. Ollgaard
R. G. Slutter
J. W. Fisher
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Recommended Citation
Ollgaard, J. G.; Slutter, R. G.; and Fisher, J. W., "Shear strength of stud connectors in lightweight and normal weight concrete, AISC
Eng'g Jr., April 1971 (71-10)" (1971).Fritz Laboratory Reports.Paper 2010.
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Shear Strength of Stud
Connectors in Lightweight
and Normal-Weight
Concrete
JORGEN G. OLLGA,ARD, ROGER G. SLUTTER
and JOHN W •. FISHER
REPRINTED FROM
I C ENGINEERING JOURNAL
Published by American I stitut of Steel Construction, 101 Park Ave., New York, N. Y. 10017
Shear Strength of Stud Connectors in Lightweight
and Normal-Weight Concrete
JORGEN G. OLLGAARD, ROGER G; SLUITER AND JOHN W. FISHER
STEEL-CONCRETE composite construction using normal tors at University of Missouri1•2•4 examined various
weight concrete has been used since early in the 1920's. sizes of stud shear connectors, the effect of haunches,
Substantial use of composite construction began mainly and the behavior of beams. These studies showed that
for bridge structures in the 1950's as a result of the work the strength of a shear connector embedded in light
done by Viest.16-18 Its primary growth in building weight concrete was 5 to 40% lower than the strength
construction during the last decade was a result of the of connectors embedded in normal-weight concrete.
simplified design provisions introduced into the 1961 Considerable variation was apparent in the pushout
AISC Specification. The development of these provisions data because of variation in specimen geometry, slab
were based on studies reported by Slutter and Dris reinforcement, and experimental techniques. Also, the
coll. 6•11 tensile strength of the stud connectors varied (from 62
The type of shear connectors has changed sub to 82 ksi) and in many instances was unknown. Because
stantially during the past 20 years. Bridge construction of these variations and the limited data, it was not
made extensive use of spiral connectors in the early possible to provide rational design recommendations.
SO's. These were replaced by the flexible channel and The purpose of this investigation was to determine
stud connectors. Today, headed studs are used exten the strength and behavior of connectors embedded in
sively for both bridge and building construction. The both normal-weight and lightweight concretes so that
first studies on stud shear connectors were undertaken design recommendations could be made. A series of
by Viest, who tested full scale pushout specimens with pushout specimens were constructed and tested to
various sizes and spacings of the studs.l6 Later studies assist with the evaluation. The tests with normal-weight
on bent and headed studs were initiated at Lehigh concrete provided directly comparable data under the
University by Thurlimann.15 A series of beam and same controlled conditions. The ultimate loads found
pushout tests were reported by Slutter and Driscoll, from tests of pushout specimens provide a lower bound
who developed a functional relationship between the to the strength of connectors in beams. 5 ·
shear connector strength and the concrete compressive A companion study on the behavior of composite
strength. 6•11 The mathematical model was comparable beams with lightweight concrete slabs was undertaken
to the useful capacity proposed earlier by ViestP at the University of Missouri. 8
Since 1961, several investigations of composite
beams using lightweight concretes have been made.
TEST SPECIMENS, PROGRAM,
Studies at the University of Colorado3•14 and at Lehigh AND PROCEDURES
University6•12•13 evaluated the strength of stud con
The test program was developed after the controlled
nectors in a number of different types of lightweight
variables were selected. The variables considered in
aggregate concretes using pushout specimens. Investiga-
cluded the basic material characteristics as determined
by standard control tests (i.e., concrete compressive
JorRgeesne aGrc. hO Allsgsaisatradn its, DFersitizg nE Enngginineeereirn, gH Lelalberourpa,t oDrye, nmLeahrikg;h f oUrmnievrelyr , strength f' c, split tensile strength f' sp, modulus of
sity, Bethlehem, Pa. elasticity Ec , and density w), the stud diameter,
Roger G. Stutter is Assoc. Professor of Civil Engineering, Fritz Engi type of aggregate, and number of connectors per slab.
neering Laboratory, Lehigh University, Bethlehem, Pa. The stud connector tensile strength, slab reinforcement,
John W. Fisher is Professor of Civil Engineering, Fritz Engineering
and geometry were considered in the experiment design
Laboratory, Lehigh University, Bethlehem, Pa.
as one-level factors.
