Concept explainers
The uniform wire ABC, of unstretched length 2l, is attached to the supports shown and a vertical load P is applied at the midpoint B. Denoting by A the cross-sectional area of the wire and by E the modulus of elasticity, show that, for δ << l, the deflection at the midpoint B is
Fig. P2.124
To prove the deflection of uniform wire ABC at midpoint B is
Explanation of Solution
Given information:
The unstretched length is
The vertical load is P.
Calculation:
Sketch the uniform wire ABC as shown in Figure 1.
Refer to Figure 1.
The value of
Find the value of vertical load
Substitute for
Find the elongation at point AB using the relation:
Substitute
Sketch the right angle triangle as shown in Figure 2.
Refer to Figure 2.
Substitute
Hence, the deflection of uniform wire ABC at midpoint B is
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Chapter 2 Solutions
EBK MECHANICS OF MATERIALS
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