(a)
Find the maximum deflection of end C.
(a)
Answer to Problem 46P
The maximum deflection of end C is
Explanation of Solution
Given information:
The mass of the collar D is
The modulus of elasticity of the steel rod is
The length of the rod AB is
The length of the rod BC is
The diameter of rod AB is
The diameter of rod BC is
Calculation:
Consider the acceleration due to gravity as
Calculate the weight of the collar (m) as shown below.
Substitute
Calculate the cross sectional area
For rod AB.
Substitute
For rod BC.
Substitute
The rod BC has the minimum area
Calculate the deflection
For rod AB.
Substitute
For rod BC.
Substitute
Calculate the maximum deflection
Substitute
Sketch the Free Body Diagram of the rod after deformation as shown in Figure 1.
Refer to Figure 1.
Calculate the strain energy
Substitute
Consider that the distance
Calculate the maximum deflection
Substitute
Hence, the maximum deflection of end C is
(b)
The equivalent static load.
(b)
Answer to Problem 46P
The equivalent static load is
Explanation of Solution
Given information:
The mass of the collar D is
The modulus of elasticity of the steel rod is
The length of the rod AB is
The length of the rod BC is
The diameter of rod AB is
The diameter of rod BC is
Calculation:
Refer to part (a).
The maximum deflection of end C is
Calculate the static load
Substitute
Substitute
Therefore, the equivalent static load is
(c)
The maximum stress occurs in the rod.
(c)
Answer to Problem 46P
The maximum stress occurs in the rod is
Explanation of Solution
Given information:
The mass of the collar D is
The modulus of elasticity of the steel rod is
The length of the rod AB is
The length of the rod BC is
The diameter of rod AB is
The diameter of rod BC is
Calculation:
Refer to part (a).
The minimum area of the rod is
Refer to part (b).
The equivalent static load is
Calculate the maximum stress
Substitute
Therefore, the maximum stress occurs in the rod is
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Chapter 11 Solutions
Mechanics of Materials, 7th Edition
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