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Problem 1: Select a W-shape beam for the following load scenario. Assume there is bracing at the ends and at midspan. Use A992 steel. The deflection limit is given as L/360. (35 points) DL = 0.75 k/ft LL = 1.00 k/ft 15 ft 15 ft a. Using AISC LRFD, compute the factored design load, Mu, acting on the member. (ANS. b. What section would you select if you did not consider the moment gradient? (ANS. c. Account for the moment gradient by calculating the lateral torsional buckling d. Would a W14x48 be adequate? (ANS. Yes. Mu < фМп, Vu < фу,, and < 300) M-281 kips) W18x55) modification factor, Cb, what section would you now select? (ANS. W14x48)

Answer 1

(a)

W_u=1.2(D.L)+1.6(L.L)

W_U=1.2(.75)+1.6(1)

W_u=2.5 kip/ft

M=W_uL²/8

M=2.5x(30)²/8

M=281.25 ft-kips

(b)

Shear of the beam=wL/2=2.5x30/2=37.5 kips

Deflection limit=L/360=30X12/360=1 in

Select a W section based on Zx value:

Zx>M/(F_y)

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Zx>281.25x12/(0.9x50)

Zx>75 in³

The Section should have design strength more than 281 kip-ft

The section should have shear 37.5 kips

The section should have live load deflection less than 1 in

All these are satisfied by W18X55 only

(c)

Consider for the moment gradient

Cb=1.30 for UDL with simply supported beam and braced at middle

M/C_b=281.25/1.30=216.3 ft-kips

The Zx value for the beam should be greater than 75 in³ from the previous step,and the LRFD moment value should be greater than 281 ft-kips

there are two possibilities

W14X48 and W12X53,for design purposes prefer the steel which is having lesser weight

Prefer W14X48

(d)

Adequacy of W14X48

M_u=281 ft-kips

M=F_yZ_x=50x78.4=3920 in-kips

Design strength=0.9*3920/12=294 ft-kips

So M_n>M_u (This is safe)

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Shear:

Shear force=WL/2=2.5x30/2=37.5 kips

From the Zx tables, V_n=141 kips

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V_n>V_u

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So it is safe in shear

Deflection:

Maximum permissible deflection=L/360=30*12/360=1 in

Deflection =5wL⁴/384EI=5x1/12x(30x12)⁴/384x29000x484=1.30 in

W14X48 is not adequate in live load deflection, adopt for sections having higher moment of inertia