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A beam carrying a uniform load is simply supported with the supports set back a distance a from the ends as shown in the figure. The bending moment at x can be found from summing moments to zero at section x. ΣM=M+21​ω(a+x)2−21​ωlx=0 or M=2ω​(lx−(a+x)2)​ where ω is the loading intensity in Ibf/in. The designer wishes to minimize the necessary weight of the supporting beam by choosing a setback resulting in the smallest possible maximum bending stress. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
If the beam is configured with a=4.05 in, 1=18 in, and w=170 lbf/in, find the magnitude of the severest bending moment in the beam. The magnitude of the severest bending moment in the beam is Ibfin,