STEEL COMMITTEE OF CALIFORNIA

T E C H N I C A L I N F O R M A T I O N & P R O D U C T S E R V I C E

JANUARY 1987

COMPOSITE BEAM DESIGN WITH METAL DECK

INTRODUCTION

The American Institute of Steel Construction(AISC) Specification has long recognized the use ofcomposite construction. In the Third Edition of theManual, 1936, steel beams were entirely encased inconcrete for composite development. The 1963AISC Specification contained provisions for both en-cased beams and beams with only a concrete slab onthe top flange. The entire horizontal shear betweenthe slab and steel beam was assumed to be trans-ferred by shear connectors welded to the top flangeof the beam.

The composite design provisions of the 1969AISC Specifications contained provisions forcomplete and incomplete (or partial) compositedevelopment. The 1978 AISC Specification wasexpanded to include design provisions for compositeconstruction with formed metal deck. Since moststeel framed buildings use metal decking as part ofthe floor system, it was only natural that thespecification recognize this type of construction.

This paper will present typical composite designexamples using metal deck. Both partial andcomplete development will be considered. It is well-known that composite design can reduce the size ofthe supporting steel beam and/or keep deflectionswithin acceptable limits. Realistic savings can oftenbe made with the use of partial composite action.

AISC Specification

Section 1.11.5. Composite Beams or Girders withFormed Steel Deck

Composite construction of concrete slabs onformed steel deck connected to steel beams orgirders shall be designed by the applicable portionsof Sects. 1.11.1 through 1.11.4, with the followingmodifications.

1.11.5.1 General

.

.

Section 1.11.5 is applicable to decks withnominal rib height not greater than 3 inches.

The average width of concrete rib or haunch,wr, shall not be less than 2 inches, but shallnot be taken in calculations as more than theminimum clearwidth near the top of the steeldeck. See Sect. 1.11.5.3, subparagraphs 2and 3, for additional provisions.

. The concrete slab shall be connected to thesteel beam or girder with welded stud shearconnectors 3/4-inch or less in diameter(AWS D1.1-77, Section 4, Part F). Studsmay be welded through the deck or directlyto the steel member.

. Stud shear connectors shall extend not less than I 1/2 inches above the top of the steeldeck after installation.

Sections 1.11.5 and 1.11.5.1 of the AISCSpecification pertaining to composite design withmetal deck have been included for a quick reference.The deck ribs can be oriented perpendicular orparallel to the steel beam or girder. Design rules forthe deck orientation are summarized in Table 1 (seepage 2, top).

,

6.

Total slab thickness, including ribs, shall beused in determining the effective width ofconcrete flange. ,

The slab thickness above the steel deck shallnot be less than 2 inches.

TABLE 1

AISC RULES - FORMED METAL DECK

ITEM RIBS PERPENDICULAR RIBS PARALLEL

1. Concrete Area BelowTop of Deck

2. Stud Reduction Factor

3 Maximum Stud Spacing

4 Deck Welding

5 Minimum Width of Rb

NEGLECT INCLUDE

0 85 Wr Hs Wr

(Nr)l/2 ( - r ) ( - r -1) 06 (-r-r)(rS-1)

32 in NOT SPECIFIED

16 m NOT SPECIFIED

2 m. DEPENDS ON Nr

Typical Design Problems

Example 1. Design a composite interior floor beam(no cover plate) for an office building See beam A inFigure 1.

40' BA IA_ 30'

B

Figure 1

Given: Span length, L = 30 ft.Beam Spacing, s = 10 ft.Slab thickness, t = 5.5 m.Concrete: f'c -- 3 0 ksiConcrete Weight = 145 pcf (n = 9)Steel: Fy = 50 ksi3 inch rfietal deck, ribs perpendicularto beamNo shoring permitted

Loads: Concrete slab including reinforcingsteel and metal deck . . . . . . . . 54 Ibs/ft2Mechanical ...................... 4 "Ceiling ....................... 6 "Partition ........................ 2 0 "Live ............................... 1 0 0 "

Page 2 Steel Tips January 1987

Solution.

