Concept explainers
The composite shaft shown in the figure is manufactured by shrink-Fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameters of the two parts are dY= 40 mm for the brass core and d2= 50 mm for the steel sleeve. The shear moduli of elasticity are Gb= 36 GPa for the brass and Gs= 80 GPa for the steel.
(a)
Assuming that the allowable shear stresses
in the brass and steel are rb= 48 MPa and
ts= 80 MPa, respectively, determine the maximum permissible torque Tmax that may be applied to the shaft.
(b)
If the applied torque T = 2500 kN · m, find
the required diameter d2so that allowable shear
stress t3is reached in the steel.
(a)
The maximum permissible torque applied to the shaft.
Answer to Problem 3.8.14P
The maximum permissible torque applied to the shaft is
Explanation of Solution
Given information:
The outer diameter of steel sleeve is
Write the expression for total torque of the system.
Here, the total torque in the system is
Write the expression for polar moment of inertia of the brass core.
Here, the polar moment of inertia of brass core is
Write the expression for polar moment of inertia of steel sleeve.
Here, the polar moment of inertia of steel sleeve is
Write the expression for torque on the brass core
Here, the torque in the bar is
Write the expression for torque in the steel sleeve.
Here, the torque in the bar is
Write the expression for maximum shear stress in brass core.
Here, the maximum shear stress in the brass core is
Write the expression for maximum shear stress in the steel sleeve.
Here, the maximum shear stress in the bar is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The maximum permissible torque applied to the shaft is
(b)
The diameter of the steel sleeve.
Answer to Problem 3.8.14P
The diameter of the steel sleeve is
Explanation of Solution
Given information:
The applied torque is
Substitute,
Substitute
Calculation:
Substitute
Conclusion:
The diameter of the steel sleeve is
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Chapter 3 Solutions
Mechanics of Materials - Text Only (Looseleaf)
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