solve these Calculate the adequacy using the LRFD requiremen

solve these

Calculate the adequacy using the LRFD requirements of a W 12x58 beam that carries a service dead load of 0.45 kip/ft and a service live load of 0.35 kip/ft. The beam is 30 feet long and braced 4 feet from each end of the beam (i.e., 4 feet from A and for feet from B, with A and B being the two end points of the beam). The Modulus of Elasticity is 29 000 ksi and Fy is 50 ksi.

Solution

Given section is W12x58

dead load = 0.45 kip/ft

live load = 0.35 kip/ft

moment at beam due to dead load = 0.45*30²/8=50.625 kip-ft

moment at beam due to live load = 0.35*30²/8=39.375 kip-ft

design moment in beam = (1.2*50.625)+(1.6*39.375)=123.75 kip-ft

unbraced length of beam = 30-4-4=22 ft

Moment capacity of beam for unbraced length of 22ft = 324-(324-205)/(29.8-8.87)*(22-8.87) = 249.3 kip-ft

The beam is adequate because strength is more than design moment