55
APRIL/1971
Table 1. Pushout Results and Average Concrete Properties
Average Concrete Properties
Individual Specimen Average Connector
Aggregate Ultimate Load, kips Compressive Tensile Density Concrete
Strength Strength Modulus
w(pcf)
Spec. No.1 Spec. No.2 Spec. No.3 /'.(ksi) f',P(ksi) E.(ksi)
A 29.3 32.5 30.6 5.08 0.51 148.1 3740
LA* 24.5 26.5 24.7 3.64 0.43 147.6 3510
SA** 19.5 20.8 19.9 4.01 0.43 147.4 3580
B 27.4 25.4 25.4 4.78 0.47 140.5 3180
LB* 18.3 18.1 17.3 2.67 0.32 138.6 2190
SB** 18.2 16.9 18.8 4.03 0.46 142.6 3170
2Bt 26.1 25.5 25.0 4.78 0.47 140.5 3180
C-t 19.9 21.3 21.0 4.69 0.24 89.1 1510
c
21.6 21.5 22.2 4.28 0.35 108.2 2060
D-t 24.1 23.0 22.7 4.72 0.32 99.2 2430
D 21.6 23.3 24.4 4.92 0.36 113.4 2530
E-t 19.6 19.2 17.8 3.60 0.30 97.7 1840
E 23.1 22.5 21.6 4.30 0.37 111.1 2190
LE* 18.7 19.5 19.7 3.22 0.32 111.4 1880
SE** 15.7 15.7 17.0 4.00 0.33 112.3 2060
2Et 21.2 23.1 22.7 4.40 0.39 111.1 2210
* L indicates series with lower compressive strength.
** S indicates series with ~~-in. connectors; all other tests on %-in. connectors.
t 2 indicates series with 2 connectors per slab.
t Specimens with lightweight aggregate and fines.
Table 2. Description of Coarse Lightweight Aggregates
Description of Specimens-Most of the specimens had
four connectors embedded in each slab, as illustrated Material Expanded Expanded Expanded
Shale (C) Shale (D) Slate (E)
in Fig. 1. However, several specimens with a single row
of two studs, located at mid-height of the slabs, were also Color Brown Gray to Black Gray to Black
tested. All specimens had the same slab reinforcement.
Max. Size 7'2-in. %-in. %-in.
The specimens were cast with the beam vertical
Shape Rounded Cubical to Cubical to
and in an inverted position, to assure that voids would
irregular irregular
not form under the studs on their bearing side. A com
mon form was fabricated so that three specimens could Production Meth. Rotary kiln Rotary kiln Rotary kiln
be cast simultaneously. Loose Unit Wt. 35 pcf 47 pcf 45 pcf
(Approx.)
Test Program-Forty-eight pushout specimens were
tested during this investigation. The program consisted Control Tests-The characteristics of the concrete
of groups of two slab specimens with three specimens slab in which the connectors were embedded were
in each group (see Table 1), to provide replication and determined by control tests. Standard 6 in. x 12 in.
permit the variability to be evaluated. control cylinders were cast along with the pushout
The normal-weight concrete was manufactured from specimens to assist in determining the characteristics of
two types of coarse aggregate. Type A was a crushed the concrete slabs. Sixteen cylinders were cast for each
limestone and Type B was a natural river gravel. group of specimens. The cylinders were moist cured for
Three different types of lightweight aggregates were 5 to 7 days, along with the pushout specimens. They
used (Types C, D, and E). Each type of lightweight were then stripped and air cured until the day of testing,
aggregate was combined with either lightweight fine along with the pushout specimens.
aggregate or with natural sand. A description of the The modulus of elasticity was obtained during the
lightweight coarse aggregate is given in Table 2. compression test of the cylinders. An averaging com
The experiment design considered the stud diameter, pressometer with a 6-in. gage length was mounted on
number of stud connectors per slab, type of concrete, the cylinder. The dial gage was read at each 10 kip
and the concrete properties. The stud tensile strength load increment. The modulus of elasticity was cal
and type specimen were considered as one-level factors. culated from the difference in readings at 10 and 50 kips.