1. Bending Moments:

a Construction loads:f

Slab = 054 kEps/ft2Steelbeam(assumed) = 003 "

Total = 057 "

MD-- 2/w____(.057x10x30) (30x12) =770k]pm8 8

b Loads applied after concrete has hardened.

wL2 (.13x10x30)(30x12)ML = 8 - 8 =175Skip-in

(Due to possible actual loading, no reducbon in hveloads were considered for these beams )

c. Mmax = MD + ML= 770 + 1755 = 2525 kip-in.

2 Maximum shear.

V = 10( 057 + .13) (30/2) = 28 1 kips

3. Effective width of concrete slab (AISC, para. 1 11 1)

b = L/4 = (30 x 12)/4 = 90 inches

b = s = 10 x 12 = 120 inches

b = 16t + bf = (16 x 5 5) + 6 0 in (assumed) = 94 in.

The 90 inch width governs.

4. Required section moduti:

5

For MD + ML, Str= 2525 = 76 5 in 333

For MD, Ss - 770 _233m333

From the "Composite Beam Selection Table"1for plain slabs:

Select W18x35, Str = 97 3 m 3 > 76 5 m 3(required) o k

AWl 6x31 beam satisfies the required sectionmodulus but does not meet the desired depthto span ratio of Fy/800. (See Commentary -Sect 1.13.1)

Sectton properties of W18x35Ss = 57 6 in 2 A sTM 10 3 n.2 tf = 425 m.Is=510m.4 d=177m, tw= 30m.

6. Calculate composite design sechon properties:

a. Moment of InertIa.

Ac= b(tc) = 90 x 2 5 = 225 in 2A'c = Ac/n = 225/9 = 25 0 m. 2Ys = d/2 = 17 7/2 = 8 85 nYc = d + hr + tc/2 = 17 7 + 3 0 + 2 5/2=21 95 in

bb .!

F '1

c

Figure 2

Flguro 3

1AISC Manual 8th Edit{on, page 2-109

Section A Y AYW18x35 10 3 8 85 91.2Concrete 25 0 21 95 548 8

353 18.13 6400

b

Yb =18.13in,ds=18 13 -8 85 =9 28mdc=21 95- 18.13 =3 82in.Io (For transformed concrete slab) = bh3/12n

Io = (90) (2 5)3/(12)(9) = 130 m.4Io [for steel beam) = 510 in '+

Itr = T Ad2 + T. Io

Sectton AW18x35 10 3Concrete 25 0

Itr = 1775 m.4

Section Moduh'

1775Str - 18 13

d Ad2 Io928 8870 5103 82 364 8 13

1251.8 + 523 = 17748

- 97 9 In.3

St = 1775 = 350 in.3(3 82 + 1 25)

7 Check concrete stress'

1755 0 557 ksl < 1 35 ksi o kfc = (350)(9) -

8. Check steel stress:

Total load Str = 97 9 in 3 > 76 5 In.3 o k

Dead Load Ss --576m3>233m.3 ok

28 1 = 5 29 ksz < 20 ks o kWeb shear, fy - (17 7) (0 30)

9. Check deflectEons

5wL4 ML2 -- - -

384EI 1920 I

(770) (30)2 = 0 71 m < 1 00 in o k.AD- (1920)(510)

(1755)(30)2 = 0 464 in. < 3'0 o.k 2AL= (1920)(1775)

10. Check to determine if shores are required:(AISC 1.11-2)

Str max ( 1.35 + 0.35 1 755

=_ 7--/ (57.6) =124 m.3

124 in.3> 979 in.3

No shores are required.

2Long term deflection due to creep is not consideredsignificant.

Steel Tips January 1987 Page 3

11. Calculate the number of shear connectorsrequired for full composite action.

Assume 3/4-nch diameter by 41/2 inch long studs.Maximum stud diameter unless located drectly overthe web s 2 5tI = 2.5 x 0 425 =1 06 m > 0 75 m o k

a Total horizontal shear:

Concrete Vh = 0 85f'c = .85 x 3 x - = 287 kips

(AISC 1.11-3)

Steel. =258k, ps

(AISC 1.11-4)Since the shear due to the steel area is less andgoverns, the number of studs will be based on 258 kips.

b. Calculate the stud reduction factor forthe deck nbsperpend,cular to the beam.

Reduct'on Factor - 0 85 (W-r) r )(Nr) l/2 -1 _< 1.0

(AISC 1.11-8)

Assume. Nr = 1, Hs = 4.5 in., wr = 4 m.Given: hr= 3 m.

