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Problem_05_34 - Problem 5.34 Given Beam ABC is simply...

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R A R C Q Problem 5.34 Given: Beam ABC is simply supported ans subjected to a linearly varying distributed load as shown. Determine the deflection of the center of the beam. Solution: Apply dummy load Q at the center and compute reaction forces R A and R C z wL/4 + Q/2 V M 2wz/L R A R C = w L 4 Q 2 + = At any z coordinate between 0 < z < L/2, the distributed load at the left end is: w z L 2 The total load over length z is w 2 z L z 2 w z 2 L = The centriod of the load is z/3 from the left end and thus: For 0 < z < L/2 V w L 4 Q 2 + w z 2 L = M w L 4 Q 2 + z w z 2 L z 3 = w L z 4 z 3 3 L
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