Explanation Given information: The flat-bed trailer has a weight of 7,000 lb and the center of gravity is at G T . A pin is connected to the cab at D . The cab has a weight of 6,000 lb and the center of gravity at G C . The load has a center of gravity at G L . Assumption: Consider the force indicating the right side as positive and the 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 the clockwise moment as negative and the anti-clock wise moment as positive wherever applicable. Apply the equation of equilibrium wherever applicable. Segment AB : Show the free-body diagram of the segment AB as in Figure 1. Case I: Assume the vertical reaction at point A is A y = 5 , 500 lb : Moment about point B : Determine the vertical reaction at point D by taking the moment about point B . ∑ M B = 0 − A y ( 13 ) + 6 , 000 ( 9 ) + D y ( 3 ) = 0 (I) Along the vertical direction: Determine the vertical reaction at point B by resolving the vertical component of forces. ∑ F y = 0 A y + B y − 6 , 000 − D y = 0 (II) Conclusion: Substitute 5,500 lb for A y in Equation (I). − 5 , 500 ( 13 ) + 6 , 000 ( 9 ) + D y ( 3 ) = 0 − 71 , 500 + 54 , 000 + 3 D y = 0 3 D y = 17 , 500 D y = 5 , 833.33 lb Substitute 5,500 lb for A y and 5,833.33 lb for D y in Equation (II). 5 , 500 + B y − 6 , 000 − 5 , 833.33 = 0 B y = 6 , 333.33 lb > 5,500 lb The vertical reaction at point B exceeds the allowable limit of 5,500 lb. Hence, the assumption is incorrect. Case II: Assume the vertical reaction at point B is B y = 5 , 500 lb : Refer to Figure 1: Moment about point A : Determine the vertical reaction at point D by taking the moment about point A . ∑ M A = 0 B y ( 13 ) − 6 , 000 ( 4 ) − D y ( 10 ) = 0 (III) Segment BC : Show the free-body diagram of the segment BC as in Figure 2. Refer to Figure 2: Along the vertical direction: Determine the vertical reaction at point C by resolving the vertical component of forces. ∑ F y = 0 D y − 7 , 000 − 2 , 000 + C y = 0 (IV) Moment about point D : Determine the distance x by taking the moment about point D : ∑ M D = 0 − 7 , 000 ( 13 ) − 2 , 000 ( 13 + 12 − x ) + C y ( 25 ) = 0 (V) Substitute 5,500 lb for B y in Equation (III). 5 , 500 ( 13 ) − 6 , 000 ( 4 ) − D y ( 10 ) = 0 71 , 500 − 24 , 000 − 10 D y = 0 10 D y = 47 , 500 D y = 4 , 750 lb Substitute 5,500 lb for B y and 4,750 lb for D y in Equation (II)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 6.6, Problem 87P

To determine

The range of values x for the position of the 2,000 lb load L so that when it is placed over the rear axle, no axle is subjected to more than 5,500 lb.

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Chapter 6.6, Problem 86P

Chapter 6.6, Problem 88P

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Engineering Mechanics: Statics

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