Concept explainers
(a)
Find the maximum deflection at point C of the cylindrical portions.
(a)
Answer to Problem 107P
The maximum deflection at point C of the cylindrical portions is
Explanation of Solution
Given information:
The cross sectional area AC and BC of each portions is
The modulus of elasticity (E) for portion AC is
The yield stress
The modulus of elasticity (E) for portion CB is
The yield stress
Calculation:
Calculate the displacement at point C to cause yielding of AC using the relation:
Here,
Substitute
Find the corresponding force along AC using the relation as follows:
Substitute
Find the corresponding force along CB using the relation as follows:
Substitute
Sketch the element C as shown in Figure 1.
Refer to Figure 1.
Find the value of P using equilibrium element.
Substitute
Since the applied load,
Refer to Figure 1.
Find the force along CB as follows:
Substitute
Determine the deflection at point C using the relation:
Substitute
Thus, the maximum deflection at point C of the cylindrical portions is
(b)
Find the maximum stress for each portion of rod.
(b)
Answer to Problem 107P
The maximum stress of rod AC is
The maximum stress of rod BC is
Explanation of Solution
Calculation:
Refer part a.
The maximum stress of rod AC is
Therefore, the maximum stress of rod AC is
Determine the maximum stress at point BC using the relation:
Substitute
Thus, the maximum stress of rod BC is
(c)
Find the permanent deflection at point C.
(c)
Answer to Problem 107P
The permanent deflection at point C is
Explanation of Solution
Write the expression of deflection and force for unloading as follows:
The value of
Substitute
Determine the deflection using the relation.
Substitute
Find the permanent deflection using the relation:
Substitute
Thus, the permanent deflection at point C is
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Chapter 2 Solutions
Mechanics of Materials, 7th Edition
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