Question

5. A straight round shaft is subjected to a torque of 5000 lb - in. Determine the required diameter, using steel with a tensile yield strength of 60 ksi and a safety factor of 2 based on initial yielding: (a) According to the maximum-normal-stress theory. (b) According to the maximum-shear-stress theory. (c) According to the maximum-distortion-energy theory. Discuss briefly the relative validity of the three predictions.

Answer 1

a. 0.95 in

b. 1.19 in

c. 1.137 in

Step-by-step explanation:

Express the factor of safety equation for maximum-normal-stress theory as:

S SF = Eau

Here, the factor of safety is SF, the yield strength is S„ and the maximum stress :I

Modify the above equation for shear stress acting on the solid rod as:

S. SF = To

Here, the combined shear stress on solid rod s

Calculate the combined shear stress for solid rod.

16T r2:1 = trd3

(1)

Here, the torque is T, and the diameter of the solid rod is d.

Substitute 5,000 'bin. for T.

— 16(5,000 lb • in ) v ird 80 000lb - in. _

rd3

60ksi 2 — 80,000lb -in. trd

Solve the above equation for d.

60 x 1031bAn? 80,00016 -in. ird3 — 2(80, 000 lb in.) d3 rrt60x103Ibfln?)

v3 d —[ 2(80,000lb-in.) rz-(60 x103112,An?) = 0.8488 in.3r3 =0.95 in.

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