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.

a. 0.95 in

b. 1.19 in

c. 1.137 in

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.  

check the attached files for clear cut details

energy can cross the boundaries of a closed system in the form of heat and mass

explanation: