Concept explainers
A steel pipe of 12-in. outer diameter is fabricated from
Fig. P7.158
Fund the normal and in-plane shearing stresses, normal and tangential stress to the weld.
Answer to Problem 158RP
The normal stress in x-axis is
The normal stress in y-axis is
The shearing stress in xy-plane is
The normal stress in the weld is
The tangential stress in the weld is
Explanation of Solution
Given information:
The outer diameter of the steel pipe is
The thickness of the plate is
The plate makes an angle with plane perpendicular to the pipe is
The magnitude of the axial force P is 40 kips.
The torque applied in the pipe T is 80 kip-in.
Calculation:
Find the inner diameter of the steel
Substitute 12 in. for
Find the area of the steel pipe (A) using the equation.
Substitute 12 in. for
Find the polar moment of inertia (J) of the steel pipe using the equation.
Substitute 12 in. for
Find the normal stress
Substitute 40 kips for P and
The normal stress in x-axis is
The normal stress in y-axis is
Find the shearing stress
Substitute 80 kip-in. for T, 12 in. for
The shearing stress in xy-plane is
Show the stress element for pipe as in Figure 1.
Therefore,
The normal stress in x-axis is
The normal stress in y-axis is
The shearing stress in xy-plane is
Consider the axes
The normal stress in weld is
The shearing stress in weld is
Find the normal stress in the weld using the equation.
Substitute 0 for
Find the tangential stress in the weld using the equation.
Substitute 0 for
Show the stress element for weld as in Figure 2.
Therefore,
The normal stress in the weld is
The tangential stress in the weld is
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Chapter 7 Solutions
Mechanics of Materials, 7th Edition
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