Stress Transformation - Plane Stress & Mohr's Circle

Stress Transformation - Plane Stress & Mohr's Circle -...

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CIVL 311 Stress Transformations – Plane Stress F n = 0: σ n = x cos 2 θ + y sin 2 + 2 τ xy sin cos n = x + y () 2 + x y 2 cos2 + xy sin2 F t = nt =− x y 2 + xy x = x + y 2 + x y 2 + xy y = x + y 2 x y 2 xy x y x y ( ) 2 + xy Principal Stress ( σ max and σ min ) and τ max : p = x + y 2 ± x y 2 2 + xy 2 at tan2 p = xy x y 2 max x y 2 2 + xy 2 at s x y 2 xy Summary: There are two principal planes, 90 ° apart, located by θ p . On these planes are the principal stress values σ p = σ max and σ min . There are two other planes containing τ max , also 90 ° apart, located by θ s . The principal planes are always separated from the τ max planes by 45 ° . The shear stress is always zero on principal planes. 1 of 2
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CIVL 311 2 of 2 Mohr’s Circle – Plane Stress
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This note was uploaded on 01/07/2012 for the course CIVL 311 taught by Professor Mills during the Spring '09 term at CSU Chico.

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Stress Transformation - Plane Stress & Mohr's Circle -...

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