L11 - Chapter 4 Bending Stress due to bending x =-My I M...

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Stress due to bending: I My x ± = σ M: moment (couple) y: distance from the neutral surface I: moment of inertia of the cross section Chapter 4: Bending
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1 ρ = M EI Curvature: 1 Absolute maximum strain: ε c m = 1 m c = 1 m Ec σ = 1 1 Mc I Ec ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠
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Deformations in a Transverse Cross Section • in-plane deformations are nonzero (deformation on the cross-sectional plane) ε y = νε x = ν y ρ z = x = y y> 0 + and + expansion in y,z y< 0 - and - contraction in y,z y z y z
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• Expansion above the neutral surface and contraction below it causes an in-plane curvature (warping) curvature c anticlasti 1 = = ρ ν expansion contraction
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Topics today: - Eccentric axial loading (cause bending) - Asymmetric bending (superposition)
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Eccentric Axial Loading in a Plane of Symmetry Eccentric loading (loading doesn’t go through the centroid of the cross sectional area) Pd M P F = = centric loading (loading goes through the centroid
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This note was uploaded on 12/14/2010 for the course ENGR 2530 taught by Professor Lindaschadlerfeist during the Fall '08 term at Rensselaer Polytechnic Institute.

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L11 - Chapter 4 Bending Stress due to bending x =-My I M...

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