Explanation Given information: The wires AB and AC are made of steel. The wire AD is made of copper. The Young’s modulus of the steel ( E s t ) is 29 × 10 6 psi . The Young’s modulus of the copper ( E c u ) is 17 × 10 6 psi . The coefficient of thermal expansion of the steel ( α s t ) is 8 × 10 − 6 / ° F . The coefficient of thermal expansion of the copper ( α c u ) is 9.6 × 10 − 6 / ° F . The force ( P ) applied is 150 lb. The length ( L A B and L A C ) of the wires ( AB and AC ) is 60 in.. The length ( L A D ) of the wires ( AD ) is 40 in.. The difference of temperature ( Δ T ) of the members is 80 ° F . The cross-sectional area ( A ) of each wire ( AB , AC , and AD ) is 0.0123 in . 2 . Calculation: Show the free body diagram of the wires as in Figure 1. Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 ( F A B × sin 45 ° ) + ( F A C × sin 45 ° ) + F A D − 150 = 0 0.707 F A B + 0.707 F A C + F A D = 150 (1) Here, F A B is force at the wire AB , F A C is force at the wire AC , and F A D is force at the wire AD . Calculate the horizontal forces by applying the equation of equilibrium: Sum of horizontal forces is equal to 0. ∑ F x = 0 ( F A C × cos 45 ° ) − ( F A B × cos 45 ° ) = 0 cos 45 ° ( F A C − F A B ) = 0 F A C − F A B = 0 F A B = F A C Show the displacement diagram of the wire AC as in Figure 2. Here δ A C is deformation at AC and ( δ A C ) T is deformation due to temperature at AC . Calculate the deformation ( δ A C ) T due to temperature at AC using the formula: ( δ A C ) T = α s t Δ T L A C Substitute 8 × 10 − 6 / ° F for α s t , 80 ° F for Δ T , and 60 in . for L A C . ( δ A C ) T = 8 × 10 − 6 × 80 × 60 = 0.0384 in . Calculate the deformation ( δ A C ) T 2 due to finial temperature at AC using the formula: ( δ A C ) T 2 = ( δ A C ) T cos 45 ° Substitute 0.0384 in. for ( δ A C ) T . ( δ A C ) T 2 = 0.0384 cos 45 ° = 0.05431 in . Show the displacement diagram of the wires as in Figure 3. Here ( δ A D ) F is deformation due to force at AD , ( δ A C ) F r is deformation due to force at AC , and δ 0 is difference of deformation due to temperatures ( δ A C ) T 2 and ( δ A D ) T Calculate the deformation ( δ A D ) T due to temperature at AD using the formula: ( δ A D ) T = α c u Δ T L A D Substitute 9

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 9.6, Problem 71P

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Find the force in each wire AB, AC, and AD.

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Chapter 9.6, Problem 70P

Chapter 9.6, Problem 72P

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Chapter 9 Solutions

Statics and Mechanics of Materials (5th Edition)

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Find the force in each wire AB , AC , and AD .

Solution Summary: The author calculates the force in each wire AB, AC, and AD based on the Young's modulus of steel and copper.

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Chapter 9 Solutions