Help with Steels Homework
Wondering if any of you could help me out with some Steel Design homework. We don't have a book, only the AISC Manual so I don't really have any examples to help me. The assignment is due Wednesday, and unfortunately the professor doesn't have office hours on Tuesdays. Anyways heres the problem.
Find the allowable bending strength of an 8.0 ft long W18X55 beam of A992 steel. The simply supported beam is laterally braced at its supports only and is subjected to a uniformly distributed load, w, in plf. Considering bending only, what is the allowable total distributed load, wa, that it can support?
My work thus far:
W18X55 beam (all of this is straight out of the manual.)
Fy = 50 ksi
Zx = 112 in^3
Lb = 8 ft
Lp = 5.9 ft
Lr = 17.6 ft
Lp < Lb < Lp therefore it is inelastic LTB
Mn/Ω = Cb[(Mp/Ω)-(BF/Ω) (Lb-Lp)] ≤ Mp/Ω
Mp/Ω = 279 kip-ft
BF/Ω = 9.15 kip
Lb = 8 ft
Lp = 5.90 ft
Cb = 1.14
Mn/Ω = 1.14 [279 - 9.15(8 - 5.90)] = 296 kip-ft
With my calculation it shows that Mn/Ω ≥ Mp/Ω, which my professor said could never happen and this is where I am stuck.
Any help will be greatly appreciated.