· "

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.

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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