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FRITZ ENGINEERINGLABORATORY LIBRARY
Thirteenth National Engineering Conference of AISCat Minneapolis, Minn., May 11, 1961
RESEARCH ON COMPOSITE DESIGN AT LEHIGH UNIVERSITY
by
Roger G. Slutter
George C. Driscoll, Jr.
In a structure consisting of a concrete slab supported
by steel beams, the compressive strength of the concrete slab
may-be used to advantage as a cover plate to increase the
load carrying capacity of the steel members. By providing
suitable shear connectors between slab and steel beam, the
two can be made to ac~ together as a unit. Shear connectors
which may be used'for this purpose are channels, angles, zees,
spir~ls and welded studs.
Early study of composite steel and concrete members was
carried out in connection with ~ridge, constr,uction. Through
observations of bridges in service and through research pro
grams, design criteria for this type of construction devel
oped. An elastic theory of des.ign evolved from this work
and has been widely 'applied using the AASHO Specifications5
as a guide. However, it has long been recognized that since
these specifications are extremely conservative, it is
possible to use more"liberal specifications for bUilding
members' subjected to static loading.
-2
The use of composite construction in buildings can
result in (1) more economical use of stee1 9 (2) savings in
depths of members 9 and (3) stiffer floor systems as deter
mined by live load deflections. The familiar elastic design
approach has been carried forward into building design and
serves largely as the basis for the recently published ASCE
ACI Recommendations for Oomposite Construction. 6
The presenttrenq toward plastic design in steel
structures and ultimate, strength design in concrete struc
tures challenges the wisdom of considering composite'design
only from the point of view of elastic concepts. ,Further
more 9 it has been shown by extensive investigations that
higher allowable loads than now permitted can safely be
carried by composite members because of the plastic action
beyond first yielding of the steel member. This suggests
that the availability of a plastic design specification
would result in a more rational as well as more economical
use of composite construction in buildings.
As in the application of elastic design concepts to
other structures, their application in composite construc
tion has resulted in designs which are not of uniform strength.
This fact is at least as important in composite design as it
is in steel design and concrete design. Elastic considerations
have resulted in undue emphasis on the problems of shrinkage
. and creep in the concrete. The strict application of elastic
-3
theory has led to requiring variable spacing of shearconnec
tors. Recent studies from the point of view of plastic
design, have shown that all of these consideration are
really unimportant.
APPLICATION OF PLASTIC DESIGN CONCEPTS
A plastic design approach presents a more logical basis
for design and has the additional advantage that .it is easier
to handle in the design office. Investigations of the feasi
bility of the plastic design of composite members have-been
the SUbject of research at Lehigh University during the p~st
three years. Many of the problems have been solved and
others are still under investigation. Sufficient progress
has been made so that specifications can be written incor-
porating a plastic design procedure.
Since composite construction in place of non-composite
construction riormally results in a ~eduction in size of the....
steel beams by one or more sizes J a vital question, which is
fundamental to a p+astic analysis J is the degree of inter
action between slab and beam J for loads all the way up to
ultimate. Any beam with intermittent shear connectors will
exhibit some degree of incomplete interaction. Adequate
theory covering the problem of incomplete interaction is
lacking and we must therefore show experimentally that the
degree of incomplete interaction is not serious for a
properly designed beam. For the present, complete inter
action will be assumed and test results will be compared with
this assumption.
-4
The method of calculating the ultimate strength of a
composite member based upon the crushing strength of concrete\
and the yield strength of steel is illustrated in Figure 1-
The assumptions involved here are~ (1) a fully plastic state
of stress is present in both steel beam and concrete slab when
the flexural capacity of the member is reached, (2) there is
complete interaction between slab and beam for all loads, and
(3) the concrete slab resists no tensile stresses. Following
accepted practice a fully plastic state of stress in the con
crete equal to 0085 f~ is assumed over a depth of slab
necessary to resist the tension force, T, produced by yield
stress~ fy~ over the entire steel section. In the case of
deep~ closely~spaced steel beams with thin slabs, the crush
ing strength of the concrete slab may be insufficient to
balance the tension force, To In this case a portion or all
of the top flange of the steel beam is assumed to be stressed
to f y in compression. That is to say, the neutral axis of
the combined section is in the steel beam. This complicates
slightly the determination of Mp but does not require any
modification of the theory.
Available beam test results have been compared with the
theory to determine whether the theory is applicable and
particularly to determine whether the assumption of complete .
interaction can be safely used. The resul~s of all tests
regardless of the type of shear connectors used are essen-
tially the same provided that the amount of shear connectors
-5
used is adequate and ,that the connectors are also capable of
preventing separation of slab and beamo Figure 2 shows non
~imensionally the results of typical load-deflection measure
ments on three composite 'beams having identical cross sections.
Beams B-5 and B=7 were fabricated with different types of
shear connectors and tested with the same loading. Beams B-7
and B~lO having ident,ical shear connectors were tested under
different loading. The upper bound of moment capacity for
complete interaction and no interaction are indi'cated by
dotted lines thus giving a direct indication of the gain in
load carrying capacity due to qomposite ,action. The design
recommendations concerning shear connectors presented in this
paper are approximately equivalent to the design pfconnectors
for the ultimate test load on these beamso The fact that the
maximum test load is in some cases less than the, theoretical
ultimate load should cause no alarm from a design point of
view~ first because' the percentage difference is small;
s'econd" because the Mp value shown was determineq. on the
basis of the actual yield strength of the steel which was
higher than the specified value of-33 ksi for A-7 steel; and
third, because the difference can be compensated for by an
appropriate choice of the load factor to be used in design.
It can be c~mcluded from this that interaction between slab
and beam is SUfficiently complete for plastic analysis to be
usedo
-6
SHEAR CONNECTOR DESIGN
Studies and tests have been con4ucted to determine the
number of shear connectors necessary to ensure that the
ultimate bending capacity can be realized. A sufficient
number of connectors must be provided to (1) transmit the
total shear force developed between slab and beam, (2) prevent
separation of beam and slab, and (3) prevent reduction of Mp
due to slip between slab and beam. It has been found that these
th.ree requirements can be satisfied with fewer connectors than
demanded by present practice.
The ultimate strength of various types of shear connectors
has been determined by many investigators by means of pushout
tests. The ultimate strength of a connector is simply the
ultimate load on the specimen divided by the number of connec
tors per specimen. The ultimate str.ength of connectors deter
mined by this method has been compared with ultimate strength
of similar connectors obtained in beam tests. The ultimate
strengths obtained by these two methods compare fairly well.
The ultimate strength of connectors in beam tests is
determined by use of the concept illustrated in Figure 3. The
slab, between the points of ultimate moment and zero moment,
is considered as a free body and the compressive force, C,
which must be transmitted across the interface by the shear
connectors, is divided by the number of connectors in the length
Ls to determine the load per connector. The assumption made
here is similar to the one used in bolted and riveted joints.
Obviously it can also be used as a design procedure once a
load factor is specified.
-7
Test results using both methods of determining the
ultimate strength of connectors are shown for welded studs
in Figure 4. , The data has been non-dimensionalized so that
results for various si~es of studs can be shown on one graph.