Reduction Factor = 0 -1) = 0 565(1)1/2 k3/k3

q = (11 5) (.565) = 6 5 kips per stud

N1 = Vh/q= 258/6 5 = 39.7

Use 80 - 3/4 in. diameter by 41/2 tach studs (40 oneach side of mid-span).

Example 2. Design a composite intenor grder (nocover plate) for an office building. See gmrder B inFigure 1. The 3-inch deck nbs are onented parallel tothe girder. Grder is assumed loaded as shown inRgure 4.

[

P P P

4 e 10 = 40'

w,/ft./

Ftguro 4

Loads: Concrete slab including reinforcingsteel and metal deck .. . . . 54 Ibs/ft2Mechanical 4 "Ceiling 6 "Partition- 2 0 "IJve-- 100"

td

d,

Yb

b/nI_

-- m m

t Y s F'"'

.I

Figure 5 ,

Soluhon:

1. Bending Moments.

a. Construction loads.

Slab = .054 kps/ft2Steel beam (assumed) -- 0 0 3 "

Total = . 0 5 7 "

Assume steel girder weighs 100 lbs/ft = .1 kap/ft.(Approx. 3 Ibs./ft2)

PD = 0.057 kips/ft2 (10) (30) = 17 1 kps

wL2 PL _-1(40)2(12) (17 1)(40)(12)MD- 8 + 8 + 2

MD = 240 + 4104 = 4344 kip-in.

b. Loads applied afterconstruction:

Reduce live load for large area supported by girder.Total dead load = 57 + 3 = 60

Given:

Page4

Span length, L = 40 ft.Beam spacing, s = 30 ft.Slab thickness, t = 5.5 m.Concrete: f'c = 3.0 ksiConcrete weight = 145 pcf (n = 9)Steel: Fy = 50 ksi3 inch rfietal deck, ribs are parallel to girderNo shoring permitted

Steel T/ps January 1987

R = 23.1 (1 + D/L) = 23 1 (1 + 60/130) = 34%(UBC-1985)Live load reduction factor = 34%

P = 0.13 x 10 x 30 x 0.66 = 25.7 kips.

ML = PL = 25.7x40x12 =6168kip-in.2 2

c. Mmax= MD + ML=4344+6168 = 10512 kp-m.

2. Maximum Shear.

V = [(.13 x 66) + (.057 + .003)]30 x 40/2 = 87 5 kips

3. Effecbvewdth of concrete slab' (AISC, para. 1.11.1)

b = L/4 = (40 x 12)/4 = 120 hnches

b = s = 30 x 12 = 360 inches

b = 16t + bf = (16 x 5.5) + 10.0 in. (assumed) = 98 in.

The 98 tach width governs.

4. Requ:red secbon moduli.

FOrMD+ML' Str _ 10,51233

- 319 m.3

FOrMD, Ss - 4344 =132in.333

5. From the "Composite Beam Selectton Table"3 forplain slabs:

Select W27x94, Str = 342 in.3 > 319 m.3 (Requtred)

Section properties of W27x94'

Ss =243in3 A=27.71n2 tf =.745m.Is = 3270 m.4 d = 26.92 m. tw = .490 in.

6 Calculate composate design section properties

a. Moment of Inertia

Ac = Concrete above deck (88x2 5) = 220 m 2Concrete tn deck area (3x44) = 132 m.2Concrete over girder (10x5 5) = 55 in,2

Total = 407 m.2

AC' = Ac/n = (98 x 2.5)/9 = 27.2 m.2.Ys = d/2 = 26 92/2 = 13.46 in.Yc =d + hr + tc/2 = 26.92 + 3.0 + 2.5/2 =31.17 in.

Section A Y AYW27x94 27 7 13.46 372 8Concrete 27 2 31.17 847.8

54.9 22.23 1220.6

3AISC MANUAL, 8th Edbon, page 2-108.

"--" 4 Deflection due to long term creep is not consideredsignhcant.

