Explanation Given information : The UDL on the member AB ( F 1 ) is 3 kN / m . The UDL on the member BC ( F 2 ) is 2 kN / m . Show the free body diagram of the forces acting on the frame as in Figure (1). Using Figure (1), Assumption : Towards right is positive. Determine the resultant of the horizontal force using the equation of equilibrium. ( F R ) x = ∑ F x = − F 2 l 2 (I) Here, the span for the force F 2 is l 2 . Assumption : Upward is positive. Determine the resultant of the vertical force using the equation of equilibrium. ( F R ) y = ∑ F y = F 1 l 1 (II) Here, the span for the force F 1 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 resultant force. θ = tan − 1 ( ( F R ) y ( F R ) x ) (IV) Assumption : Anti-clockwise is positive. Determine the line of action of the resultant force by taking the moment about point A . ( M R ) A = ∑ M A ( F R ) x ( x ) + ( F R ) y ( y ) = − F 1 l 1 ( l 1 2 ) − F 2 l 2 ( l 2 2 ) (V) Determine the line of action of the resultant force that intersects a vertical line. d = l 2 − x (VI) Conclusion : Substitute 2 kN / m for F 2 and 4 m for l 2 in Equation (I). ( F R ) x = − 2 × 4 = − 8 kN = 8 kN ( ← ) Substitute 3 kN / m for F 1 and 3 m for l 1 in Equation (II)

Engineering Mechanics: Statics Plus Mastering Engineering with Pearson eText -- Access Card Package (14th Edition) (Hibbeler, The Engineering Mechanics: Statics & Dynamics Series, 14th Edition)

14th Edition

ISBN: 9780134160689

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.9, Problem 155P

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The equivalent resultant force, the direction of the resultant force, and the line of action of the resultant that intersects a vertical line along the member BC, which is measured from point C.

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Chapter 4.9, Problem 154P

Chapter 4.9, Problem 156P

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Chapter 4 Solutions

Engineering Mechanics: Statics Plus Mastering Engineering with Pearson eText -- Access Card Package (14th Edition) (Hibbeler, The Engineering Mechanics: Statics & Dynamics Series, 14th Edition)

Ch. 4.4 - P41. In each case, determine the moment of the...Ch. 4.4 - P42. In each case, set up the determinant to find...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...

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The equivalent resultant force, the direction of the resultant force, and the line of action of the resultant that intersects a vertical line along the member BC, which is measured from point C .

Solution Summary: The author shows the free body diagram of the forces acting on the frame as in Figure (1).

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The equivalent resultant force, the direction of the resultant force, and the line of action of the resultant that intersects a vertical line along the member BC, which is measured from point C.

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Chapter 4 Solutions