Question

A steel shaft 50 mm diameter and 500 mm long is subjected to a twisting moment of 1100 n-m, the total angle of twist being 0.6 find the maximum shearing stress developed in the shraft and modulus,

Answer 1

The question involves calculating the maximum shearing stress and modulus for a steel shaft subject to a twisting moment by using the formulas for shear stress and shear modulus in relation to the dimensions and properties of the shaft.

Step-by-step explanation:

The student's question involves calculating the maximum shearing stress and modulus of a steel shaft subjected to a twisting moment. To find the shear stress (τ), we can use the formula τ = T*r/J, where T is the twisting moment, r is the radius of the shaft, and J is the polar moment of inertia for a circular cross-section. The modulus, specifically the shear modulus (G), relates to the total angle of twist (θ) using the formula G = T*L/(J*θ), where L is the length of the shaft.

To calculate these values:

• Maximum shearing stress: τ = T*r/J, with T = 1100 N-m, r = 25 mm (0.025 m), and J for a circular cross-section is π*r^4/2.
• Modulus (shear modulus G): G = T*L/(J*θ), with L = 500 mm (0.5 m) and θ = 0.6 radians.

Substitute the known values into the formulas to find the maximum shearing stress and shear modulus of the steel shaft.