The beam loaded as shown below experiences maximum bending stress at the point 9

Question

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?

Explanation / Answer

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

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