Question

the allowable shearing stress is 15 ksi in the 1.5-in.-diameter steel rod ab and 7.2 ksi in the 1.8-in.-diameter brass rod bc. neglecting the effect of stress concentrations, determine the largest torque t that can be applied at a. T A Steel B Brass The largest torque T that can be applied at A is 0.55 * kip-in.

Answer 1

0.55 kip-in

Step-by-step explanation:

To determine the largest torque T that can be applied at A, we need to consider the allowable shearing stress for both the steel rod AB and the brass rod BC.

First, we need to calculate the cross-sectional area of each rod. For the steel rod AB, the cross-sectional area is:

A = π * (d/2)^2 = 3.14 * (1.5/2)^2 = 1.77 in^2

For the brass rod BC, the cross-sectional area is:

A = π * (d/2)^2 = 3.14 * (1.8/2)^2 = 2.52 in^2

Next, we need to calculate the maximum allowable shear force for each rod based on the allowable shearing stress. For the steel rod AB, the maximum allowable shear force is:

F = A * σ = 1.77 in^2 * 15 ksi = 26.55 kips

For the brass rod BC, the maximum allowable shear force is:

F = A * σ = 2.52 in^2 * 7.2 ksi = 18.144 kips

Finally, we can use these values to calculate the maximum torque that can be applied at A:

T = F * r = 18.144 kips * 1.8 in = 0.55 kip-in

Therefore, the largest torque T that can be applied at A is 0.55 kip-in.