Concept explainers
Two sections of steel drill pipe, joined by bolted flange plates at B, arc subjected to a concentrated torque 4000 kip-in. at x = 3 ft, and a uniformly distributed torque t0= 50 kip-ft/ft is applied on pipe BC. Let G = 11,800 ksi and assume that pipes AB and BC have the same inner diameter, d = 12 in. Pipe AB has a thickness tAB= 3/4 in., and pipe BC has a thickness tBC= 5/8 in. Find the reactive torques at A and C and the maximum shear stresses in each segment.
The reaction torque at A and the reaction torque at B .
The twist angle at the center of the bar.
Answer to Problem 3.8.9P
The reaction torque at A is
The twist angle at the center of the bar is
Explanation of Solution
Given information:
The concentrated torque is
Write the expression for polar moment of inertia of left bar.
Here, polar moment of inertia of the left bar is
Write the expression for polar moment of inertia of right bar.
Here, polar moment of inertia of the right bar is
Write the equilibrium Equation for torques.
Here, torque at A is
Write equilibrium equation for AD .
Here, torque at D is
Write equilibrium equation for DB .
Write the equilibrium Equation for BC .
Here, torque in segment BC is
Write the expression for angle of twist for AD .
Here, angle of twist is
Write the expression for angle of twist for B .
Here, angle of twist is
Substitute
Write the expression for angle of twist for BC .
Write the compatibility equation for angle of twist.
Here, angle of twist for C is
Write the expression for maximum shear stress in AB .
Here, maximum shear stress is
Write the expression for maximum shear stress in BC .
Here, maximum shear stress is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The reactive torque at A is
Negative sign is due to selected coordinate.
Substitute
The obtained torque is negative so reverse the direction of torque.
The reactive torque at C is
Substitute
The maximum shear stress in segment AB is
Substitute
The maximum shear stress in the segment BC is
Conclusion:
The reactive torque at A is
The reactive torque at C is
The maximum shear stress in segment AB is
The maximum shear stress in the segment BC is
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Chapter 3 Solutions
Mechanics of Materials (MindTap Course List)
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