Solution-3D+frame - Final 2009 Question 1 The horizontal...

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2010/11/20 66 Final 2009: Question 1 The horizontal homogeneous platform ABCED of uniform thickness, weights 1500 kN. The platform is supported by the cable CF, a ball and socket at A, and a connection at B that provides support in the x and y direction only, determine the force in the cable and reaction components at B. Step 1: The platform is equivalent to a solid rectangle (20m x 6m) minus a triangle which has a negative weight (force acting up in red color). Step 2: Getting coordinates of key points A (0,0,0); B(0,0,20); C(6,0,20); D(3,0,10); F(0,12,8); G(5,0,10). G is the centriod of the triangle. Step 3: Express unknown tension in Cartesian vector Step 4: Taking moment of all forces about A Solve the equation above, we got T=875kN; Bx=116.7kN; By=166.7kN k T j T i T k j i T r C F T r r T T CF CF CF ) 3 2 ( ) 3 2 ( ) 3 1 ( ) 18 12 12 6 ( ) ( ) ( + = + = = = 0 0 500 0 10 0 5 0 2000 0 10 0 3 0 20 0 0 3 2 3 2 3 1 20 0 6 2 1 = + + + = × + × + × + × = k j i k j i B B k j i T T T k j i W r W r B r T r M Y X AG AD AB AC A
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2010/11/20 68 Final 2008: Question 3 An L-shaped pipe bracket is supported by a ball-and-socket at A, by a ball-and-socket at D which has been modified to permit movement in the z direction, and by cable BE. The mass of the pipe segment AC is 2 kg/m whereas the mass of segment CD can be neglected. Determine the tension in cable BE and the components of the reaction at D. Step 1: Coordinates of key points A(0,0,1) B(2,0,1) D(3,0,0) E(3,2,0) F(1.5,0,1) Step 2: Express Tension T in Cartesian vector notation Step 3: Express two reaction components at D and the self-weight Step 4: Find position vectors r AB , r AF and r AD Step 5: Take moment about point A mm d MPa d d kNm I y LF M mm d I X X 6 . 422 8 ) 150 ( 12 1 ) )( 5 . 0 )( 9 . 1 )( 8 . 18 ( ) 150 ( 12 1 3 max max max 4 3 = = = σ N k T j T i T T r B E T r r T u T T BE BE BE BE ) ) 4082 . 0 ( ) 8165 . 0 ( ) 4082 . 0 (( 6 ) 1 , 2 , 1 ( + = = = = = r r r N j W N k j D i D D y x ) 86 . 58 ( ; ) 0 ( = + + = r r k j i A D r k j i A F r k j i A B r AD AB AB 1 0 3 0 0 5 . 1 0 0 2 + = = + + = = + + = = r r r N T D D N D k j i D D k j i T T T k j i W r D r T r M z y x y x AF AD AB A 1 . 54 , 0 , 0 , 2 . 44 0 0 86 . 58 0 0 0 5 . 1 0 1 0 3 4082 . 0 8165 . 0 4082 . 0 0 0 2 = = = = = + + = × + × + × = r r r r r r F
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2010/11/20 70 Final 2007: Question 5 A uniformly thick steel plate is supported by a ball-and-socket at B, two pin-connected bars CE and CF located at C, and the cable AD. The plate which weights 20 kN supports a vertical force of 40 kN located at Q. (a) sketch the FBD of the plate on the space provided, and
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Solution-3D+frame - Final 2009 Question 1 The horizontal...

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