ME85-lecture19

# ME85-lecture19 - Lecture 19 Beam Bending Step 3 Step 3 Pure...

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Lecture 19 Beam Bending

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Step 3 Step 3 Pure bending

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Examples of Pure Bending
Pure Bending Pure Bending : Prismatic members subjected to equal and opposite couples acting in the same longitudinal plane

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Bernoulli-Euler Kinematic Assumption
Bending Deformations Beam with a plane of symmetry in pure bending: member remains symmetric bends uniformly to form a circular arc cross-sectional plane passes through arc center and remains planar length of top decreases and length of bottom increases a neutral surface must exist that is parallel to the upper and lower surfaces and for which the length does not change stresses and strains are negative (compressive) above the neutral plane and positive (tension) below it

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Symmetric Member in Pure Bending = = = = = = M dA y M dA z M dA F x z x y x x σ 0 0 These requirements may be applied to the sums of the components and moments of the statically indeterminate elementary internal forces. Internal forces in any cross section are equivalent to a couple. The moment of the couple is the section bending moment . From statics, a couple M consists of two equal and opposite
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ME85-lecture19 - Lecture 19 Beam Bending Step 3 Step 3 Pure...

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