MARCH 1991

by Ron Vogel, Computers and Structures, Inc.

March, 1991

LRFD-COMPOSITE BEAM DESIGN

WITH METAL DECK

INTRODUCTION

This is the companion paper to the "STEEL TIPS" dated January 1987 entitled "CompositeBeam Design with Metal Deck". The original paper used allowable stress design (ASD). This"STEEL TIPS" utilizes the same three original examples but designed by the Load andResistance Factor Design (LRFD) Method. The purpose is to show the design procedure, theadvantages of the method, and the ease of using the AISC First Edition (LRFD) for design.

Three main areas have been revised from the ASD Approach:

1. Determination of effective slab width2. Shored and unshored construction requirements3. Lower bound moment of inertia may be utilized.

A number of papers have been written about these differences and the economies of the LRFDmethod. The reader is referred to the list of references included.

Table 1

S U M M A R Y OF AISC-LRFD SPECIFICATION SECTIONS I3 & I5

SECTION ITEM SUMMARY

I3.1 Effective Width, b = Beam Length/8 (L/8)on each side of beam = Beam Spacing/2 (s/2)(lesser of the 3 values) = Distance to Edge of Slab

I3.5a General hr < 3.0 in. (Height of Rib)Wr > 2. 0 in. (Width of Rib)ds < 3/4 in. (Welded Stud Diameter)Hs = hr + 1 1/2 in. (Minimum Stud Height)

= hr + 3 in. (Maximum Stud Height value for computations)tc > 2.0 in. (Minimum concrete above deck)

15.1 Material Hs > 4ds

I5.2 Horizontal = 0.85f'cAcShear Force = AsFy(lesser of the 3 values) -- Qn

I5.3 Strength of Stud Qn = 0.5 Asc (f'c Ec) (but not more than Asc Fu)= 0.5 Asc (f'c wc)3/4 (using E = wcl'5 fxc in above formula)

I5.6 Shear Connector = 6 ds LongitudinalPlacement and Spacing = 4 ds Transverse (See LRFD Manual Fig. C-I5.1, pg. 6-177)

AISC-LRFD

Table 2

RULES - F O R M E D M E T A L DECK

(Sections I3.5b and I3.5c)

ITEM RIBS PERPENDICULAR RIBS PARALLEL

1. Concrete Area Below Top of Deck NEGLECT INCLUDE

06wrl, 1} 1.02. Stud Reduction Factor (N0'85 [rrjWrl{SrS- 1}-< 1'0 ' [hrrJ [ h r - - 1224 kip--ft O.K

or from Table page 4-33 for Y2 = 3.5 and TFLOMn = 1230 kip-ft

c. Design for deflection

Initial deflection during construction

19PL3 (19)[(10)(30)(54 + 6)](480)3A=

384Eis (384)(29,000,000)(2100)

= 1.62 in.

Camber 1 1/2 inches.

Composite deflection using Lower Bound Itr (Ilb).

From Table on page 4-46 of LRFD Manual,

with Y2 = 3.5 D.L. = 90 psfPNA = TFL . Construction D.L. = 60 psfIlb = 4780 in4 L.L. = 60 psf

19PL3 (19)[(10)(30)(90 - 60 + 60)1(480)3ATL- 384EI- (384)(29,000,000)(4780)

= 1.07 inches or L/450

ALL= (60/90)(1.07)= 0.71 in. or L/673 O.K.

NOTE: The mooment of inertia using the gross areaequals 5510 in.

Page 8 Steel Tips March 1991

d. Shear Connectors

= AsFy For full composite action

= 1120 kips

( ' " ' 1 [ ]Reduction Factor = 0.6 [hr J[ 1 _< 1.0% /

= 0.6 -1 = 0.8

Use 0.8 for stud reduction factor.

Qn = (0.8)(21.1) = 16.9 kips (See Example 1)

1120No.- - - - - - - 67 StudsQn 16.9

67 Studs are required from Zero to Maximum Moment.

Total = 134 $uds,

Use equal spacing for full length.

e. Check Shear

Vu --- 1.5 (Pu) = 1.5 (61.2) = 92 kips Vn = (0.6 Fy) d tw = (0.9) (0.6) (50) (23.92) (.44)

= 284 kips > 92 kips Q.K.

NOTE: The original Steel Tips design, based upon ASD,used a W27X94 with 92 studs.

Partial Composite Action

Example 3

Design Beam in Example 1 for pfial composite action.

SOLUTION:

a. Determine required shear studs

Estimate number of shear studs for partial composite actionusing the following approximate equation

Mu - Mp ' ,QnNo. [Mn - *Mp ) Qn

Where Mu = Moment demand Mp = Steel Beam Capacity with ) = 0.85 Mn = Full Composite Beam Capacity

Mu = 297 kip-ft{Mp = Fy Z = (0.85) (36) (66.5)/12 = 170 kip-ft{Mn = 356 kip-ft

= AsFy = 371 kips

Qn = 21.1 kips

= [356-170) ,21.1) 0.47 (17.6)= 8.2

Try 9 studs on each 1/2 beam.

Total = 18 studs.

b. Check flexural strength

Qn = (9)(21.1) = 190 kips

From Eq. C-I3-4 in commentary of LRFD Manual

190a = 0.85f'cb- (.85)(3.0)(90)- 0.83 in.

