A beam with regular cross section is under fluctuating bending moment with a max

Question

A beam with regular cross section is under fluctuating bending moment with a maximum and minimum moments of 1800 lb in and 600 lb in respectively. The material is AISI 1020 hot-rolled steel having yield and ultimate strengths of 30 ksi and 55 ksi respectively. The corrected endurance strength not accounting for fatigue stress concentration corrections is 20 ksi. The fatigue stress concentration factor is 1.2. If the thickness of the beam is specified to be 0.5 in, the determine the height of the beam, using a safety factor of 2, Under fluctuating load conditions using Soderberg and Goodman criteria. Also, under a static equivalent mean value of bending moment.

Explanation / Answer

FOr a rectangular beam under bending, s=Mc/I=M(h/2)/(bh3/12) =6M/(bh2) sa = 6Ma/(bh2)=6(600)/(0.5h2) = 7200/h2 sm = 6Mm/(bh2)=6(1200)/(0.5h2) = 14400/h2

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