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Hello students, in this question we are asked to calculate the determine the equivalent state of stress at a point which represents principal stresses.
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Principal stresses.
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That is a and b.
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The maximum in -plane shear stress.
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In -plane shear stress.
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To calculate both of these things, let's assume a system of weights having stresses, different stresses acting at different points.
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This is sigma 1, this is sigma 2 and this is sigma 3.
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We only need two stresses.
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Sigma 1 and sigma 2 at the end points.
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So the equivalent stress for principal stress, for the equivalent stress can be written down.
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Sigma equivalent will be equal to square root of sigma 1 square plus sigma 2 square plus or minus sigma 1 times sigma 2.
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This will give you the equivalent stress at that point.
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The average, sigma average will be equal to sigma 1 plus sigma 2 by 2.
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So you can use this equation to find that out.
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Now to find the maximum planar stress, b part.
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The maximum planar stress, the current stress also known as tresca stress...