Statics and Mechanics of Materials (5th Edition)
Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 13, Problem 1RP

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.

Chapter 13, Problem 1RP, The post has a circular cross section of radius c. Determine the maximum radius e at which the load

Expert Solution & Answer
Check Mark
To determine

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 c4_.

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.

Statics and Mechanics of Materials (5th Edition), Chapter 13, Problem 1RP , additional homework tip  1

Apply the normal stress

σA=0 (1)

Apply the stress formula as shown below.

σA=PA+MyI (2)

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).

PA+MyI=0 (3)

Determine the area of cross section as shown below.

A=πr2

Here, r is the radius of the cross section.

Substitute c for r .

A=πc2

Determine the moment of inertia as shown in below:

I=π4r4

Substitute c for r .

I=π4c4

Sketch the free body diagram of the moment at the point as shown in Figure 2.

Statics and Mechanics of Materials (5th Edition), Chapter 13, Problem 1RP , additional homework tip  2

Refer to Figure 2.

Find the moment using the calculation.

M=Pe

Substitute P for P, πc2 for A, π4c4 for I, and Pe for M in Equation (3).

Pπc2+(Pe)cπ4c4=0Pπ(1c2+4ec3)=01c2+4ec3=04ec3=1c2

e=c4

Therefore, the maximum radius e at which the load P can be applied is c4_.

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Chapter 13 Solutions

Statics and Mechanics of Materials (5th Edition)

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