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L17 - Mohrs Circle for Plane Stress Estimate stress...

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Estimate stress graphically using Mohr’s circle For a known state of plane stress - plot center ( ave ) - plot point X ( , - ) - plot point Y ( y , ) - connect X and Y through C 2 2 2 2 x y x y ave xy R σ σ σ σ σ τ + = = + The principal stresses are obtained at A and B . max,min 2 tan 2 ave xy p x y R σ σ τ θ σ σ = ± = Mohr’s Circle for Plane Stress σ σ x σ τ xy τ xy
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Mohr’s Circle for Plane Stress For the state of stress at an angle with respect to the xy axes, construct a new diameter X’Y’ at an angle 2 with respect to XY . Normal and shear stresses are obtained from the coordinates X’Y’. θ θ
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The three circles represent the normal and shearing stresses for rotation around each principal axis. min max max 2 1 σ σ τ = Radius of the largest circle yields the maximum shearing stress. Mohr’s Circle for Three-Dimensional Analysis of Stress
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Mohr’s Circle for Three-Dimensional Analysis of Stress b) the maximum shearing stress for the element is equal to the maximum “in- plane” shearing stress a)
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