beam analysis experimentation

# beam analysis experimentation - Bending Stress Calculation...

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Unformatted text preview: Bending Stress Calculation Area b of Area h of Area A = bh y measurement to centroid of Area A*y I = bh^3/12A(Yc­y)^2 I composite A1 1.5 0.25 0.38 2.88 1.08 0 0.71 0.71 A2 0.5 2.5 1.25 1.5 1.88 0.65 0 0.65 A3 1.5 0.25 0.38 0.13 0.05 0 0.71 0.71 Sum A = 2 Sum of A*y 3 Total Amount of Wood = 8 Yc = Location of Neutral Axis = Sum of A*y/ Sum of A = 1.5 Moment of Inertia, I compostite, about neutral axis = I1 + A1(Yc­y1)^2 + I2 +A2(Yc­y2)^2 + I3 + A3(Yc­y3)^2 = Sum Moment of Inertia = 2.07 Free Body Diagram = 1850/1.5 = 1233.3333 ( Maximum Moment M) 1233.33 Y1 = distance from Yc to top of beam = Y2 = distance from Yc to bottom of beam = 1.5 1.5 Flexural Stress on upper surface SIGMA = M*Y1/I Flexural Stress on upper surface SIGMA = M*Y2/I Shear Stress Calculation Area b of Area h of Area A = bh Distance of area's centroid to NA (y) A*y Q A4 0.5 1.25 0.63 0.63 0.39 t A1 1.5 0.25 0.38 1.38 0.52 I First Moment of Area (Q) = Sum Ay 0.91 in ^3 V Max horizontal shear @ neutral axis Tau = Q*V/I*t 43.72 0.91 0.5 2.07 50 composite 2 + I3 + A3(Yc­y3)^2 = Sum of I composites er surface SIGMA = M*Y1/I er surface SIGMA = M*Y2/I 892.46 892.46 Bending Stress Calculation Area b of Area h of Area A = bh y measurement to centroid of Area A*y I = bh^3/12A(Yc­y)^2 I composite A1 1.5 0.25 0.38 2.88 1.08 0 0.62 0.62 A2 0.5 2.5 1.25 1.5 1.88 0.65 0.01 0.66 A3 1 0.25 0.25 0.13 0.03 0 0.54 0.54 Sum A = 1.88 Sum of A*y 2.98 Total Amount of Wood = 7.5 Yc = Location of Neutral Axis = Sum of A*y/ Sum of A = 1.59 Moment of Inertia, I compostite, about neutral axis = I1 + A1(Yc­y1)^2 + I2 +A2(Yc­y2)^2 + I3 + A3(Yc­y3)^2 = Sum Moment of Inertia = 1.82 Free Body Diagram = 1850/1.5 = 1233.3333 ( Maximum Moment M) 1233.33 Y1 = distance from Yc to top of beam = Y2 = distance from Yc to bottom of beam = 1.41 1.59 Flexural Stress on upper surface SIGMA = M*Y1/I Flexural Stress on upper surface SIGMA = M*Y2/I Shear Stress Calculation Area b of Area h of Area A = bh Distance of area's centroid to NA (y) A*y Q A4 0.5 1.16 0.58 0.58 0.34 t A1 1.5 0.25 0.38 1.28 0.48 I First Moment of Area (Q) = Sum Ay 0.82 in ^3 V Max horizontal shear @ neutral axis Tau = Q*V/I*t 44.87 0.82 0.5 1.82 50 composite 2 + I3 + A3(Yc­y3)^2 = Sum of I composites er surface SIGMA = M*Y1/I er surface SIGMA = M*Y2/I 954.27 1078.49 Bending Stress Calculation Area b of Area h of Area A = bh y measurement to centroid of Area A*y I = bh^3/12A(Yc­y)^2 I composite A1 1 0.25 0.25 2.88 0.72 0 0.47 0.47 A2 0.5 2.5 1.25 1.5 1.88 0.65 0 0.65 A3 1 0.25 0.25 0.13 0.03 0 0.47 0.47 Sum A = 1.75 Sum of A*y 2.63 Total Amount of Wood = 7 Yc = Location of Neutral Axis = Sum of A*y/ Sum of A = 1.5 Moment of Inertia, I compostite, about neutral axis = I1 + A1(Yc­y1)^2 + I2 +A2(Yc­y2)^2 + I3 + A3(Yc­y3)^2 = Sum Moment of Inertia = 1.6 Free Body Diagram = 1850/1.5 = 1233.3333 ( Maximum Moment M) 1233.33 Y1 = distance from Yc to top of beam = Y2 = distance from Yc to bottom of beam = 1.5 1.5 Flexural Stress on upper surface SIGMA = M*Y1/I Flexural Stress on upper surface SIGMA = M*Y2/I Shear Stress Calculation Area b of Area h of Area A = bh Distance of area's centroid to NA (y) A*y Q A4 0.5 1.25 0.63 0.63 0.39 t A1 1 0.25 0.25 1.38 0.34 I First Moment of Area (Q) = Sum Ay 0.73 in ^3 V Max horizontal shear @ neutral axis Tau = Q*V/I*t 45.93 0.73 0.5 1.6 50 composite 2 + I3 + A3(Yc­y3)^2 = Sum of I composites er surface SIGMA = M*Y1/I er surface SIGMA = M*Y2/I 1157 1157 ...
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