
Concept explainers
Both portions of the rod ABC are made of an aluminum for which E = 70 GPa. Knowing that the magnitude of P is 4 kN, determine (a) the value of Q so that the deflection at A is zero, (b) the corresponding deflection of B.
Fig. P2.19 and P2.20
a)

The value of (Q) when the deflection at A is zero.
Answer to Problem 19P
The value of (Q) when the deflection at A is zero is
Explanation of Solution
Given information:
The Young’s modulus of the aluminium (E) is
The force at the point A (P) is
The force at the point B is Q.
The diameter of the rod AB
The diameter of the rod BC
The length of the rod AB
The length of the rod BC
Calculation:
Calculate the cross-sectional area of the rod AB
Substitute
Calculate the cross-sectional area of the rod BC
Substitute
Calculate the defection of the rod AB
Substitute
Calculate the defection of the rod BC
Substitute
Calculate the force at the point B (Q):
Substitute
Hence, the value of (Q) when the deflection at A is zero is
b)

The deflection of B
Answer to Problem 19P
The deflection of B
Explanation of Solution
Given information:
The Young’s modulus of the aluminium (E) is
The force at the point A (P) is
The force at the point B is Q.
The diameter of the rod AB
The diameter of the rod BC
The length of the rod AB
The length of the rod BC
Calculation:
Calculate the cross-sectional area of the rod AB
Substitute
Calculate the cross-sectional area of the rod BC
Substitute
Calculate the defection of the rod AB
Substitute
Calculate the defection of the rod BC
Substitute
Calculate the force at the point B (Q):
Substitute
Calculate the deflection of B
Substitute
Hence, the deflection of B
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