Mechanics 1R

Mechanics 1R - 2.001 - MECHANICS AND MATERIALS I Lecture...

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2.001 - MECHANICS AND MATERIALS I Lecture # 11/1/2006 Prof. Carol Livermore Recall equations of isotropic linear elasticity: 1 ±² ± xx = σ xx ν ( σ yy + σ zz ) E 1 ± = σ ν ( σ xx + σ ) E 1 ± xx = σ ν ( σ xx + σ ) E 1 ± xy = 2 G σ xy 1 ± xz = σ xz 2 G 1 ± yz = σ 2 G Thermoelastic Behavior: Δ T> 0 L L + α Δ TL α is the coefficient of linear thermal expansion ”CTE”. Therma lStra in(Foranunconstra inedb lock) ± T = α Δ T xx ± T = α Δ T ± T = α Δ T 1 15
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σ xx = σ yy = σ zz = σ xy = σ yz = σ xz =0 Note: If the block were constrained, there could be a ”thermal stress.” Total Strain: Elastic + ± Thermal ± xx = ± xx xx ± = ± E + ± T ET ± = ± + ± Equations of Linear, Isotropic, Thermoelasticity 1 ±² ± xx = σ xx ν ( σ + σ )+ α Δ T E 1 ± = σ ν ( σ xx + σ ) α Δ T E 1 ± xx = σ ν ( σ xx + σ ) α Δ T E 1 ± xy = σ xy 2 G 1 ± xz = σ xz 2 G 1 ± = 2 G σ EXAMPLE: Block in a frictionless channel Subject block to an increased T T> 0 Find ± T , σ ± xx σ xx =?
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Mechanics 1R - 2.001 - MECHANICS AND MATERIALS I Lecture...

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