Yb=22 23 m.,ds = 22.23 - 13 46=8 77mc = 31.1 7 - 22.23 = 8.94 in,!o (For transformed concrete slab) = bh3/12n

Io = (98)(2.5)3/(12)(9) = 14.2 m.4Io (For steel beam) = 3270 m.4

Itr = [ Ad2 + T Io

Sechon A dW27x94 27.7 877Concrete 27.2 8.94

Itr = 7588 in. 4

Ad2 Io2130 32702174 144304 + 3284 = 7588

*NOTE. Only the area above the metal deck has beenused to calculate the transformed section propertiesA more refined method of using all of the concretearea is usually not warranted. Neglecting the concretein the nb area is slightly conservabve. For thzsexample, takmg all of the concrete into accountdecreased the deflection about 5% and the concretestress about 15%

b. Sechon Moduli

7588 - 341m3Str = 2223

7588St= (8 94+1.25) = 745m'3

7 Check concrete stress:

fc- 6 1 =092ksl

10 Check to determine f shores are required.(ALSO 111-2)

6168 (243) = 449 m.3Str max = 1.35 + 0 35 4344!

449 m.3 > 341 m.3 No shores are required

11. Calculate the numberof shear connectorsrequired for full composite action.

Assume 3/4 inch dameter by 41/2 inch long studs

a Total horizontal shear:,%. - 407Concrete. Vh = 0.85f'c -- = .85 x ; x -2- = 519 kps

(AISC 1.11-3)

Steel Vh = As __FY = 27.7 x -- = 693 kips2

(ALSO 1.11-4)

Since the shear due to the concrete area s less andgoverns, the number of studs wdl be based on519 kips.

b. Calculate the stud reducbon factor forthe decknbs oriented parallel to the girder.

Reduction Factor= 0 6 ( r/hrWr'- -1.0) < 1 0(AISC 1.11-9)

(wr) 9

(hr) 3- 3>1.5

Since this rabo s larger than 1.5 no reduction in studshearvalue is necessary. (wr was assumed 9 roches,the actual wdth will probably be closer to the flangewdth or 10 roches.)

Allowable Icad per stud = 11.5 kips.

NI= 519/11 5 = 45.1 Use 92 studs per girder, 46 oneach sde of mid-span.

c. Due to concentrated loads check stud spacing:

Mrnax = 6168 in.-kips at md- span

Moment at concentrated Icad 10 feet from support:

M = 3PLJ8 = (3 x 25.7 x 40 x 12)/8 = 4626 in. leps

Check for N2 (the number of studs required betweenthe concentrated Icad and the point of zero moment):(AISC 1 11-7)

N1 x -1)N2= 13 - I ; 13= Str/Ss =341/243=1 4

46[(4626 X 1 4/6168) -1] =5 75N2= I 4-1

Since 6 studs is less than the numberrequired for N1, formula 1.11-7 does not apply

of studs

Partial Composite Construction

Example 3 Design beam A, Example 1, using partialcomposite action.

Given. Same data as Example 1.

Soluhon: Steps 1 through 6 are the same as Example1. The maximum calculated shear due to dead and IweIcad is 28.1 kips Full composite acbon was based onthe steel area, and therefore the honzontal shear s258 Ips as determined by AISC formula 1 11-4

In order to dlustrate the reduchon in the number ofshear studs required, partal composite acbon wdl beconsidered 75%, 50%, and 25% development f ap-propnate. It should be noted that 25% s the minimumlevel permitted by AISC

a. 75% development

Serf = Ss + [V'h/Vh]l/2 (Str- Ss)

V'hNh = 0 75

Serf = 57.6 + [.7511/2(97.9 - 57.6) = 92 5 m.3

92.5 m. 3 > 76.5 m.3 o.k.

( AISC 1 11-1)

N =V'h/q = (.75 x 258)/6 5 = 29 8

Use 60 - 3/4 inch diameter by 41/2 tach long studs(30 on each side of md-span).

Check Deflection.

left = !s + [V'h/Vh]l/2(Itr - Is) (AISC 1 11-6)

left = 510 +[.75)1/2(1775-510) = 1606 m.4

'L = (1775/1606)(0 464) = 0 513 m.

0 5131n

b. 50% development:

V'h/Vh = 0.50

Serf = 57.6 + [.5011/2(97.9-57.6) = 86.1 in.3

86.1 in.3 > 76.5 in.3 o.k.