Y2= Yc-a/2= 5.5-0.41 = 5.09

From Table on page 4-23 of the LRFD Manual

for W18X35Y2 = 5.0 - 5.09 in.

Qn = 187 - 190 kips ( PNA = BFL approx.)

) Mn = 296 kip-ft (approx. equal 297 kip-ft required) O.K.

Therefore, partial composite action with 18 total studs isadequate for the required moment.

Steel Tips March 1991 Page 9

c. Check deflection

For deflection computation use the lower bound value givenin the Table on page 4-49 of the LRFD Manual.

For W18x35PNA = BFL +Y2 = 5.0 +_

4Ilb = 1170 in.

A TOTAL = (1775/1170) 0.46 = 0.70 in.ADL = 0.16 in.ALL = 0.54 in. or L/667 O.K.

Obviously any number of studs from 9 (47%) to that for fullcomposite action may be used (per 1/2 Beam Span) with theassociated increase in moment capacity and decrease in de-flection.

Location of. a/2 . effec'ive concreteb

Y2{ m. t 1). . - ' - ' T I ' - - : t (pt s)

...[.. ( Y1(varies - Sgure below)

I I

Y1 = Distance from top of steel flange to any of the seventabulated PNA locations.

qn (@ point 5) + qn (@ point 7) qn (@ point 6) =

2

qn (@ point 7) = .25AsFy

Bo$/l{Top Flange

4equ spaces

I 1 ,, BFLPNA Flange Locations

Figure 10

DISCUSSION

With the use of the First Edition AISC-LRFD manual,composite beam design can be simplified, particularywith partial composite action. As in the past, AISChas tried to incorporate enough tables and charts tomake repetitive design computations easier. Deter-mining preliminary beam sizes, number of weldedstuds and composite beam deflections is now verystraight forward. With a minimum of assumptions (i.e.location to the compressive force, Y2) preliminarycomparative designs can be done in minutes with theuse of the tables.

The reader is encouraged to read the LRFD ManualPART 4 (Composite Design), PART 6 (Specificationsand Commentary), especially Section I on CompositeMembers, and the other references listed. The numberof articles dealing with LRFD composite membersdesign is growing as designers are becoming morefamiliar with the method and the AISC-LRFD manual.

Page 10 Steel Tips March 1991

NOMENCLATURE

AcA'cAsAsc

BFL

CD.L.E

EcFyFu

HsIIbIoItrLL.L.

MnMpMuNr

PPNAQ.

Area of concrete (in.2)Area of concrete modified by modular ratio (in.2)Area of steel (in.2)Area of welded stud (in.2)Bottom of flange locationCompressive force (kips)Dead load (psf)Modulus of elasticity of steel (29,000,00 psi)Modulus of elasticity of concrete (ksi)Minimum yield strength of steel (ksi)Minimum tensile strength of steel (ksi)Welded stud height (in.)Lower bound moment of inertia (in.4)Moment of inertia (in.Transformed moment of inertia (in.4)Span length (ft)Live load (psf)Nominal flexural strength 0dp-ft)Plastic bending moment (kip-fOFactored Moment (Required flexural strength) (kip-ft)Number of stud connectors in one rib at a beamintersection

Factored point load (kips)Plastic neutral axisWelded stud shear capacity (kips)

S.R.F.

TTFLVaVuY1Y2YcZa

b

ddsf'chrntc

tftwWc

Wr

wu

A

Stud reduction factorTensile force (kips)Top of flange locationShear capacity (kips)Shear demand (kips)Distance from top of beam flange (in.)Distance from top of beam to concrete flange force (in.)Total thickness of concrete fill and metal deck (in.)Plastic section modulus (in.3)Effective concrete flange thickness (in.)Effective concrete flange width (in.)Depth of steel beam (in.)Welded stud diameter (in.)Concrete compressive strength at 28 days. (ksi)Nominal rib height of metal deck (in.)Modular ratio (E/Ec)Thickness of concrete above metal deck (in.)Steel beam flange thickness (in.)Steel beam web thickness (in.)Unit weight of concrete (lbs./cu. ft)Average metal deck rib width (in.)Factored uniform load (kip/fODeflection (in.)Resistance factor

,

2.

3.

4.

5.

6.

7.

REFERENCES

"Manual of Steel Construction, "First Edition, AISC, Chicago, 1986.

STEEL TIPS, "Composite Beam Design with Metal Deck," Steel Committee of California, January 1987.

STEEL TIPS, "The Economies of LRFD in Composite Floor Beams," Steel Committee of California, May 1989.

Smith, J.C., "Structural Steel Design - LRFD Approach," John Wiley & Sons, Inc., N.Y., 1991.

Salmon, C. and Johnson, J., "Steel Structures," Third Edition, Harper & Row, N.Y., 1990.

McCormac, J., "Structural Steel Design - LRFD Method," Harper & Row, N.Y.,1989.

Vinnakota, S., et al., "Design of Partially or Fully Composite Beams, with Ribbed Metal Deck, Using LRFDSpecifications," AISC Engineering Journal, 2nd Quarter, 1988.

Steel Tips March 1991 Page 11

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