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 "Composite Beam 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 and Resistance Factor Design (LRFD) Method. The purpose is to show the design procedure, the advantages 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 width 2. Shored and unshored construction requirements 3. Lower bound moment of inertia may be utilized. A number of papers have been written about these differences and the economies of the LRFD method. The reader is referred to the list of references included.
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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.
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)
NOTE: The purpose and advantage of using the lower bound Itr value found in the LRFD Manual tables is to avoidthe above computations. If the deflections using the lower bound Itr are acceptable, the actual deflectionswill be conservatively less. Lower bound Itr is based upon the area of the beam and an equivalent concrete
area of and is applicable for full as well as partial composite action.
Page 6 Steel Tips March 1991
Example 2.
Design a composite interior girder (without cover plate) for anoffice building. See Girder B in Figure 1. The 3-inch deck ribsare oriented paralled to the girder. Girder is assumed loaded asshown in Figure 7.
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 ,, BFL
PNA 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
Ac
A'cAs
Asc
BFL
C
D.L.E
EcFy
Fu
Hs
IIbIoItrL
L.L.
MnMp
MuNr
P•
PNAQ.
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 location
Compressive 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-fO
Factored Moment (Required flexural strength) (kip-ft)Number of stud connectors in one rib at a beamintersection
Factored point load (kips)Plastic neutral axis
Welded stud shear capacity (kips)
S.R.F.
TTFL
VaVuY1
Y2
Yc
Za
b
d
dsf'c
hrn
tc
tf
twWc
Wr
wu
A
Stud reduction factor
Tensile 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.)
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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