Question

Q4) Select a W-shape beam for the following conditio Beam spacing 8 ft - Span length 32 ft Slab and deck combination weight- 50 psf Partition load 20 psf; - Ceiling weight 7 psf Live load 120 psf; The maximum live load deflection cannot exceed L/360. F, = 50 ksi

structural design in steel

Answer 1

GIVEN DATA Properties of Steel section Grade of steel Span of beam, Beam spacing Slab & deck weight Partition load, Ceiling weight Live Load Live load deflection limit A 992 32 ft 8 ft 50 psf 20 psf 7 psf 120 psf L/ 360 CALCULATIONS Yield stress of steel Modulus of Elasticity of steel 50 ksi E29000 ksi 77 psf x 0.616 kip/ft W120 psf x - 0.96 kip/ft Total Dead Load (udl), 8 ft Live load (udl), 8 ft W 1.2 wD +1.6 w Factored Load 2.275 kip/ft Factored moment = 2.275 x 322 291.2 ft-kips Assume "compact section" that is S, or both the flange and the web Design strength of beam is Taking Therefore, required plastic section modulus is: = 29 1.2 x 12 0.90 x 50 77.66in 2 Select section such that Z>Z (required) Beam Section Plastic section modulus Moment of inertia, Width/thickness ratios W 21x 44 z, = 95.4 in 843 in b,/2tf-7.22 h/t53.6

heck for compact secti 65 L = 7.22 < [ λ,- 2t = 9.19 ] OK 640 λ 53.6 < [ケー 90.51 OK Hence, the section is COMPACT Dead load including self-weight, 1000 wo = 0.616 t 0.66 kip/ft Factored Load w, = 1.2 w D +1.6 WL 2.328 kip/ft Factored moment 2.328 x 322 298 ft-kips Design strength of beam x 50 12 ft-kips 0.9 x 95.4 357.75 ft-kips SAFE 298 ft-kipsM Hence CHE R DEFLECTION SERVICE LOAD Total service load, 0.616 + 0.044+ 0.96 w - 1.62 kip/ft Maximum deflection (at mid-span) 384EI 5 x 1.62 /12) 32 x 12 29000 х 1.563 in > 1.067 in [:L/360 384 x 843 Hence, NOT SATISFIED 5 1.62 /12)0 Hence,revised moment of inertia, 32 x 12 384 x 29000 x 1.067 1236 in Select section such that l > Beam Section Moment of inertia, required) W 24x 55 = 1350 in 4 Maximum deflection (at mid-span) 384EI -5 x (1.62 /12) 32 x 12 384 X 0.976 in < 29000 x 1350 [=1 / 360 ] 1.067 in

Hence, SATISFIED W 24x 55 Hence, selected beam size is: