Concept explainers
A 5-in.-diameter pipe is supported every 9 ft by a small frame consisting of two members as shown. Knowing that the combined weight of the pipe and its contents is 10 lb/ft and neglecting the effect of friction, determine the magnitude and location of the maximum bending moment in member AC.
Fig. P7.17
The bending moment of the couple exerted at the point
Answer to Problem 7.17P
The magnitude of the bending moment of couple exerted at the point
Explanation of Solution
Sketch the free body diagram for the
Write the equation of the axial force exerted at the axial point of the pipe from x direction.
Here, the pipe is supported by a small frame on the member is
Write the equation of the axial force exerted at the point on the pipe from y direction.
Here, the force exerted on the pipe at y direction in equilibrium condition is
Sketch the free body diagram for the frame as shown in the Figure 2.
Write the equation of the moment of couple formed in the bending moment of the frame at the point
Here, the force exerted on the member of the pipe at point
Write the equation of the axial force exerted at the point on the pipe from y direction (Refer fig 2).
Here, the force exerted on the member of the pipe on frame at the point
Write the equation of the axial force exerted at the axial point of the pipe from x direction (Refer fig 2).
Sketch the free body diagram for the member of the frame from the point
Write the equation of the moment of couple formed in the bending moment supported at the point
Here, the distance of the frame
Sketch the free body diagram for the member of the frame from the portion
Write the equation of the moment of couple formed in the bending moment supported at the point
Sketch the free body diagram for the member of the frame from the portion
Write the equation of the moment of couple formed in the bending moment supported at the point
Conclusion:
Substitute
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Substitute
Therefore, the magnitude of the bending moment of couple exerted at the point
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Chapter 7 Solutions
Vector Mechanics for Engineers: Statics, 11th Edition
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