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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.
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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
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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
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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
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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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