This permitted the direct evaluation of the various Often the modulus of elasticity is taken as the tangent
types of aggregates and concrete properties on the modulus at zero load. Obviously, this would result in
connector shear strength. slightly higher values than the secant modulus deter-
56
AISC ENGINEERING JOURNAL
;-- f--
;~-=-, ,-=-.:::::\
i /"
CD I ~
~:e:1 ~:
r 3;4" Stud, H , 3"
~ ~ 1 ~
# 4 Bars
Fig. 7. Details of pushout specimen. ~~: f
..:. : I :
·- B I I : : B # 5 Bars
ol lo ~ I"
'- iD=I ~I
'" " II II II II I 6" I slt4" I 6" I
_.L_r ~--J.-----,._(____j_ . : 1' -a'14" : .
SECTION B-B
N
mined from the deformations at 10 and 50 kips. The there was no sudden failure evident. After further de
concrete tensile strength was obtained from split cylinder formation accompanied by a decrease in load, failure
tests, and the density of the concrete was determined was evidenced by a shearing off of the stud connectors
from the weight and volume of the cylinders. or by failure in the concrete slab.
All stud shear connectors were provided from the The average load-slip curves for a group of three
same lot. The physical properties of the connectors were specimens are compared in Fig. 2b for normal-weight
determined from standard tension tests. The average and lightweight concrete pushout tests. It is apparent
ultimate strength was 70.9 ksi for the %-in. studs and that the average curves are nearly the same for each
70.2 ksi for the %-in. studs. specimen group. Two specimens from each group were
unloaded after reaching an average load of 10 kips per
Pushout Tests-The pushout specimens were tested in a connector. Subsequent reloading did not change the
300-kip capacity hydraulic testing machine. The speci shape of the overall load-slip relationship (Fig. 2b).
mens were placed on sheets of 0.5-in. homosote in
order to obtain a uniform load distribution on the bear
ing surface of the slabs.
Testing was usually conducted on the 28th day
after casting. Loads were in 10-kip incremen.ts, main
tained constant at each load level while the vertical Light Weight
slips between the slab and beam were measured.
One specimen from each group was loaded to
ultimate load without unloading. The remaining two
pushout specimens were loaded to approximately the
working load level for the connectors, then unloaded, a(;;/:.): 0
and reloaded to their ultimate load.
0 (a) Normal vs. light weight concrete load -slip curves
a::
0
1-
TEST RESULTS u
w
z
The average properties of the cylinders that correspond z
0
to the pushout specimen are listed in Table 1. This u
a::
includes the concrete compressive strength, j' c , the aw. o BB +I
split tensile strength, f'sp, the modulus of elasticity, ;:;,. BB +2
0 o BB +3
Ec, and the concrete density, w. g<I
All lightweight concrete mixes, except C, satisfied the
requirements of ASTM C330. The C-mix was com
posed of lightweight coarse and fine aggregates and did
not yield a satisfactory level of split tensile strength as
proportioned and used. ASTM C330 requires an average
split tensile strength of 290 psi for structural lightweight
concrete. The C-concrete provided a strength of 244 psi.
0 0.02 0.04 0.06 0.08 0.10
Typical load-slip curves for a normal weight and a AVERAGE SLIP, IN.
lightweight concrete specimen with two slabs are shown (b) Replicate load-slip curves
in Fig. 2a. Both types of concrete exhibited substantial
inelastic deformation before failure. At ultimate load, Fig. 2. Typical Load-Slip curves.
