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.