Explanation Given information : The downward vertical force F 1 is 300 N. The inclined downward force F 2 is 250 N. The downward inclined force F 3 is 500 N. The moment ( M ) is 400 N ⋅ m . Show the free body diagram as in Figure (1). Use Figure (1). Assumption : Towards Right is positive. Determine the resultant of horizontal force by using the equation of equilibrium. ∑ F R x = ∑ F x ( F R ) x = − F 2 ( 4 5 ) − F 3 cos θ (I) Here, the horizontal resolving angle of F 2 is ( 4 5 ) and the horizontal resolving angle of F 3 is θ . Assumption : Upward is positive. Determine the resultant of vertical force by using the equation of equilibrium. ∑ F R y = ∑ F y F R y = F 1 − F 2 ( 3 5 ) − F 3 sin θ (II) Here, the vertical resolving angle of F 2 is ( 3 5 ) and the vertical resolving angle of F 3 is θ . 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 : Counterclockwise is positive. Determine the line of action ( x ) that intersects member CD measured from C by using the principle of moments. ( M R ) C = ∑ M C F R y ( x ) = { − M + F 3 cos θ ( a ) + F 3 sin θ ( b ) + F 2 ( 3 5 ) ( c ) + F 1 ( d ) } (V) Here, the vertical distance between F 3 and point C is a , the horizontal distance between F 3 and point B is b , the horizontal distance between F 2 and point C is c , and the distance between F 1 and point C is d . Show the calculation of resultant force, direction, and line of action as follows: Conclusion : Substitute 250 N for F 2 , 500 N for F 3 , and 60 ° for θ in Equation (I)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 4.8, Problem 121P

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The equivalent resultant force, direction of the resultant force, and specify where its line of action intersects member CD measured from C.

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Chapter 4.8, Problem 120P

Chapter 4.8, Problem 122P

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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 specify where its line of action intersects member CD measured from C .

The equivalent resultant force, direction of the resultant force, and specify where its line of action intersects member CD measured from C.

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