57
APRIL/1971
The ultimate load per shear connector for each push shows the four studs that were embedded in one slab
out specimen is listed in Table 1. The ultimate loads did which sheared off. The other slab was still connected
not vary much between the replicate specimens of a to the steel beam. The photograph also indicates that
test group. Very seldom did the standard deviation the studs did not shear off at the same slip levels since
exceed 1 kip. It is apparent that the connector strengths the gaps between the studs and the slab are not the same
were decreased significantly (from 15 to 25%) when size indicating that different amounts of plastic deforma
the connectors were embedded in lightweight concrete. tion occurred.
The sanded lightweight concretes provided slightly A typical specimen which exhibited concrete failure
higher shear strengths than did the all lightweight con is shown in Fig. 3b. The connectors were pulled out
crete mixes. of the slab together with a wedge of concrete. Both
In this study the tensile strengths of all the %-in. normal-weight and lightweight concrete slabs had
and %-in. connectors were the same (approximately wedges of similar shape pulled out of the slab. The
70.7 ksi). Hence, the results of the tests on different cracks in the slabs were more numerous and larger in
diameter connectors provided direct information on the lightweight concrete than in the normal-weight concrete
influence of connector diameter. Stud connectors of specimens.
both sizes were embedded in the two normal-weight The pushout specimens with only one pair of con
concretes and one lightweight concrete. The results nectors in each slab all failed by shearing off the studs.
show that the connector shear strength is nearly propor One reason for this observation could be that the dis
tional to the cross-sectional area of the stud. tance from the studs to the end of the slab was greater
and the slab force smaller. Also, since the reinforcement
Failure Modes-Most specimens were subjected to in the slab was identical to that used in the other speci
additional loading and deformation after the ultimate mens, more reinforcement would be available per con
load was reached. Often, slab cracks were visible just nector. However, the ultimate shear strength per con
after ultimate load was reached. The loading was nector did not increase for this type of specimen.
normally continued until one or both slabs separated The observed mode of failure after slab separation
from the steel beam. This occurred at large slips. There was not applicable to the ultimate load. In order to
were basically two separation modes observed. In one, evaluate the failure mode and determine the state of
the studs were sheared off the steel beam and remained deformation and type of failure, two specimens were
embedded in the slab after unloading occurred. In the sawed longitudinally through the slab and connectors.
other, the concrete failed in the region of the shear One specimen had a normal-weight concrete slab and
connectors. In many tests both types of failures were the second had a lightweight concrete slab. Loading
observed in the same specimen. was discontinued just after the ultimate loads were
Specimen A2, which had normal-weight concrete reached in these two specimens and unloading started
slabs, exhibited the typical stud shear failure. Figure 3a to occur.
(a) Studs sheared off. (b) Studs and concrete failure.
Fig. 3. Typical failure VIews after slab separation.
58
AISC ENGINEERING JOURNAL
The slabs were cut using a diamond disk saw. The It is also apparent that the concrete in front of the studs
cuts were placed so one side of the disk saw would is crushed.
match the center line of the studs. To avoid cutting The observed behavior at ultimate load confirmed
through the entire length of the steel beam flange, the that the concrete is the controlling medium. For this
flange was burned off so that only two small plates reason, variation in the tensile strength of the shear
remained. The cross section of the sawed test specimens connector would not be as critical a parameter as is
are shown in Fig. 4. sometimes believed. It also appears reasonable to
The crack pattern in the concrete slabs is very similar assume that smaller diameter connectors would be more
for both specimens. The cracks near the head of the dependent on the stud tensile strength, since the con
studs are different for the upper and lower connectors. crete forces would not be as great.
