Concept explainers
Bar AB has a cross-sectional area of 1200 mm2 and is made of a steel that is assumed to be elastoplastic with E = 200 GPa and σY = 250 MPa. Knowing that the force F increases from 0 to 520 kN and then decreases to zero, determine (a) the permanent deflection of point C, (b) the residual stress in the bar.
Fig. P2.122
*2.123 Solve Prob. 2.122, assuming that a = 180 mm.
(a)
The permanent deflection of point C.
Answer to Problem 123P
The permanent deflection of point C is
Explanation of Solution
Given information:
The distance between member AC (a) is
The cross sectional area A of section AB is
The modulus of elasticity E is
The yield stress
The force F is
Calculation:
Determine the force to yield portion AC using the relation:
Substitute
Sketch the bar ACB as shown in Figure 1.
Find the load
Substitute
Find the length
Refer to Figure 1.
Find the deflection at point C using the relation:
Here,
Substitute
Find the stress in rod along CB using the relation:
Substitute
Calculate the load
Here,
Substitute
Find the force
Substitute
Determine the deflection at point C
Substitute
Calculate the stress at along AC using the relation:
Substitute
Calculate the stress along BC using the relation:
Substitute
Determine the permanent deflection at point C using the relation:
Substitute
Thus, the permanent deflection of point C is
(b)
Find the residual stress in bar AC and CB.
The residual stress in bar AC is
The residual stress in bar CB is
Explanation of Solution
Calculation:
Find the residual stress in bar AC using the relation:
Substitute
Thus, the residual stress in bar AC is
Find the residual stress in bar BC using the relation:
Substitute
Thus, the residual stress in bar CB is
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Chapter 2 Solutions
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