Explanation Given information: The engine hoist is used to support the 200-kg engine. Assumption: Consider the state of member as tension where the force is pulling the member and as compression where the force is pushing the member. Consider the force indicating the right side as positive and left side as negative in horizontal components of forces. Consider the force indicating upward is taken as positive and downward as negative in vertical components of forces. Consider clockwise moment as negative and anti-clock wise moment as positive wherever applicable. Apply the Equation of equilibrium wherever applicable. Acceleration due to gravity is g = 9.81 m/sec 2 . The member AB is a two-force member. Conversion: Convert the mass into weight using the relation: W = m g Substitute 200 kg for m and 9.81 m/sec 2 for g . W = ( 200 × 9.81 ) N Geometry ABC : Show the free-body diagram of the geometry ABC as in Figure 1. Using Figure 1, Length of member AB : Determine the length of member AB using the relation: l A B = l A C 2 + l B C 2 − 2 ( l A C ) ( l B C ) cos 80 ° (I) Determine the angle θ 1 using sine rule: sin θ 1 850 = sin 80 ° l A B (II) Conclusion: Substitute 350 mm for l A C and 850 mm for l B C in Equation (I). l A B = 350 2 + 850 2 − 2 × 350 × 850 × cos 80 ° = 122 , 500 + 722 , 500 − 103 , 320.67 = 861.21 mm Substitute 861.21 mm for l A B in Equation (II). sin θ 1 850 = sin 80 ° 861.21 sin θ 1 = sin 80 ° 861.21 × 850 θ 1 = 76.41 ° Segment GAC : Show the free-body diagram of the segment GAC as in Figure 2. Using Figure 2, Moment about point C : Determine the force in the member AB by taking the moment about point C . ∑ M C = 0 200 × 9.81 × 1.60 − F A B sin θ 1 ( 0.35 ) = 0 (III) Along the vertical direction: Determine the vertical reaction at point C by resolving the vertical component of forces. ∑ F y = 0 F A B sin θ 1 − 200 × 9.81 − C y = 0 (IV) Along the horizontal direction: Determine the horizontal reaction at point C by resolving the horizontal component of forces. ∑ F x = 0 C x − F A B cos θ 1 = 0 (V) Conclusion: Substitute 76.41 ° for θ 1 in Equation (III). 3 , 139.2 − F A B sin 76.41 ° ( 0.35 ) = 0 F A B = 3 , 139.2 0.35 × sin 76.41 ° F A B = 9 , 232.94 N × 1 kN 1,000N F A B = 9

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 6.6, Problem 81P

To determine

The force acting in the hydraulic cylinder AB, the horizontal and vertical components of force at the pin C, and the reactions at the fixed support D.

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Chapter 6.6, Problem 80P

Chapter 6.6, Problem 82P

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Chapter 6 Solutions

Engineering Mechanics: Statics

Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 3FP Ch. 6.3 - Determine the greatest load P that can be applied...Ch. 6.3 - Identify the zero-force members in the truss....Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 1P Ch. 6.3 - Prob. 2P Ch. 6.3 - Determine the force in each member of the truss,...Ch. 6.3 - Determine the force in each member of the truss,...

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The force acting in the hydraulic cylinder AB , the horizontal and vertical components of force at the pin C , and the reactions at the fixed support D .

The force acting in the hydraulic cylinder AB, the horizontal and vertical components of force at the pin C, and the reactions at the fixed support D.

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Chapter 6 Solutions