Concept explainers
The principal stresses at point A.
Answer to Problem 1RP
The principal stresses at point A
Explanation of Solution
Calculate the normal stress
Here,
Sketch the internal forces and moment in free body diagram at point A as shown in Figure 1.
Apply Equilibrium equations to find the value of moment at point A.
Sum of moments in y-direction is equal to 0.
Sum of moments in x-direction is equal to 0.
Sum of forces in z-direction is equal to 0.
Find the moment of inertia of the section
Outer radius of the pipe is 1.5 in. and the inner radius of the pipe is 1.375 in.
Find the polar moment of inertia of the section
Sketch the cross section at point A as shown in Figure 2.
Find the first moment of area at point A
Here,
Refer to Figure 2.
Substitute
Find the shear stress
Substitute
Sketch the state of stress at point A as shown in Figure 3.
Refer to Figure 3.
The value of normal stresses are
The value of shear stress is
Find the principal stresses
Substitute
Therefore, the principal stresses
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Chapter 9 Solutions
MECHANICS OF MATERIALS
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