At the upper studs, the crack is nearly vertical to the
free end. The crack at the lower stud propagated toward ANALYSIS OF RESULTS
the surface of the steel beam at about a 45° angle. In order to compare the ultimate loads from all the
This could result in a lower ultimate strength for the specimens, including different connector sizes, the
upper pair of studs. The specimens containing only one average shear strength ( Q,J A,) was used. An examination
row of two connectors appeared to have crack patterns of the data obtained in this study indicated that the
similar to the lower pair of studs, because the distance average shear strength was proportional to the cross
to the free end was greater. Since the ultimate loads per sectional area of the studs for specimens having compar
connector were the same for one or two pairs of con able concrete properties; for example, series LA vs. SA,
nectors, the connector shear strength for both the upper series B vs. SB and series C vs. SE. This observation was
and lower studs was about the same. also confirmed by statistical tests which indicated that
The deformed shape of the studs was different in the the mean strengths ( Q,J A,) of two of the three combina
normal-weight and lightweight concrete specimens, as is tions were not significantly different. Earlier studies
apparent in Fig. 4. In the normal-weight concrete, also considered the average shear strength.U The %-in.
greater restraint of the stud is apparent from the curva connectors used in this study were all furnished from the
ture (see Fig. 4c). In the lightweight concrete slab the same lot and had an average tensile strength of 70.9 ksi.
stud was nearly straight (see Fig. 4d). In both slabs the The %-in. connectors were also furnished from one lot
studs were rotated through a large angle at the weld. and had about the same tensile strength (70.2 ksi).
(a) Normal weight concrete specimen LAT. (b) Lightweight concrete specimen LE2.
(c) Detail of connector and concrete (LA1). (d) Detail of connector and concrete (LE2).
Fig. 4. Sawed sections of lightweight and rwrmal weight slabs and connectors.
59
.... .
• .. •
.. ..
•
••
t•o
I~
oo
~140
'0C IQo oo 0
Ou Ou
As Stud Concrete As Stud Concrete
(KSI) Diameter Light- Normal (KSI) Diameter Light- Normal
(in.) Weight We..ig ht (in.) Weight We..ig ht
5/8 I:J. 5/8 I:J.
3/4 0 • 3/4 0 •
0 1.0 2.0 0 0.2 0.4
R; (fi<'S'I) f~p , KSI
Fig. 5. Connector strength as a function of concrete compressive Fig. 6. Connector strength as a function of concrete tensile strength.
strength.
Influence of Concrete Properties-Since the material Figure 6 compares the average shear strength of the
characteristics of the concrete were carefully determined stud connectors with the split tensile strength of the
throughout this study, it was desirable to determine concrete. No trends are apparent for the lightweight
whether or not the connector strength and the measured aggregate concretes. The normal-weight concrete speci
concrete and stud shear connector properties could be mens do indicate a decrease in connector shear strength
correlated. The properties of concrete considered in with a decrease in split tensile strength. Taken together,
cluded the compressive strength, the split tensile strength, all data provide a trend of decreasing shear strength
the modulus of elasticity, and the unit weight. with a decrease in tensile strength. The variability of
Earlier studies by Slutter and Driscoll11 had rel~ted the test data islarge.
the connector shear strength to the compressive strength Figure 7 compares the connector shear strength as a
of normal-weight concrete. The relationship suggested function of the concrete density. The density was deter
. by Viest17 for useful capacity was modified and used. mined from the concrete control cylinders. The weight
This resulted in the relationship of concrete varied from 89 to 148 pcf. Although there is
no trend within the various types of concrete, the overall
Qu = 37A5A. vj'; (kips) (1)
tendency, is, again, a decreasing shear connector strength
where As is the nominal area of the stud shear connector, with a decrease in concrete density.
in in.\ and j' c is the compressive strength of the con The relationship between the shear strength and the
crete, in ksi. measured concrete modulus of elasticity is summarized
The results of this study are plotted as a function of in Fig. 8. Good correlation is evident for both tne
the square root of the compressive strength of concrete normal-weight and lightweight concrete data. Since the
in Fig. 5 to ascertain whether or not this relationship concrete modulus of elasticity was in reasonable agree
was applicable to this study. It is visually apparent ment with the value suggested by ACI, the compressive
that the relationship is not in agreement with the results strength and density of concrete could also be used to
of this study and does not account for the difference determine the modulus and provide a comparable
between normal-weight and lightweight concrete. relationship.
Equation (1) was based on limited data from beams
Connector Shear Strength and Concrete Properties
and pushoff tests. 5•11 The expression was only intended
In order to obtain a mathematical relationship between
to be valid for concrete strengths up to 4 ksi. It was
the ultimate shear strength of a stud connector and the
noted that the beam test results yielded higher values,
material properties of the concrete, multiple regression
because of friction and redistribution of the connector
analyses (least squares fit) were made. All 48 two-slab
forces. In addition, the data was taken from several
pushout specimens were used. The shear strength
sources and experimental techniques as well as other
(QuiA.) was used as the dependent variable, and the
uncontrolled variables all contributed to the higher
measured concrete properties were considered as in
values predicted by Eq. (1).
dependent variables.
A study of the test data does indicate a decrease in
A general exponential model given by Eq. (2),
connector strength when the concrete strength de
which considered all concrete properties, was initially
creases substantially. However, no definite trend is
selected.
apparent for the concrete strengths between 3.5 and 5.0
ksi for either normal-weight or lightweight concrete. (2)
60
AISC ENGINEERING JOURNAL
• •
·. J .l
t
?It • •
4,0 ...
6> 0 0 0
6§
0
0 I
Ou Ou
As Stud Concrete As Stud Concrete
(KSI) Diameter Light- Normal (KSI) Diameter Light- Normal
(in.) Weight Weight (in.) Weight Weight
...
5/8 "' 5/8 "' "
3/4 0 • 3/4 0 •
0 0
DENSITY , W, PCF CONCRETE MODULUS, Ec , KSI
Fig. 7. Connector strength as a function of concrete density. Fig. 8. Connector strength as a function of Modulus of Elasticity of
concrete.
In order to obtain linear equations for the regression
analysis, the model was linearized by making a log
arithmic transformation. Table 3. Results of Regression Analyses Using Logarithmic
Results from regression analyses, using all possible Transformations
combinations of the four concrete properties as in
dependent variables, are summarized in Table 3. The
Coeffi-
results are listed in order of fit. The largest coefficient Obtained Exponents cient of Model
of correlation was obtained with Model 1, which con
Corre- Num-
sidered all variables. However, the first four models pro a b c d lation ber
vided about the same fit. Models 3 and 4, which ignored·
0.435 -0.229 0.395 0.306 0.90 1
the split tensile strength, f' sp , provided nearly identical 0.325 -0.148 0.527 - 0.89 2
values of the coefficient of correlation. It is also apparent 0.334 - 0.385 0.092 0.89 3
that including the concrete density had a negligible 0.304 - 0.439 - 0.89 4
0.640 -0.211 - 0.887 0.87 5
effect of the correlation coefficient, since Model 4
0.542 - - 0.675 0.86 6
yielded about the same correlation as Model3. - - 0.706 -0.413 0.85 7
When only two variables were considered, as with - 0.019 0.698 -0.418 0.85 8
Models 4 and 6, the combination of compressive strength - -0.041 0.509 - 0.83 9
and modulus of elasticity provided a better fit than the - - 0.484 - 0.83 10
combination of compressive strength and density. The 0.301 0.470 - - 0.75 11
- 0.389 - 0.244 0.70 12
test data are compared with Model 4 in Fig. 9a. It is - 0.551 - - 0.68 13
apparent that the compressive strength and modulus - - - 0.612 0.64 14
of elasticity of concrete provide a reasonable estimate 0.469 - - - 0.50 15
of the ultimate strength of stud shear connectors em
bedded in both normal- and lightweight concrete.
•
Ou Ou
As Stud Concrete As Stud Concrete
(KSI) Diameter Light- Normal (KSI) Diameter Light- Normal
(in.) Weight Weight (in.) Weight Weight
5/8 ... 5/8 "' "
•
0
I~ 0.3 Eg.44 ~,KSI
(a) Correlation with model 4 (b) Effect of rounding the exponents
Fig. 9. Comparison of connector strength with concrete strength and Modulus of Elasticity.
61
APRIL/1971
.
. .......
.,..
Effect of Rounding Off Exponents-Since it is desir .. ...
