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Four Point Bending
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Other Types of Bending Bending by Eccentric LoadingCantilever Bending
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Various Boundary Conditions of Beams
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Features of Beam Deformation
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Neutral Plane and Axis of Symmetry
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Assumptions for Beam Theory Kirchhoff Hypotheses--- The cross-sections remain a straight plane perpendi- cular to the mid plane. The vertical segments are not stretched. Bernoulli-Euler Beams
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Deformation of Beams under Pure Bending
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Curvature under Pure Bending Neutral AxisConstant Curvature
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Strain Analysis for Bending = L’ – L = ( -y) – = -y x = / L = -y -y x | max = c x = (-y c) x | max
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Stress Distribution in Bending x = (-y c) x | max = (-y/c) m m = Mc/I Neutral plane should pass through the centroid.
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Stress/Strain Distribution in Beams under Pure Bending
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Section Modulus and Bending Stiffness m = Mc/I x = (-y/c) m { x = -My/I Define Section Modulus as S = I/c Then m = M/S Also x = -y -y My/I = Ey/ = 1/ = M/EI (EI: Bending Stiffness) Note: /L = P/EA, /L = T/GJ
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Beams with Irregular Cross-sections
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Stress Distribution in Beams with Irregular Cross-sections
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Asymmetric Bending of Symmetric Beams
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Pure Bending of Asymmetric Beams
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Composite Beams
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Stress Distribution in Composite Beams
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Bending Due to Eccentric Loading
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