Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.
The maximum shear stress.
The maximum angle of twist.
Answer to Problem 3.4.8P
The maximum shear stress is
The maximum angle of twist is
Explanation of Solution
Given information:
The concentrated torque is
Write the expression for torque at B.
Here, torque at B is
Write the expression for torque at AD.
Here, torque at AD is
Write the expression for polar moment of inertia of section BC .
Here, polar moment of inertia is
Write the expression for polar moment of inertia of section AB .
Here, polar moment of inertia is
Write the expression for maximum shear stress for section BC .
Here, maximum shear stress for section BC is
Write the expression for maximum shear stress for section BC .
Here, maximum shear stress for section BC is
Write the expression for angle of twist.
Here, function for angle of twist is
Write the expression for angle of twist.
Write the expression for angle of twist.
Here, dummy variable is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
The maximum shear stress in section AB is
Substitute
The maximum shear stress in section BC is
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The maximum angle of twist occurs at C .
Convert twist angle in degrees.
Conclusion:
The maximum shear stress is
The maximum angle of twist is
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Chapter 3 Solutions
Mechanics of Materials (MindTap Course List)
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