Explanation Given information: The cross-sectional area of the two steel wires ( A ) is 2 mm 2 . The initial tension in the wires ( T ) is 50 N The horizontal force applied to the ring ( P ) is 50 N The modulus of elasticity of the steel ( E ) is 200 GPa . The yield stress of the wire σ Y is 300 MPa . The length of wire AC ( L A C ) is 2 m . The length of wire BC ( L B C ) is 3 m . Calculation: Show the free-body diagram of the wire as in Figure 1. Refer Figure 1. Here, P 1 is horizontal force of the wire AC , P 2 is horizontal force of the wire CB , and δ C is displacement of point C . Calculate the horizontal forces by applying the equation of equilibrium: Sum of horizontal forces is equal to 0. ∑ F x = 0 20 − ( 50 + P 1 ) + ( 50 − P 2 ) = 0 20 − P 1 − P 2 = 0 P 1 + P 2 = 20 (1) Refer Figure 1. Calculate the horizontal force of two wires ( P 1 and P 2 ) using the geometry: δ C = P 1 L A C A E = P 2 L B C A E P 1 L A C = P 2 L B C (2) Substitute 2 m for L A C and 3 m for L B C in Equation (2) P 1 × 2 = P 2 × 3 P 1 = 3 P 2 2 P 1 = 1.5 P 2 (3) Substitute 1.5 P 2 for P 1 in Equation (1) 1.5 P 2 + P 2 = 20 2.5 P 2 = 20 P 2 = 20 2.5 P 2 = 8 N Substitute 8 N for P 2 in Equation (1) P 1 + 8 = 20 P 1 = 20 − 8 P 1 = 12 N Calculate the force of wire AC ( F A C ) : F A C = T + P 1 (4) Substitute 50 N for T and 12 N for P 1 in Equation (4)

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 4.9, Problem 4.103P

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The force in each wire (FAC and FBC) .

The smallest force P that must be applied to the ring to reduce the force in wire CB to zero

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Chapter 4.9, Problem 4.102P

Chapter 4.9, Problem 4.104P

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The force in each wire ( F A C and F B C ) . The smallest force P that must be applied to the ring to reduce the force in wire CB to zero

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The force in each wire (FAC and FBC) . The smallest force P that must be applied to the ring to reduce the force in wire CB to zero

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Chapter 4 Solutions

The force in each wire (FAC and FBC) .

The smallest force P that must be applied to the ring to reduce the force in wire CB to zero