Using E = 200 GPa, determine (a) the strain energy of the steel rod ABC when P = 25 kN, (b) the corresponding strain-energy density in portions AB and BC of the rod.
Fig. P11.10
(a)
The strain energy of the steel rod ABC.
Answer to Problem 10P
The strain energy of the steel rod ABC is
Explanation of Solution
Given information:
The diameter of the steel rod AB is
The diameter of the steel rod BC is
The length of the rod AB is
The length of the rod BC is
The modulus of elasticity of the steel is
The applied load
Calculation:
Calculate the area of the rod (A) as shown below.
For the steel rod AB.
Substitute
For the steel rod BC.
Substitute
Calculate the strain energy (U) as shown below.
Calculate the strain energy for rod ABC as shown below.
Substitute
Therefore, the strain energy for the steel rod ABC is
(b)
The strain energy density in rod AB and rod BC
Answer to Problem 10P
The strain energy density in rod AB is
The strain energy density in rod BC is
Explanation of Solution
Given information:
The diameter of the steel rod AB is
The diameter of the steel rod BC is
The length of the rod AB is
The length of the rod BC is
The modulus of elasticity of the steel is
The applied load
Calculation:
Refer to part (a).
The area of rod AB is
The area of the rod BC is
Calculate the stress
For the rod AB.
Substitute
For the rod BC.
Substitute
Calculate the strain energy density (u) as shown below.
For the rod AB.
Substitute
Hence, the strain energy density in rod AB is
For the rod BC.
Substitute
Therefore, the strain energy density in rod BC is
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Chapter 11 Solutions
Mechanics of Materials, 7th Edition
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