The allowable stresses that are generally used in practice are 4 ksi for main power transmitting shaft, 6 ksi for line shaft carrying pulleys and 8.5 ksi for small short shaft/countershaft, etc. With these allowable stresses what will be the simplified formula to determine transmitted HP, diameter of the shaft or even the rpm(N)?

A shaft is subjected to a maximum torque of 14 KN-m and a maximum bending moment of 10 KN- m at 
a particular section. Determine the diameter of the shaft according to maximum shear stress theory if the 
elastic limit in simple tension is 180 MPa

The boom AC is a 4-in. square steel tube with a wall thickness of 0.25 in. The boom is supported by the 0.-in, diameter pin at A, and the 0.375-in diameter cable BC. The working stresses are 25 ksi for the cable. 18ksi for the boom, and 13.6 ksi for shear in the pin. Neglecting the weight of the boom, determine the largest safe load P that can be applied as shown. 

A simply supported beam having a span l =3.6m is to carry a uniformly distributed load of
intensity w = 1600kg/m. The cross-section is to be rectangular with depth h and width b = h/2. If
the allowable bending stress in tension or compression is σ w = 84 kg/cm 2 . What is the required
depth h for the cross-section?