Beam test results include specimens with 1/2" headed and "L"
studs -;S··well as 3/4" headed studs. l Pushout test results
for studs.I/2" through 1~1/4" diameters are represented. 3 ,4
The horizontal line to the right is the approximate tensile
strength of the connector material•. This provides a suitable
desifRl value for studs with height to diameter ratios greater
than.4.2. It has been observed in tests that studs fail in
tension .rather than shear, and the tensile strength theref9re
determines the ultimate strength of studs in t~is application.
studs.hav~ng height to diameter ratios less than 4.2 are
penalized because of the possibility of their ultimate strength
being reduced by fracture of the concrete. The relationship of
strength (stress in ksi) to stud H/d ratio, given by the ex..
pression.Q = 222 Hd~9/As was used to plot the sloping line
beginning at the origin and joining the horizontal line at
(H/d) = 4.2. These lines may be taken as a lower bound of
connector strengths when they are anchored in concrete slabs
having sufficient strength to develop the full value of the
studs. Concrete strengths of 3000 psi and higher will fully
develop the connector. Data plots below the lines al;'e the re
sults of pushout specimens having low concrete strength, which
failed by cracking of the concrete slab. They serve to point
out the need for keeping concrete strengths in mind when
-8
determining connector strengths. Connector values shown here
are not intended for use with low strength or lightweight
concrete.
Heretofore~ the capacity of stud connectors has been
computed by equations of the form Q = kld~ for long studs
and Q = k2 Hdlf~ for short studs~ where "d" is diameter and
"H" is the height of the studo This form of the equation is
given for the purpose of comparison with present specifications.
The AASHO Bridge Specifications5 use values of kl = 330 and
k2 = $0 for determining the "useful capacity" of connectors as
compared with results given herel~4 of kl = 932 and ~2 = 222.
The connector strengths being presented here are the~efore
approximately 2.8 times the values given by AASHOo A sui~able
load factor must be used with either set of values. The load
factor used in the case of AASHO Specifications is between 3.0
and 4.0 whereas a load factor of 2.0 is suggested herein.
The ultimate strength of other types of connectors cannot
be determined by calculating the tensile strength of connectors
as was done for studs ~ and therefore empirical relat,ionships
must be used. For channel connectors, the relationship
commonly used for "useful capacity" is an equation of the form
Q :: k(h /Oo5t)w1fb where "h" is flange thickness, "t" is web
thickness and "w" is the width of the channel connector.
Figure 5 presents the results of ultimate strength tests of
channel connectors in terms of load per inch of connector.
-9
1 2Most of the data points shown are from pushout tests' and
the curve is drawn as a lower bound of these test results.
The two beam test results included indicate that this curve
is conservative. A value of k = 550 has been determined
from Figure 5. This value is approximately 3.0 ti~es the
value given in AASHO Specifications of k = 182 •
.There is published information available on the ultimate
strength of other types of connectors, based upon pUShout tests.
These results have not been presented here because of:'.lack of
confirming beam tests. The types of connectors, being consid
ered must satisfy the second requirement of preventing
separation of slab and beamo Channels, zees, spirals, and
studs satisfy this requirement.
The third requirement, that slip resulting from deformation
of shear conn~ctors must not SUbstantially r~duce Mp , must also
be considered. Early stUdies, reflecting the point of view of
elastic design arbitrarily based -- _. the "useful capacity" of
connectors on a maximum allowable slip of 0.004 inches. The
"usefUl, capacity" of connectors was then determined from. t,ests
to b~the.load which would cause this amount of slip. For
fatigue loading a maximum slip criteria for design of connec"!"
tors may be necessary, but for static loading the need for
such a criteria is questionable.
The seriousness of slip between slab and beam must be
jUdged from the results-of beam tests and cannot be determined
-10-
from pushout specimenso Typical results for beam tests show
ing slips which occurred during tests to ultimate are given
in Figure 6 and the previously established limit of 0.004
inches for the maximum permissible slip is indicated. It is
obvious that slips much longer than 0.004 inches can be-
tolerat~q~ It appears that the only limitation on the ,amount
of slip ~llowed at ultimate load is the amount which connectors
can deform without failure. Valu~s for this can again be ob
tained from pushout testso Maximum slips observed in pushout
tests"are",generally larger than those observed at ultimate
load in beam:: tests. Beams such as specimen B-ll shown in
Figure 6, with approximately uniform loading, exhibit larger
slips than similar beams with concentrated loading.
