Concept explainers
The assembly ABC is made of a steel for which E = 200 GPa and σY = 320 MPa. Knowing that a strain energy of 5 J must be acquired by the assembly as the axial load P is applied, determine the factor of safety with respect to permanent deformation when (a) x = 300 mm, (b) x = 600 mm.
Fig. P11.15
(a)
Find the factor of safety with respect to permanent deformation when
Answer to Problem 15P
The factor of safety with respect to permanent deformation 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 yield strength of steel is
The strain energy acquired by the assembly is
Calculation:
Calculate the area of the rod (A) as shown below.
For the steel rod AB.
Substitute
For the steel rod BC.
Substitute
Hence, the minimum area of the rod
Calculate the load
Substitute
Calculate the strain energy
Calculate the strain energy for rod ABC as shown below.
Substitute
Calculate the factor of safety
Substitute
Therefore, the factor of safety with respect to permanent deformation is
(b)
Find the factor of safety with respect to permanent deformation when
Answer to Problem 15P
The factor of safety with respect to permanent deformation 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 yield strength of steel is
The strain energy acquired by the assembly is
Calculation:
Refer to part (a).
The area of the steel rod AB is
The area of the steel rod BC is
The load acting on the assembly is
Calculate the strain energy
Substitute
Calculate the factor of safety
Substitute
Therefore, the factor of safety with respect to permanent deformation is
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Chapter 11 Solutions
Mechanics of Materials, 7th Edition
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