problem 1 a shaft abcd is supported by a clamp at point a and is subje

Question

Problem 1
A shaft ABCD is supported by a clamp at point A and is subjected to point torques at B, C and D,
as shown in the figure. The shaft has variable cross-section and is solid in segments AB and CD
and hollow in segment BC. The lengths and diameters of each segment are shown in the figure.
Assume that the deformation is linear elastic and take the shear modulus of elasticity G = 12.1 x
10⁰ psi.
a) Using method of sections, plot the torsion moment diagram.
b) Find the angle of twist for the free end (point D) with respect to the fixed support at A, AD
and the angle of twist for point C with respect to the fixed support at A, QC/A. Find both
angles in degrees.
d₁ = 4 in
A
20 in
d₂0 = 3.5 in, d₂ =2.5 in
20 kip-in
25 kip-in
B
25 in
с
30 in
Figure 1. Shaft with variable cross-section
d₂ = 3.0 in
D
10 kip-in