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Problem 3.152 The frame ACD is hinged at A and D and is supported by a cable which passes through a ring at B and is attached to hooks at G and H. Knowing.

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Presentation on theme: "Problem 3.152 The frame ACD is hinged at A and D and is supported by a cable which passes through a ring at B and is attached to hooks at G and H. Knowing."— Presentation transcript:

1 Problem The frame ACD is hinged at A and D and is supported by a cable which passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 450 N, determine the moment about the diagonal AD of the force exerted on the frame by portion BH of the cable. y z x m 0.75 m 0.5 m 0.35 m m A B O C D P H G 0.75 m

2 1. Determine the moment M OL of a force about a given axis OL. M OL is defined as M OL =. M O =. ( r x F ) where is the unit vector along OL and r is a position vector from any point on the line OL to any point on the line of action of F. y z x m 0.75 m 0.5 m 0.35 m m A B O C D P H G 0.75 m Solving Problems on Your Own The frame ACD is hinged at A and D and is supported by a cable which passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 450 N, determine the moment about the diagonal AD of the force exerted on the frame by portion BH of the cable. Problem 3.152

3 Problem Solution M AD =  AD. ( r B/A x T BH ) Where AD = (4 i _ 3 k) r B/A = (0.5 m ) i 1 5 Determine the moment M AD of a force about line AD. d BH = ( ) 2 + ( 0.75 ) 2 + ( _ 0.75 ) 2 = m T BH = ( i j _ 0.75 k ) = ( 150 N) i + ( 300 N) j _ ( 300 N) k 450 N M AD y z m 0.75 m 0.5 m 0.35 m m A B O C D P H G T BH AD r B/A x 0.75 m

4 Problem Solution M AD = AD. ( r B/A x T BH ) M AD = _ _ 300 = [( _ 3)(0.5)(300)] 1 5 M AD = _ 90 N. m Finally: M AD y z m 0.75 m 0.5 m 0.35 m m A B O C D P H G T BH AD r B/A x 0.75 m


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