Explanation The eyebolts are placed at the three points A , B and C . The free body diagram of the given arrangement is given by Figure 1. Figure 1 The position vector of the point A with respect to O is given as, r A = ( 12 in . ) i The position vector of the point B with respect to O is given as, r B = ( 8 in . ) j The position vector of the point C with respect to O is given as, r C = ( 10 in . ) k The reaction at A is given as, A = A y j + A z k Here, A is the reaction vector, A y is the y coefficient of the reaction at A and A z is the z coefficient of the reaction at A . The reaction at B is given as, B = B x i + B z k Here, B is the reaction vector, B x is the x coefficient of the reaction at B and B z is the z coefficient of the reaction at B . The reaction at C is given as, C = C x i + C y j Here, C is the reaction vector, C x is the x coefficient of the reaction at C and C y is the y coefficient of the reaction at C . The net force on the point O is zero. This means that the sum of the moments of the force will also be zero. r A × A + r B × B + r C × C + M = 0 Here, M is the couple introduced. Substitute the vector values and determine the cross product. | i j k 12 0 0 0 A y A z | + | i j k 0 8 0 B x 0 B z | + | i j k 0 0 10 C x C y 0 | + ( 600 lb ⋅ in . ) j = 0 ( 8 B z − 10 C y ) i + ( − 12 A z + 10 C x + 600 lb ⋅ in . ) j + ( 12 A y − 8 B x ) k = 0 (I) Equate the coefficients of i in (I). 8 B z − 10 C y = 0 C y = 0

12th Edition

ISBN: 9781259977268

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Chapter 4.3, Problem 4.128P

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The reaction at A,B and C.

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Chapter 4.3, Problem 4.127P

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The reaction at A , B and C .

Solution Summary: The author explains the reaction at A,BandC. The free body diagram of the given arrangement is given by Figure 1.

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