N = V'h/q = (.50 x 258)/6.5 = 19.8

Use 40 - 3/4 inch diameter by 41/2 inch long studs(20 on each side of mid-span).

Check Deflection:

left = 510 + [.5011/2(1775-510) = 1404 in.4

AL = (1775/1404)(0.464) = 0.587 in.

0.587 in. < L/360 = 1.00 in, o.k.

c. 25% development

V'h/Vh = 0.25

Serf = 57.6 + [.2511/2(97,9 -57.6) = 77.7 in.3

77.7 in. 3 76.5 in.3 o.k.

N = V'h/q = (.25 x 258)/6.5 = 9.9

Use 20 - 3/4 inch diameter by 41/2 inch long studs(10 on each side of mid-span).

Check Deflection:

left = 510 + [.25]1/2 (1775-510) = 1143 in.4

AL = (1775/1143)(0.464) = 0.721 in.

0.721 in. < L/360 = 1.00 in. o.k.

Example 4. Check girder B to determine if partialcomposite action would decrease the number ofshear studs.

Given: Same data as Example 2.

Solution: From AISC Formula 1.11-1 - (Assume Serf =required Sir); rearrange Formula 1.11-1 and solve forV'h.

Vh (Serf-Ss)2V'h=

(sir' Ss)2

519(319 -243)2V 'h = (341 -243)2 = 312 kips

V 'h 312

Vh 519- .60 or 60% development

N = (312)/(11.5) =' 27,1 or 28'studs on each side ofmid-span

Check Deflection:

left = 3270 + [.6011/2(7588 - 3270) = 6615 in.4

'L = .0639(7588/6615) = 0.733 in.

0,733 in < L/360 = 1.33 in. o.k.5

5Deflection due to long term creep is not consideredsignificant.

T A B L E 2

S U M M A R Y OF STUD REQUIREMENTS

Composite Construction

Beam ATotal StudsRequired

LL Def. in.

Full Vh100%

80

0.464

Partial Vh75% 60% 50% 25%

60 48 40 20

0.513 0.553 0.587 0.721

Girder BTotal StudsRequired

LL Def.in.

92

0.639

68 56

0.692 0.733

Will not developrequired shear transfer

SteelTips January 1987 Page 7

GENERAL DISCUSSION

Composite construcbon on medium to long spans canbe used to reduce construction costs Where appro-pnate the use of parbal composite acbon wdl generate ad-ditional savings As noted in Table 2, 40 to 60% of theshear studs mght be ehmmated when only the studs re-quired for the assumed loading condibons are consid-ered

Following are some general observations that shouldbe cons;tiered when using composite construction.

1 In most cases, composite construcbon should beconstdered for spans 25 feet and longer

2 It s more economical to use a rolled beam on shorterspans than a rolled beam with a cover plate Long spanbeams or girders fabricated from three plates may havethe bottom flange smaller than the top flange. Be surethe top flange is large enough to support all constructzonloads unbl the concrete has obtained its requiredstrength

3. The composite design tables in AISC for plato slabscan be used for preliminary estimates of required trans-formed sechon modulus when using metal deck.

4 For most condbons in steel framed bufidngs, onlythe concrete above the metal deck need be consJderedwhen determining the section properbes Ths assump-hon is slightly conservatwe However concrete belowthe top of the metal deck s to be included an calculatingthe concrete area for honzontal shear (AISC FormulaI 11-3)

5 References 2 and 3 point out addrt,onal refinementsthat can be made to gve a more accurate ndicaton ofthe deflections and stress levels

6 Composite beams should be designed as selfsupporting for most bufiding construcbon Except forunusual condJbons shonng should not be required as ftis too expensive The shonng may cost more than thesawngs generated by composite construction

On long spans, consideration must be given to theweight of additonal concrete' due to deflectEon of thegtrder when no shores are used Girders or beams onlong spans should be cambered to reduce the extraconcrete and dead load due to the members deflection

GENERAL NOMENCLATURE

Ac

Ac'

Actual area of effective concrete flange incomposite design (square inches)

Effecbve area of concrete diwded by modularrabo (in 2)

As Area of steel beam in composite design On 2)

MD Moment produced by dead load

ML Moment produced bylve load

Nr Number of stud shear connectors on a beam Enone nb of metal deck, not to exceed 3 ncalculations

