problem solution_ch1_ch3 - Chapter 1, Problem 7...

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Unformatted text preview: Chapter 1, Problem 7 Pin-connected members ADB and CD carry a load W applied by a cable-pulley arrangement, as shown in Figure P1.7. Determine ( a ) The components of the reactions at A and C . ( b ) The axial force, shear force, and moment acting on the cross-section at point G . Given: The pulley at B has a radius of 150 mm. Load W = 1 . 6 kN. Figure P1.7 Chapter 1, Solution 7 ( a ) C E D D x D y 0.25 0 15 R Cy R Cx 1.6 B y 1.6 B x 150 1.6 B Free body pulley B F B kN x x = = → ∑ 16 : . N ↑ F B k y y = = ∑ 16 : . Free body CED M R R kN D Cx Cx = − = = ← ∑ 0 4 16 015 0 6 : ( . ) . ( . ) , . N ← D y F D D k x x x = − − + = = ∑ 0 6 16 1 : . . , F R y Cy = = ∑ 0: Free body ADB M D B D kN R kN A y y y Cy = − = = = ↑ ∑ 0 5 15 4 8 4 8 : ( . ) ( . ) , . , . kN ↓ 32 . N → 0 6 . kN F R D B R x Ay y y Ay = − + − = = ∑ : , F R D B R k x Ax x x Ax = + − = = ∑ : , ( b ) M N m V G G = = ⋅ = 16 0 6 960 16 . ( . ) , . F k G N = 16 . M G F G B G V G 0 6 1. 1 6 Chapter 1, Solution 11 Free body-entire frame ∑ M R R kips A y y = − − = = 30 3 18 4 12 34 : ( ) ( ) ( ) , . Free body-member BC ∑ M R R C x y = − = 9 12 : ( ) ( ) and R k x = = 4 3 34 4 533 ( . ) . ips Thus F R kip BC = = + = ( . ) ( . ) . 4 533 34 5 666 2 2 s C B A 4 3 R x R y R 9 3 4 kips 3 12 18 Chapter 1, Problem 17 A thin triangular plate ABC is uniformly deformed into a shape AB ’ C , as shown by the dashed lines in Figure P1.17. Determine ( a ) The normal strain along the centerline OB. ( b ) The normal strain along the edge AB. ( c ) The shear strain between the edges AB and BC . Chapter 1, Solution 17 , 2 1.4142 OB AB BC L a L L a = = = = a (a) 0.0012 1200 OB a a ε µ = = (b) 1 2 2 2 ' ' (1.0012 ) 1.41506 1.41506 1.41421 601 1.41421 AB CB AB BC L L a a ε ε µ ⎡ ⎤ = = + = ⎣ ⎦ − = = = a (c) 1 ' 2 tan 89.931 1.0012 a AB C a − ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ o Decrease in angle ABC is 90 – 89.931 = 0.069 ° . Thus 0.069 1200 180 π γ µ ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ Chapter 1, Problem 19 A thin rectangular plate, a = 200 mm and b = 150 mm (Figure P1.19) is acted on by a biaxial tensile loading, resulting in the uniform strains ε x = 1000 μ and ε y = 800 μ ....
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This note was uploaded on 03/24/2010 for the course ME 031 taught by Professor Kim during the Winter '10 term at Korea Advanced Institute of Science and Technology.

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problem solution_ch1_ch3 - Chapter 1, Problem 7...

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