Explanation Given information: The weight ( P ) of the triangular plate is 36 lb. Calculation: Draw the free body diagram of point D of the triangular plate as in Figure (1). By symmetry the tension in wire T D B = T D C . The force applied at the point D are T D B , T D C , T D A and P . Write the weight of the triangular plate in vector as below: P = ( 36 lb ) j Express the vector D A → as below: D A → = ( 16 in . ) i − ( 24 in . ) j Calculate distance of the member DA as below: D A = 16 2 + ( − 24 ) 2 = 256 + 576 = 28.844 in . Calculate the unit vector ( λ D A ) using the relation: λ D A = D A → D A Substitute ( 16 in . ) i − ( 24 in . ) j for D A → and 28.844 in . for DA . λ D A = ( 16 in . ) i − ( 24 in . ) j 28.844 = 0.5547 i − 0.8321 j Calculate the tension force ( T D A ) in wire DA using the relation: T D A = T D A λ D A Substitute 0.5547 i − 0.8321 j for λ D A . T D A = ( 0.5547 i − 0.8321 j ) T D A Express the vector D B → as below: D B → = − ( 8 in . ) i − ( 24 in . ) j + ( 6 in . ) k Calculate distance of the member DB as below: D B = ( − 8 ) 2 + ( − 24 ) 2 + ( 6 ) 2 = 64 + 576 + 36 = 26 in . Calculate the unit vector ( λ D B ) using the relation: λ D B = D B → D B Substitute − ( 8 in . ) i − ( 24 in . ) j + ( 6 in . ) k for D B → and 26 in . for DB . λ D B = − ( 8 in . ) i − ( 24 in . ) j + ( 6 in . ) k 26 = − 0.3077 i − 0.9231 j + 0.231 k Calculate the tension force ( T D B ) in wire DB using the relation: T D B = T D B λ D B Substitute − 0.3077 i − 0.9231 j + 0.231 k for λ D B . T D B = ( − 0.3077 i − 0.9231 j + 0.231 k ) T D B Express the vector D C → as below: D C → = − ( 8 in . ) i − ( 24 in . ) j − ( 6 in . ) k Calculate distance of the member DC as below: D C = ( − 8 ) 2 + ( − 24 ) 2 + ( − 6 ) 2 = 64 + 576 + 36 = 26 in

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 2.5, Problem 2.103P

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The tension in wire DA(TDA),DC (TDC) and DB (TDB).

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Chapter 2.5, Problem 2.102P

Chapter 2.5, Problem 2.104P

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The tension in wire DA ( T D A ) , DC ( T D C ) and DB ( T D B ) .

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The tension in wire DA(TDA),DC (TDC) and DB (TDB).

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