To further illustrate effects of slip upon composite action,
a beam'was tested which cpntained only approximately half the
numberof connectors required to transmit the compressive force,
C, across the interface at ultimate moment Mp • The slip versus
moment curve for this beam~ B~6, is shown in Figure 7 along
with a similar curve for a beam, B~5, having an adequate number
of cpnnectors. It is obvious that much larger slips occurred
in the beam with an inadequate amount of connectors even at
rela:t~vely low loads. The load deflection curves' for the same
two beams given in Figure 8 show that the beam with inadequate
connectors still performed essentially as ,a composite member
and 82% of Mp was, reached in the test. The load deflection
curves in the region of design load are not affected
-11
appreciably by the differences in magnitude of the end slip
fOI' the two beams 0 The magnitude of slip for beam B-6 at
desigp load is much less than would occur in a non=composite
beam designed for the same loadingo The conclusion is there
fore reached that slip is not a matter for serious concern in
the design of composite structures for static loads.
Since larger values of slip than previously allowed are
permissible without danger of connector failure, it is not
necessary to space connectors in accordance with the shear
diagram of a membero The connectors may be spaced uniformly
and considered to act as a group with redistribution of loads
assumed as presented in Figure 30
Observations have been made during tests to determine if the
full width ot"' the concrete slab remains effective at high
loadso In spite of observed deformations of the slab near
ultimate load in the form of warping and separation of slab
and beam, strain measurements indicate that the longitudinal
component of stress remains uniform across the top of the
slabo This was true for beam B=6 having inadequate shear
connectors as well as for all beams with adequate shear connec
torso Deformations of the slab may seriously alter the Tee
beam action of the composite member if the spacing between shear
connectors is too large 0 For this reason it appears to be
desirable to limit connector spacing to some arbitrarily choos·en
value, such as six times the slab thickness for example 0
-12
Values o~ ultimate strength of shear connectors as given
. by any empirical criteria are 9nly valid wi thin certain limits.
For this reason it seems desirable to place limitations on
such factors as maximum diameter and minimum steel strength
in the case of stud connectors and maximum web and flange thick-
nesses in the case of channels •
.LOAD FACTORS FOR DESIGN
In order to establish plastic strength as a design pro
cedure, it is necessary to choose suitable design, load factors.
The load factors selected must ensure safety and restrict de
flection to desirable limits. A study of all composite beam
tests suggests the selection of a load factor of 2.0 for pro
porti();ning the cross section. This load factor all()wsmaximum
economy which is obtainable in view of safety and deflection re~
quirements •. Figure 9 shows a typical load-deflection curve for\
a composite beam. Design load based upon a load factor of,2.0
is indicated and the load at which yielding of the bottom ,flange
occurs is also shown. The deflection of L/360 commonly used as
a limit for live load deflections in buildings is also shown.
Since the section properties of composite beams vary
greatly because of a wide range of possible combinations of
slab and beam dimensions, it is necessary to 'investigate
further the relative position of design load with respect to-
yield load to be sure that design load is never appreciably
above ,yield load. If unshored construction is considered,
the str~sses in the steel beam will be higher than for shored
const~uctioni b~t the value of Mp is not affected by the method
of construction.
When the condition of unshored construction is considered,
.c~rtain restrictions on the cross section are necessary to ensUre'
that design load will be below yield load for all ratios of dead
load to live load so that deflections will be stable. A recent
ASCE~ACI Joint Co~ittee report6 proposes a limiting ratio of
composite section modulus to steel beam section modu+~~.as. a
means of accomplishing this. It is also necessary tq lim~t the
load or stress on the steel section, alone before the concre~e
has hardened in order to avoid damage to the steel section during
construction.
