The solid steel shaft fits loosely inside of the aluminum tube as shown. Both the shaft and tube are rigidly constrained at the left end.
A pin is installed through pre-drilled holes in the tube and shaft at the right end. Due to assembly tolerances the holes in the tube and shaft had an angular misalignment.
A torque, T0, of 800 Nm was applied to the steel shaft in order to align the holes and install the pin. After installation of the pin the torque was released from the steel shaft.
Based on the information provided, select the most apporpriate responses to the following questions.
Modulii of Rigidity:
Steel: G=80 GPa
Aluminum: G=28 GPa
The magnitude of the maximum torsional shear stress developed in the steel shaft during the assembly process prior to insertion of the pin will be equal to:
A) 31.8 MPa
B) 63.7 MPa
C) 78.6 MPa
D) 109 MPa
E) None of the choices are within 10% of the correct value
The polar moment of inertia for the aluminum tube will be equal to 5.39 x 10-7 m4.
The magnitude of the maximum torsional shear stress developed in the aluminum tube in the final assembled condition will be equal to:
A) 63.8 MPa
B) 38.6 MPa
C) None of the choices are within 10% of the correct value
D) 91.3 MPa
E) 18.5 MPa
The polar moment of inertia for the steel shaft will be equal to 2.51 x 10-7 m4.
The magnitude of the angle of twist developed in the steel shaft in order to install the pin will be equal to:
A) None of the choices are within 10% of the correct value
B) 6.85 degrees
C) 2.30 degrees
D) 4.38 degrees
E) 3.14159 degrees
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