Explanation Given information: Weight of the cable is 6 lb/ft. Span of the cable is 100 ft. Length of the cable is 150 ft. Write the equation for deflection curve as follows: x = ∫ d s [ 1 + 1 F H 2 ( ∫ w ( s ) d s ) 2 ] 1 / 2 (I) Integrate the Equation (I). x = ∫ d s [ 1 + ( 1 F H 2 ) ( w 0 s + C 1 ) 2 ] 1 / 2 (II) Take ( 1 F H ) ( w 0 s + C 1 ) as u , so that d u = ( w 0 F H ) d s . Integrate the Equation (II). x = F H w 0 ( sinh − 1 u + C 2 ) (III) Substitute ( 1 F H ) ( w 0 s + C 1 ) for u in Equation (III). x = F H w 0 ( sinh − 1 ( ( w 0 s + C 1 ) F H ) + C 2 ) (IV) Determine the constants using the equation below (Equation 7.14). d y d x = 1 F H ∫ w 0 d s = 1 F H ( w 0 s + C 1 ) (V) Condition 1: d y d x = 0 at s = 0 : Substitute 0 for d y d x , 6 lb/ft for w 0 , and 0 for s in Equation (V). 0 = 1 F H ( 6 ( 0 ) + C 1 ) C 1 = 0 Substitute 6 lb/ft for w 0 and 0 for C 1 in Equation (V). d y d x = 1 F H ( 6 s + 0 ) = 6 s F H (VI) Condition 2: s = 0 at x = 0 : Substitute 0 for x , 6 lb/ft for w 0 , 0 for s , and 0 for C 1 in Equation (IV). 0 = F H 6 ( sinh − 1 ( ( 6 × 0 + 0 ) F H ) + C 2 ) sinh − 1 ( 0 F H ) + C 2 = 0 C 2 = 0 Substitute 6 lb/ft for w 0 , 0 for C 1 , and 0 for C 2 in Equation (IV). x = F H 6 ( sinh − 1 ( ( 6 s + 0 ) F H ) + 0 ) x = F H 6 ( sinh − 1 ( 6 s F H ) ) s = F H 6 sinh ( 6 x F H ) (VII) Substitute F H 6 sinh ( 6 x F H ) for s in Equation (VI)

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 7.4, Problem 113P

To determine

The sag h and the minimum tension in the cable.

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Chapter 7.4, Problem 112P

Chapter 7.4, Problem 114P

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Chapter 7 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

Ch. 7.1 - Determine the normal force, shear force, and...Ch. 7.1 - Determine the normal force, shear force, and...Ch. 7.1 - Determine the normal force, shear force, and...Ch. 7.1 - Determine the normal force, shear force, and...Ch. 7.1 - Determine the normal force, shear force, and...Ch. 7.1 - Assume A is pinned and B is a roller. Prob. F7-6 Ch. 7.1 - Assume the support at B is a roller. Point C is...Ch. 7.1 - Determine the shear force and moment at points C...Ch. 7.1 - If the suspended load has a weight of 2 kN and a...Ch. 7.1 - Prob. 4P

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