E Modulus of eiasbcity of steel (29,000 kps persquare inch)

Fy Specified minimum yield stress of the type ofsteel being used (kips per square inch)

Hs

left

lo

Itr

Length of a stud shear connector after welding(inches)

Effective moment of inertia of composite secbonsfor deflection computations (inches4)

Moment of inertia of steel beam or concrete fill forits effectwe flange width (inches4)

Moment of inertia of transformed compositesection (in.4)

N1

N2

Number of shear connectors required betweenpoint of maximum moment and point of zeromoment

Number of shear connectors required betweenconcentrated load and point of zero moment

Serf Effectwe section modulus corresnding topartial composite action (inches')

Ss Section modulus of steel beam used incomposite design, referred to the bottom flange(inches3)

t Section modulus of transformed composrte crosssection, referred to the top of concrete (inches3)

Page 8 Steel Tips January 1987

G E N E R A L N O M E N C L A T U R E (cont/nued)

Str

Vh

V'h

b

bf

SectIon modulus of transformed compositecross section, referred to the bottom flange;based upon maximum permitted effecbve widthof concrete flange (inches3)

Total honzontal shear to be resisted byconnectors under full compos;te action (kips)

Total horizontal shear provided by theconnectors mn prowding parhal composIte action(kips)

Effectwe width of concrete flange

Flange wdth of rolled beam or plate girder(Inches)

fc Concrete compression working stress (kzps persquare inch)

f'c Specified compressive strength of concrete(kps per in.2)

fv Computed shear stress (kxps per square tach)

hr Nominal nb height for steel deck (roches)

n Modular ratio (BE c)

q Allowable horizontal shear to be resisted by ashear connector (kps)

tf Flange thtckness (inches)

tw 'V thfckness (inches)

wr Average wdth of nb or haunch of concrete slab onformed steel deck 0nches)

8 Rabo Str/Ss or Serf/Ss

A Displacement of the neutral axis of a loadedmember from ts posaton when the member snot loaded (inches)

REFERENCES

1 Manual of Steel Construction, EJghth EdJtlon, AISC,Chicago, 1980

2 Effectwe Width Criteria for Composite Beams -Vallemlla and Bjorhovde, AISC EngmeenngJournal, 4th Quarter, 1985, Vol. 22, No. 4.

3. Concrete Slab Stresses in Partml CompositeBeams and Grders - Lorenz and Stockwell, AISCEngmeenng Journal, 3rd Quarter, 1984, Vol 21,No 3.

4 Compomte Beams with Formed Steel Deck - Grant,Slutter and Fsher, AISC Engineenng Journal, 1 stQuarter, 1977, Vol 14, No. 1.

5 Comparative Tests on Composite Beams wrthFormed Metal Deck - Allan, Yen, Slutter, and Fisher,Fntz Engineering Laboratory Report No.200.76 456.1, Lehigh University, Bethlehem, Pa.,Dec. 1976.

7 Analyszs of Tests of Composite Steel andConcrete Beams with Mahon Steel Decking -Errera, Structural Engineenng Department,Cornell Umversty, Ithaca, New York, Dec 1967

8 Tests of Laghtweght Concrete Members wth MetalDecking - Slutter, Fritz Engmeenng LaboratoryReport No 200 68 458 1, LehJgh UnJversty,Bethlehem, Pa, March 1969

9

10

11

Composite Beam Incorporating Cellular SteelDecking - Robinson, Journal of the StructuralDwsson, Amencan Society of Ctvd Engineers, Vol95, No ST3, March 1969

Flexural Strength of Steel-Concrete ComposrteBeams - Slutter and Dnscoll, Journal of theStructural Division, American Society of CwdEngineers, Vol. 91, No ST2, April 1965.

Design of Composite Beams with Formed MetalDeck - Fisher, AISC Engineering Journal, AmericanInsbtute of Steel Construcbon, Vol. 7, No 3, July1970.

6. Partal-lnteraction Design of Composite Beams -Johnson and May, The Structural Engineer, Vol.53, No 8, Aug 1975.

12 Tests of Composite Beams with Cellular Deck -Robinson, Journal of the Structural Dwsion,American Society of Clwl Engineers, Vol. 93, No.ST4, Aug. 1967.

Steel T/ps January 1987 Page 9