.. ·--
able to use more convenient exponents, analyses were 'v,~.·~l- •:- -...
..v Jar~:-
made to determine the effect of rounding the exponents
v~~
obtained for Models 4 and 6. Several sets of exponents .-..
were examined for each model. Rounding the exponents ~~~0
decreased the coefficient of correlation by less than 1. 7%. Ou ~ o Stud Concrete
Hence, the exponents can be rounded off without signifi As Diameter Light- Normal
(KSI) (in.) Weight We..ig ht
cantly affecting the overall fit to the test data. 20 1/2 v •
The test data are compared with the modified 351/84 A0 ••·
Model 4 in Fig. 9b. The dashed line is the least squares 718 0 •
I
fit to the test data when both exponents were rounded
40 60
to 0.5. The solid line was determined by forcing the
model to conform to the origin. It is apparent that the fit ~~ 0.3 E2"44
to the data is not appreciably affected when the intercept (a) Correlation with model 4
is ignored.
As noted earlier, the modulus of elasticity for the
concrete can be determined from the concrete com 60
pressive strength and density by use of the ACI formula.
Hence Model 6, which includes concrete compressive
strength and density, can be transformed into Model 4,
Concrete
which considers compressive strength and the modulus Ou Stud
As Diameter Light- Normal
of elasticity of concrete. For design purposes, Eq. (3) (in.) Weight We.i.g ht
(KSI)
provides a reasonable estimate for both Models 4 and 6 1/2 v •
5/8 A
3/4 0 ••
(3) 7/8 0 •
I
This relationship provides a good estimate of the ultimate 0 30 60 90
strength of shear connectors embedded in both normal ~,KSI
weight and lightweight concrete slabs. Equation (3) (b) Correlation with equation 3
expresses the shear connector strength as a function
Fig. 10. Comparison of earlier studies with Model 4 and Equation 3.
of the stud connector area and concrete properties.
The influence of the type of aggregate is reflected in the
modulus of elasticity. vestigations of specimens with reinforced slabs. When
the slabs were reinforced, the ultimate shear strength was
Comparison with Earlier Studies-Test data are substantially higher than for larger studs. These speci
available from a number of investigations that were mens were not considered due to their small scale.
made prior to this study. Driscoll and Slutter5 observed Other tests were also ignored when the welds were
that the height-to-diameter ratio (H/d) for studs em bad or the loading eccentric. The moduli of elasticity
bedded in normal-weight concrete should be equal to was not reported in a number of studies. For such tests,
or larger than 4 if the full capacity of the connector is the moduli were estimated from the compressive strength
to be developed. Specimens which did not satisfy this and the density of the concrete using the ACI formula.
requirement were not considered. The test data from other investigations2•4·6-9•12-14,16
Only specimens which had one or two connectors are compared with Model 4 and Eq. (3) in Fig. 10.
per row were considered, since increasing the number It is apparent that both Model 4 and Eq. (3) are in
of connectors has been shown to influence the shear reasonable agreement with the test data, although
strength per stud when the slab width and reinforce the scatter is greater for the test results from other
ment are not changed.16 investigations. The mean regression line for all test
A number of haunched specimens were tested at the data was not appreciably different from the mean rela
University of Missouri.2 Shear strength per connector for tionship developed from this study. The coefficient of
this type of specimen was lower than other solid slab correlation was decreased 18% to 0.72 and the standard
· specimens. They are not included in the comparison. error of estimate increased 90% to 8.46 ksi.
Investigators at the University of Sydney10 examined An examination of Fig. 10 also suggests that an
small scale lightweight concrete .specimens with %-in. upper bound to the connector strength is approached
Vj'
studs. Most of the concrete slabs were not reinforced. when cEc ,...._, 130, as the test data tends to plot
The shear strength ( Qu ! A for the specimens without along a horizontal line. This corresponds to a value of
8)
reinforcement were in the range of data from other in- Qui A 65 ksi. This appears reasonable and is probably
8 ,...._,
62
AISC ENGINEERING JOURNAL