Question

A beam has the cross section shown. If it is made ofsteel that has an allowable stress of σ allow=24 ksi,determine the largest internal moment the beam can resist if themoment is applied (a) about the z axis,(b) about the y axis. I need some help here if someone could get it started and couldshow me how to finish it it would be a huge help. Thanks.

Answer 1

Moment of inertia about z-axis, I_z = 1/12 * (6) *(6.5³) - 1/12 * (5.75) *(6³)
                                               I_z = 33.8125 in⁴

Moment of inertia about y-axis, I_y = 2 [1/12* (0.25) * (6³)] + 1/12 * (6) * (0.25³)
                                               I_y = 9.0078 in⁴

(a)When moment is applied about the z-axis:
   M_z = (σ * I_z)/c
           = 24 *(33.8125)/3.25
           =249.7 kip.in = 20.8 kip.ft

(b) When moment is applied about the y-axis:
      M_y = (σ *I_y)/c
           = 24 * (9.0078)/3
           = 72.0625 kip.in = 6 kip.ft

I hope now you know how to calculate for the answer.In case of any confusion let me know.