problem 2 a beam ab is fixed at point a and free at point b and consis

Question

Problem 2
A beam AB is fixed at point A and free at point B and consists of an outer steel tube and an
aluminum core. They are press-fitted, so there is no sliding at the interface between the aluminum
core and the steel tube. The geometry and cross-section of the shaft is shown in Figure 2. The
shaft is subjected to a torque at its free end equal to T₁-300 N-m. The shear modulus of clasticity
for the two materials are: Gel-78 GPa and Galuminum - 28 GPa.
c=50 mm
c=45 mm
B
Aluminum
Steel
2.5 m
Figure 2. Shaft subjected to torque at its end.
Given the information provided above
(a) Find the absolute maximum shear stress in the steel tube.
(b) Find the absolute maximum shear stress in the aluminum rod.
(c) Find the angle of twist (in degrees) at point B due to Ta
(d) For this part assume that the shaft length is unknown, but that the radii and material
properties for the aluminum rod and the steel tube remain the same. If the absolute value
of the allowable angle of twist at B is equal to quAll-1.5 x 10³ rad, find the maximum
length the shaft can have when subjected to a T₁-300 N-m at its free end B.