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Lecture21-Notes

# Lecture21-Notes - ME 382 Lecture 21 YIELD OR FRACTURE Can...

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ME 382 Lecture 21 1 Y IELD OR F RACTURE ? Can design by comparing fracture load to load required for either (i) Onset of yield ( ˜ σ H = σ Y anywhere on section) (ii) Net section yield or "plastic collapse" ( ˜ σ H = σ Y across section) - upper bound on failure load The two are equivalent for uniaxial tension Yield only occurs along planes of maximum shear Load for onset of yield ( P e ) = load for net section yield ( P p ): P e =P p = (2 b -2 a ) t σ Y Two possible loads for yield: P e = P p = (2 b - a ) t σ Y P Y = P p = 3 . (2 b - 2 a ) t σ Y (for yield of ligament) (inverse of hardness test - complex stress between cracks) Ligament yields only if a > 4 b / 5 Onset of yield and net section yield are different in bending Moment for onset of yield (rectangular beam): M e = tb 2 σ Y /6 Moment for net section yield (rectangular beam): M p = tb 2 σ Y /4

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ME 382 Lecture 21 2 Net section yield of beam of width b & crack of length a : M p = t b a ( ) 2 σ Y /4 Complication of beam with single crack and axial load ...... Moment at cracked section: M = Pa /2 Maximum nominal stress on cracked section (ignoring stress singularity): σ = M b a ( ) 2 12 t b a ( ) 3 + P b a ( ) t = 2 a + b ( ) P
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Lecture21-Notes - ME 382 Lecture 21 YIELD OR FRACTURE Can...

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