It has been shown that a number of applications of loads
larger than the proposed design load does not result in pro
gressive~y increasing deflections. All beams tested at Lehigh
were first loaded ten times to a level equal to the ·.theoretical
ultimateload divided by a load factor of 1.85 ,rather than by
2.00 as proposed. There was a resid-qal deflection after the
first application of load but the residual deflection after
10 applications of load did not increase appreciably. This
characteristic of residual deflections after initial loading
is not unlike results obtained in tests of other types of
members.
In selecting a load factor for~stablishingworking loads
for shear connectors p the choice should be such that ,the shear
connectors would n~t fail until the ultimate moment is reached.
Test results do not indicate a need for this factor being
larger than 2.0 for static loading.
One continuous beam was tested and the results compated
with values predicted by plastic theory. In calculation of
the ultimate moment capacity considering redistribution of
moment p the value of Mp at the negative support is that of the
steel beam alone while MP' in positive moment regions is that
of the composite section. The comparison of predicted and
observed values verifies theory satisfactorily.
CONCLUSIONS
The' .application of plastic design theory to composite
beams has been presented. Tests of 13'composite beams and a
considerable number of pushout specimens have been considered
and typical results only have been presented to demonstrate
the validity of plastic theory. It is felt that the research
work that has been done on this type of member makes avail~ble
sufficient information to serve as a basis for writing speci
fications for plastic design. It has been shown that such a
method offers sufficient advantages as compared with elastic
design to warrant its adoption. Studies in connection with
plastic design of members have revealed that substantial
saving in steel beams and shear connectors are possible re
gardless of the method of design employed.
3.
-16
REFERENCES
I. Culver, Charles, Zarzeczny, P. J., Driscoll, G.C. Jr.,"Tests of Composite Beams for Buildings", ProgressReport Noo 1, June 1960, Progress Report No.2,January 1961 9 Unpublished Reports.
2. Siess, Co Po, Viest, I. M., and Newmark, N. M.,"Studies of Slab and Beam Highway Bridges, Part IV:Full Scale Tests of Channel Shear ConriectorsandComposite T-beams"" Bulletin 405" Univ. 6f IllinoisEng. Exp. StaG 19520If
Thurlimann, B0,"Fatigue and Static Strength of Stud Shear Coimections",Journal, American Concrete Inst., Vol. 30, No. 12,pp 1287=1302" 19590
4. Viest" I. Mo"Tests of Stud Shear Connectors, Parts I, II, III andIV," Engineering Test Data, Nelson Stud Welding,Lorain" Ohio.
5. American Association of State Highway Officials,"Standard Specifications for Highway Bridges", 7thEdition" 1957. '
6. Tentative Recommendations for the Design and Constructionof Composite Beams and Girders for Buildings, Journal,Structural Division ASCE Vol. 86, No ST12, December 1960.
t
b
"I. -0.85 f~...C.
I I~-.t - ---.-'. ....
I I N.A. .T
e
...d T ...
r
c= T = 0.85 f~ bef y
T = As fy
e=~ a+t --2 2
Mp = Te
Stress Distribution ot Mp
Fig.l CALCULATION OF PLASTIC MOMENT (Mp)
It-J(»6
~ 3011
=151
-01
~
0-810 I/~' L-Studs
5432
[u.pper Bound - Complete Interaction
r ---------.-------------------I
II
II
I
r Upper Bound - No Interact ion__ L _
A A ~PAAR12 181172 75 ~ 75 75 ·'5
,./;., t i ..o-B5 3u4 Connectors
I II·-87 ~2 t L- Studs
Deflection / t. Deflection at Yield·
"M--.!! My>-.. 1.5C..CQ)
E 1.00~
~
"'- 0.5....CQ)
E0~
~0
t.Fig. 2 TYPICAL LOAD DEFLECTION CURVES FOR COMPOSITE BEAMS
p/2 • PI .t--- Ls--......._b _+--- b _ 2I . . .~ .•
~ ·Ls 1~ ,~.-- C =0.85 f~ba"""r'~~-"~~""~
Connector Forces
Q=
--Force per Connector
CNo. of Connectors
Equlibrium of Slob
Fig. 3 CALCUh4TION OF SHSAR CONNECTOR
N
100~..0•..0 .
