Concept explainers
The post has a circular cross section of radius c. Determine the maximum radius e at which the load P can be applied so that no part of the post experiences a tensile stress. Neglect the weight of the post.
Find the maximum radius e at which the load P can be applied.
Answer to Problem 1RP
The maximum radius e at which the load P can be applied is
Explanation of Solution
Given information:
The post has a circular cross section of radius c.
Neglect the weight of the post.
Calculation:
Sketch the Free Body Diagram of the applied load P as shown in Figure 1.
Apply the normal stress
Apply the stress formula as shown below.
Here, P is the applied load, A is the area of the cross section, M is the moment at the point, y is the centroid, and I is the moment of inertia.
Equate the Equation (1) and (2).
Determine the area of cross section as shown below.
Here, r is the radius of the cross section.
Substitute c for r .
Determine the moment of inertia as shown in below:
Substitute c for r .
Sketch the free body diagram of the moment at the point as shown in Figure 2.
Refer to Figure 2.
Find the moment using the calculation.
Substitute
Therefore, the maximum radius e at which the load P can be applied is
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