Explanation Given information : The moment ( M c ) 1 is 450 lb ⋅ ft . The moment ( M c ) 3 is 300 lb ⋅ ft . The moment ( M c ) 2 is 250 lb ⋅ ft . Calculation : Determine the position vector for point OA . r O A = r A − r O = ( x A i + y A j + z A k ) − ( x O i + y O j + z O k ) = ( x A − x O ) i + ( y A − y O ) j + ( z A − z O ) k (1) Here, the position vector for point A is r A , the position vector for point O is r O , the distance of point A from the origin along x direction is x A , the distance of point A from the origin along y direction is y A , the distance of point A from the origin along z direction is z A , the distance of point O from the origin along x direction is x O , the distance of point O from the origin along y direction is y O , the distance of point O from the origin along z direction is z O , the vector component along x direction is i, the vector component along y direction is j, and the vector component along z direction is k. Determine the modulus of position vector for point OA . | r O A | = ( x A − x O ) 2 + ( y A − y O ) 2 + ( z A − z O ) 2 (2) Determine the unit vector for point OA . u O A = r O A | r O A | (3) Determine the position vector for point OB . r O B = r B − r O = ( x B i + y B j + z B k ) − ( x O i + y O j + z O k ) = ( x B − x O ) i + ( y B − y O ) j + ( z B − z O ) k (4) Here, the position vector for point B is r B , the distance of point B from the origin along x direction is x B , the distance of point B from the origin along y direction is y B , and the distance of point B from the origin along z direction is z B . Determine the modulus of position vector for point OB . | r O B | = ( x B − x O ) 2 + ( y B − y O ) 2 + ( z B − z O ) 2 (5) Determine the unit vector for point OB . u O B = r O B | r O B | (6) Determine the moment vector ( M c ) 1 as follows: ( M c ) 1 = | ( M c ) 1 | u O A (7) Determine the moment vector ( M c ) 2 as follows: ( M c ) 2 = − | ( M c ) 2 | k (8) Determine the moment vector ( M c ) 3 as follows: ( M c ) 3 = | ( M c ) 3 | u O B (9) Here, the negative sign indicates that the ( M c ) 3 acting in negative z direction. Determine the resultant couple moment acting on the assembly using the formula. ( M C ) R = ( M c ) 1 + ( M c ) 2 + ( M c ) 3 (10) Conclusion : Substitute –2.0 ft for x A , 0 ft for x O , 2.0 ft for y A , 0 ft for y O , 3.5 ft for z A , and 0 ft for z O in Equation (1). r O A = ( − 2 − 0 ) i + ( 2 − 0 ) j + ( 3

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 3.6, Problem 23FP

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Find the resultant couple moment acting on the assembly.

Solution Summary: The author explains how to find the resultant couple moment acting on the assembly. The position vector for point OA is r_A.

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