Explanation Given information : The uniformly varying load at point A ( F 1 ) is 100 lb / ft . The uniformly varying load at the top of the inclined member F 2 is 50 lb / ft . The uniformly distributed load on the horizontal member F 3 is 50 lb / ft . Show the free body diagram of the forces acting on the frame as in Figure (1). Show the free body diagram of the force geometry as in Figure (2). Assumption : Towards right is positive. Determine the resultant of horizontal force using the equation of equilibrium. F R x = ∑ F x = 1 2 × ( F 1 − F 2 ) × l 1 × sin θ + F 2 × l 1 × sin θ (I) Here, the span for the inclined member is l 1 and the angle for the inclined member is θ . Assumption : Upward is positive. Determine the resultant of vertical force using the equation of equilibrium. F R y = ∑ F y = − 1 2 × ( F 1 − F 2 ) × l 1 × cos θ − F 2 × l 1 × cos θ − F 3 × l 2 (II) Here, the span for the horizontal member is l 1 . Determine the resultant force F R . F R = ( F R x ) 2 + ( F R y ) 2 (III) Determine the direction θ of the resultant force. θ = tan − 1 ( F R y F R x ) (IV) Assumption : Anti-clockwise is positive. Determine the couple moment by taking the moment about the point A . ( M R ) A = ∑ M A = − 1 2 × ( F 1 − F 2 ) × l 1 × l 1 3 − F 2 × l 1 × l 1 2 − F 3 × l 2 × ( l 1 cos θ + l 2 2 ) (V) Conclusion : Substitute 100 lb / ft for F 1 , 50 lb / ft for F 2 , 6 ft for l 1 , and 60 ° for θ in Equation (I). F R x = 1 2 × ( 100 − 50 ) × 6 × sin 60 ° + 50 × 6 × sin 60 ° = 130 + 259.8 = 389.8 lb Substitute 100 lb / ft for F 1 , 50 lb / ft for F 2 , 6 ft for l 1 , 60 ° for θ , 50 lb / ft for F 3 , and 4 ft for l 2 in Equation (II)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 4.9, Problem 152P

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The equivalent resultant force, direction of the resultant force, and the couple moment at point A.

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Chapter 4.9, Problem 151P

Chapter 4.9, Problem 153P

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Chapter 4 Solutions

Engineering Mechanics: Statics

Ch. 4.4 - F41. Determine the moment of the force about point...Ch. 4.4 - F42. Determine the moment of the force about point...Ch. 4.4 - F43. Determine the moment of the force about point...Ch. 4.4 - Neglect the thickness of the member.Ch. 4.4 - F45. Determine the moment of the force about point...Ch. 4.4 - F46. Determine the moment of the force about point...Ch. 4.4 - F47. Determine the resultant moment produced by...Ch. 4.4 - F48. Determine the resultant moment produced by...Ch. 4.4 - F49. Determine the resultant moment produced by...Ch. 4.4 - Express the result as a Cartesian vector.

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The equivalent resultant force, direction of the resultant force, and the couple moment at point A .

The equivalent resultant force, direction of the resultant force, and the couple moment at point A.

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Chapter 4 Solutions