lecturei2mohrstr

lecturei2mohrstr - Mohr-Plane Construction e2 Starting...

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Mohr-Plane Construction e 2 E ( λ 1 e 1 γ e 2 Θ 1 • Starting Point: – Strain vector in n = e 1 ) material plane (=measurement plane) E ( e 1 ) = 1 e 1 + e 2 e 1 λ 1 = ε 11 (rel. length variation) = ε 12 (distortion) 1.033/1.57 Mechanics of Material Systems
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2. Strain Vector in Mohr Plane e 2 E ( λ 1 e 1 γ e 2 Θ 1 γ OE ( n = e 1 ) e 1 ) Θ 1 n=e 1 1 Same Angle Θ 1 in both planes 1.033/1.57 Mechanics of Material Systems
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3. 2 nd Strain Vector λ γ e 2 E ( n 2 = e 2 ) λ 2 n γ t 2 OE ( e 2 ) OE ( e 1 ) OE ( e 1 ) and OE ( e 2 ) are two points on the Mohr Circle 2 1 t = e 1 Θ 2 Θ 2 1.033/1.57 Mechanics of Material Systems
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4. Center of Mohr Circle OE ( e 2 ) λ γ e 1 e 2 OE ( e 1 ) λ c = ( 1 + 2 ) / 2 2 1 c 1.033/1.57 Mechanics of Material Systems
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5. Mohr Circle λ γ e 1 e 2 OE ( e 1 ) λ 1 c R 2 OE ( e 2 ) 1.033/1.57 Mechanics of Material Systems
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6. Principal Strains e 2 γ λ 2 e 2 ) OE ( e 1 ) 1 λ c R I,II = c ± R e 1 Ι ΙΙ OE ( 1.033/1.57 Mechanics of Material Systems
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7. Principal Strain Vector in M-Plane e 2 γ OE ( e 1 ) λ 2 λ c R OE ( u I ) 2 e 2 ) e 1 Ι ΙΙ OE ( 1.033/1.57 Mechanics of Material Systems
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lecturei2mohrstr - Mohr-Plane Construction e2 Starting...

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