I need a full solution for the question. Full solution will be rated A thin, hig

Question

I need a full solution for the question. Full solution will be rated

A thin, high-strength steel rule (E = 30 times 106 psi) having thickness t = 0.175 in. and length L = 48 in. is bent by couples M0 into a circular are subtending a central angle alpha = 40 degree what is the maximum bending stress sigmamax in the rule? By what percent does the stress increase or decrease if the central angle is increased by 10%? What percent increase or decrease in rule thickness will result in the maximum stress reaching the allowable value of 42 ksi?

Explanation / Answer

(a)

=L/ =48/(40/180)= 68.755 in.

max_a = E[(t/2)/] = (30,000 ksi) [(0.175/2)/68.755] = 38.2 ksi

(b)

=L/(1.1) = 62.504 in.

max_b = E[(t/2)/] = (30,000 ksi) [(0.175/2)/62.504] = 42.0 ksi

(max_b-max_a)/max_a = 10%

(c)

a =E[(tc/2)/] = 42 ksi

30000[(t/2)/68.755] = 42   =>

tc = 0.193 in.

(tc-t)/t = 10%

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