Deflection Analysis
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Deflection analysis (Double integration method) Radius of curvature, rps rps=d2yd2x-1=EIM M=EI (d2yd2x)
From the above diagram, M= 12woLx-12wox2=EI (d2ydx2) EI dydx=14woLx2-16wox3+C1 EI y=112woLx3-124wox4+C1x+C2 When x=0, y=0, C2= 0, When x=L, y=0, 0=112woL4-124woL4+C1L C=-124woL3 Hence, EI y=112woLx3-124wox4-124woL3x Deflection maximum occur, ymax =δ, when x=12L EI y=112woL12L3-124wo12L4-124woL312L y=-5woL4384EI
From the above diagram, M= 12woLx-12wox2=EI (d2ydx2) EI dydx=14woLx2-16wox3+C1 EI y=112woLx3-124wox4+C1x+C2 When x=0, y=0, C2= 0, When x=L, y=0, 0=112woL4-124woL4+C1L C=-124woL3 Hence, EI y=112woLx3-124wox4-124woL3x Deflection maximum occur, ymax =δ, when x=12L EI y=112woL12L3-124wo12L4-124woL312L y=-5woL4384EI
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