• •80 Ii •
00
00 8 0 0
0• .~ 0
flS 0
-- am932 d
2 Ii';en 600 0
~ 0b o 0
01c As
~ 0 0--en 40 I 0 Stud Failure- Pushouten 01Q) -...
I • Stud Failure - Beam~
en222 HdJr;20 I 0 Cone. Failure - Pushout
As I • Cone. Failure - BeamII\}
2 4 6 8 10 120
0
Height / 0 iameter of StudFig. 4 ULTIMATE STRENGTH OF STUD SHEAR CONNECTORS
10 20
(h +O.5t)~ for Channel
CDQ..-.¥ 30C.--Q)CC0
20.c0....0
.s:::.uc: 10.-"-CDQ.
-CC0
..J 0
q=550 (h +0.5t)~
•
oo
o
•
o
o Ultimate - Pushout
• Ultimate -Beam
30 40I.I\)
~
Fig. 5 ULTIMATE STRENGTH OF CHANNEL SHEAR CONNECTORS
r-~---------------------------~--
II\)I\)
0.20
N- - -- ~-.D•-.D
oo
0.150.10
~ 30"= 151-0
11 .1.Specimen BII
Uniform Connector Spacin
o
o
100
80
enQ..-~ 60C.--a..
40'"'CC0-J
Maximum End Slip in inchesFig. 6 LOAD SLIP CURVE FOR TEST OF BEAM B-ll
, .' .'.. .:, .
M"'OM- YCD .-->-
"" '.:' .," ...
..1..50
.B5~0--9..c:: ,rCD 0 00E 0
R ~ \01.0 86 72 72:E ~ ~ {IS- i .
0' ~1 0
AI :it)},.
" I 85 - 3 LJ 4 Connectors+-c::
0~5 (adequate)Q)
E 0 0
III 4>0 86-'2 L-Studs:E ( inadequate)
~ 0 0.04 0.08 0.12 0.16
Maximum Slip at Ends - InchesIn II\)W
Fig. 7 COMPARISON OF LOAD SLIP CURVES FOR BEM4S B-5 AND B-6
,--------- --~- -- - ~ -- -~---- -------------
,f\)
+=-
I\}
~.. .
.,[)
7 8-By
65432
t. Deflection / ~ Deflection at Yield
I .
I 85 . -.-0--0 .I ~o..;....o . -0... · " . .I_~~O 0----0
" .' ~V-""0-0-70-0-0-0- ..........0.
/~_~Cf' 86 . A~ A. ~(J(j 7.2 II 7.2Ja . IS·1'---------'-------------- A! 1 A
I 85 - 3 u 4 Connectorso 0 (adequate)
/ I"A\o 86 - 2" 't' L-Studs(inadequate)
+c:CPEo 1.0~
~
'"C 0.5Q)
Eo.~
~ 0
Fig. 8 CONPARISON OF LOAD DEFLECTION CURVES FOR BEAMS B-5AND B-6
\
If\)
\Jl.
o
f}2 F}2j18" i .
~..- - .....87-51
~; t L~ Studs
@ First MHIScale Flak.
, 00
L-360
Deflection, in inches
. ' 'r------------ ---- ~-- -- - - - -.-- -- -- --~- - ---
L360
, -Centerline
II .
,~
I ",.0__0-.....-_0 'I ' 0-___-",.00I 0#2
. , , ,cr- ." 0'
"./~'.0/,', / ' ,
I '," ,
40' . ,. /1 '
I 00
'. Desiqn I 'ILoad I 1 '
IIIIII
o
--
""C 20o.3
'enQ.--~
c:
Fig. 9 LOAD DEFLECTION CURVE FOR BEAM 'B7 SHOWING RECOMMENDED DESIGN LOAD