Solution-truss+design

Solution-truss+design - Final 2009: Question 3 The steel...

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2010/11/20 94 Final 2009: Question 3 The steel truss below is supported by a pin at A and a roller at B. For the given truss determine: (a) the force in member DK, JK, and EF. (members HJ and JK are in the same direction, i.e. HJK is a straight line) (b) Assuming the force in member KL is 1750 kN in tension, calculate the minimum overall width b for member KL knowing the cross section is hollow square as shown. The yield stress for steel is 300 MPa. (c) Calculate the elongation of member KL if E = 200 000 MPa. Step 1: Solve the whole structure as one object to get Ay and By (Ax=0) Step 2: Method of Section to solve member DK and JK Step 3: Analyze Joint E, summing all forces on x-axis, we got force in member EF is 229 compression. Step 4: The total area of the hollow section is b 2 -(200)(200) mm 2 , and we need Step 5: kN B B M Y Y A 126 0 ) 24 ( ) 16 ( 120 ) 8 ( 120 ) 4 ( 36 = = + = kN A B A F Y Y Y Y 150 0 120 120 36 = = + = + kN B B M Y Y A 126 0 ) 24 ( ) 16 ( 120 ) 8 ( 120 ) 4 ( 36 = = + = 150kN F DE F DK F JK ) ( 287 0 ) 4 ( 36 ) 75 . 0 3 )( 1394 . 8 8 ( ) 8 ( 150 T kN F F M JK JK D = = + + + = ) ( 7 . 78 0 ) 0208 . 6 5 . 4 ( ) 1394 . 8 5 . 1 ( 36 120 150 C kN F F F F DK DK JK Y = = = + ) ( 229 0 ) 4 ( 120 ) 8 ( 36 ) 5 . 1 3 ( ) 12 ( 150 C kN F F M DE DE K = = + + + = mm b mm mm b kN MPa load yield 214 ) 200 )( 200 ( 1750 300 2 σ mm mm mm L MPa mm mm kN L L E A P E 10 . 6 ) ) 750 ( ) 4000 ( ( 200000 ) 200 ( ) 214 ( 1750 ) ( 2 2 2 2 + Δ = Δ = = ε
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2010/11/20 96 Final 2008: Question 5 For the given truss shown supported by a pin at A and a roller at H a) determine the forces in members EJ, LK, and IF b) determine the cross section of member LK if the failure stress for the material is 100 MPa and the load (safety) factor is 1.8. Assume a square cross section. c) determine the elongation of member LK* . The modulus of elasticity E of the material is 200 000 MPa. * It shows member BM in the hard copy, that was a typo. Step 1: analyze the whole truss and find the external reactions at A and H, we have Hy=66kN, Ax=18kN, Ay=74kN Step 2: cut the truss as shown and analyze the right segment. taking moment about K, we solve EJ=-118kN(compression) Step 3: cut the truss as shown and analyze the right segment. taking moment about D, we solve LK=58.5kN(tension), IF=0 (zero force member) Step 4: design member LK Step 5: Calculate elongation of member LK mm L mm L L L MPa E MPa mm mm kN A P 833 . 0 3000 10 786 . 2 ) 200000 ( 73 . 55 ) 4 . 32 )( 4 . 32 ( 5 . 58 4 = Δ Δ = Δ = × = = = = = = ε σ Ay Ax Hy Hy Hy mm mm mm A MPa A kN A LF P yield load factored 4 . 32 4 . 32 1053 100 ) 8 . 1 )( 5 . 58 ( ) )( ( 2 × = = = =
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2010/11/20 98 The truss shown which is supported by a roller at A and a pin at B is loaded as shown. Determine: (a) the reaction components at A and B
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Solution-truss+design - Final 2009: Question 3 The steel...

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