Explanation Given information: The force applied at A of the assembly is P . The flexibility stiffness of the assembly is E I . The torsion of the assembly is T . The torsional stiffness of the assembly is G J . The length of the segment AD , BD , and CD ( L ) is L 2 . Calculation: Show the free body diagram of the assembly as in Figure 1. Refer to Figure 1. Show the deflected shape of the segment AD of the assembly as in Figure 2. Refer to Figure 2. Calculate the deflection at A ( υ A ) 1 due to point load ( P ) : ( υ A ) 1 = P ( L 2 ) 3 3 E I = P L 3 24 E I Calculate the torsion of the assembly ( T ) : T = P × L 2 = P L 2 Calculate the angle of the segment AD ( θ ) using the formula: θ = T L G J Substitute P L 2 for T and L 2 for L . θ = P L 2 × L 2 G J = P L 2 4 G J Calculate the deflection at A ( υ A ) 2 due to angle ( θ ) : ( υ A ) 2 = θ L Substitute P L 2 4 G J for θ and L 2 for L . ( υ A ) 2 = P L 2 4 G J × L 2 = P L 3 8 G J Show the deflected shape of the segment CD of the assembly as in Figure 3

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.4, Problem 57P

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Find the vertical deflection at A (υA).

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Chapter 16.4, Problem 56P

Chapter 16.4, Problem 58P

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Find the vertical deflection at A ( υ A ) .

Solution Summary: The author shows the free body diagram of the assembly as in Figure 1.

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Find the vertical deflection at A (υA).

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Chapter 16 Solutions