Problem 9 Select the lightest equally spaced filler beam Bea

Problem 9 Select the lightest equally spaced filler beam, \"Beam 1.\" A992 steel The loads shown do not include beam self-weight. Live load reduction applies. Loads Slab + Deck- 65 psif Mech. -6 psf Ceiling- 5 psf Misc. - 2 psf Live Load-150 psf 27\" Beam 1 a. Select a trial section based on b. Evaluate the trial section for c. Evaluate the trial section for flexural strength. construction load deflection. live load deflection, which 31\' Partial Floor Framing Plan 30\" (Not to Scale) cannot exceed L/360

Solution

a)dead load = 65+6+5+2=78 psf

live load = 150 psf

factored load = (1.2*78)+(1.6*150)=333.6 psf

tributary width of beam = 27/3=9 ft

factored load on beam1=333.6*9=3002.4 plf=3 kip/ft

maximum moment in beam = 3*30²/8=337.5 kip-ft

the lightest beam that has bending capacity greater than 337.5 kip-ft is W21x44

b)construction load = 65 psf (dead load) + 20 psf (live load)=85 psf

uniform construction load on beam =(85*9)+44=809 plf=0.809 kip/ft=0.067 kip/in

moment of inertia of beam = 843 in⁴

deflection ob beam 1 for construction load = (5/384)*0.067*(30*12)⁴/(29000*843)=0.603 in

c)live load on beam = 150*9=1350 plf=0.1125 kip/in

deflection of beam = (5/384)*0.1125*(30*12)⁴/(29000*843)=1 in

L/360=(30*12)/360=1\"

therefore, the beam deflection due to live load is at the limit of L/360