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Solution_06

# Solution_06 - CIV-100 Section B/E Solutions Fall 2011...

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CIV-100 Solutions Section B/E Fall 2011 Assignment 6 Due on Monday, October 24 th 2011 Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required. 1- The frame shown is supported by pins at A and B. Pulley F has a radius of 50mm. Determine: (a) the reaction components at A and B, (b) the force components at C on segment BCF. Solution : (a) Treat the structure as a whole and the FBD is as follows: W=(2800kg)(9.81N/kg)=27.468kN = = + = kN R W R M AX AX B 4 . 115 0 ) 05 . 0 1 ( ) 25 . 0 ( 0 = = + = kN R W R M BX BX A 4 . 115 0 ) 05 . 0 1 ( ) 25 . 0 ( 0 = + = + 0 0 W R R F BY AY Y ……………….(1) Separate all segments and analysis them respectively, the FBD is as follows Analyze the straight bar, = = = kN R W R M BY BY C 4 . 82 0 ) 75 . 0 ( ) 25 . 0 ( 0 Substitute R BY in (1), we have kN R AY 8 . 109 = (b) Analyze straight bar again, kN R W R R F CX CX BX X 9 . 87 0 0 = = + = + kN R W R R F CY CY BY Y 9 . 109 0 0 = = + = + R BX R BY R CX R CY W W B C W W F F W W R CX R CY R AX R AY A C W W R AX R AY R BX R BY

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CIV-100 Solutions Section B/E Fall 2011 Assignment 6 Due on Monday, October 24 th 2011 Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required. 2- The shown frame is supported by pins at A and C. Point B is an internal pin in the frame. Find: (a) The reaction components at the supports A and C. (b) The magnitude of force acting on the pin at B. Hint: Split the frame into 2 bodies AB and BC Solution : (a) The FBD for the entire frame has 2 unknown reaction components at A and 2 at B. But since I have only 3 equilibrium equations, how can I solve 4 unknowns? The key lies in the pin at B. Let’s work with what we have first. Applying the equilibrium equations: Σ M A = 0 -(3)(2) – (2.4)(3) + (3.2)(1.5) + (Cy)(3)=0 Cy = 2.8 kN Σ M C = 0 -(3)(2) + (3.2)(1.5) - (Ay)(3)=0 Ay = -0.4 kN (Negative value means that it is opposite to the direction shown) To find Ax and Cx I cannot use Σ Fx = 0. Thus I must split the frame at B which will expose 2 internal forces Bx and By.
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