The beam loaded as shown below experiences maximum bending s

The beam loaded as shown below experiences maximum bending stress at the point 9ft to the right or point A Calculate the internal shear B moment in the beam at this point. Considering only the maximum tensile/compressive stress sigma, calculate the minimum value of section modulus that provides a factor of safety of 1.2 with respect to yielding. Then choose the most economical wide flange beam (A36 steel: sigma y = 36 ksi E = 29,000 ksi) that meets this requirement. For the wide flange beam geometry selected in part (B) what is the maximum transverse shear stress in the beam at point C?

Solution

First calculate Reaction at RB at B Take moments about E Forces acting are 20kip at point A at distance of 13 ft from E Uniformly distributed load of 60Kips with CG at a distance of 5ft from E 20kip force at distance of 2 ft from E Rb at a distance of 10 ft from E Rb = (20x13+60*5+20x2)/10 60 kip Re = Reaction at E =(20+60+20)-60 40 kip Part (a) Shear Force at 9ft from A =-20+60-10*4 0 kip Bending Moment at 9ft From A = 20*3-(60-20)*6+40*2 -100 KipFt 1200000 lbin Steel Yield Strength y 36 ksi E 29000 ksi Factor of saety 1.2 Allowable Max Stress 30 ksi 30000 Lbin Section Modulus =Bending Moment/Allowable stress 40 in3 The following sections have suitable section modulus W16x31 Wt/Ft length = 31 W14x30 W16x31 Wt/Ft length = 30 W12x35 Wt/Ft length = 35 W10x39 Wt/Ft length = 39 Part (b) Chose Economical Section with minimum weight W14x30 Find Max Shear stress at Point C Shear Force at Point C = (-20+60) 40 Kips 480000 Lbin Iz = Moments of Inertia from tables 291 in4 h= height of section 13.84 in Part © Shear Stress = Shear Force xh2/(8Iz) 39493.9381 psi