StressTransfmationExampl

# StressTransfmationExampl - Stress Transformation Examples...

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Hide Text Example I Example II Special Cases of Mohr's Circ (a) Determine the stress components for an element rotated 25° clockwise. (b) Determine the principal stresses, maximum in-plane shear, and the principal angle. s Hide Text 2 These are typical questions that need to be answered in practice when working with stress. (The questions in part (b) are generally the most common and most important, since they deal with maximums and minimums.) Following the general advice we received earlier, we will solve part (a) using the stress transformation equations and part (b) using Mohr's circle. Consider first part (a) … (a) Determine the stress components for an element rotated 25° clockwise. (b) Determine the principal stresses, maximum in-plane shear, and the principal angle. s Hide Text 3 To use the stress transformation equations, we need to identify the proper angle to use. The only trick is to get the sign right, which is not difficult since you can rely on the basic right-hand rule. In this case we have 25° clockwise, so the angle is negative and the corresponding sine and cosine are calculated as shown. (a) Determine the stress components for an element rotated 25° clockwise. (b) Determine the principal stresses, maximum in-plane shear, and the principal angle. s Hide Text 4 To compute σ x ', we use the equation we derived earlier. To evaluate this equation we need to identify σ x , σ y and τ xy from the figure. Again, the only hard part is getting the signs right. Stress Transformation Examples: 1

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(a) Determine the stress components for an element rotated 25° clockwise. (b) Determine the principal stresses, maximum in-plane shear, and the principal angle. s Hide Text 5 Before you go on, see if you can correctly identify the components on the figure. Remember that tension is positive, and compression is negative for normal components, while positive shears consist of positive directions on positive faces. (a) Determine the stress components for an element rotated 25° clockwise. (b) Determine the principal stresses, maximum in-plane shear, and the principal angle. s Hide Text 6 Once we have the original stress components and the angle, we simply plug the relevant values into the equation. (a) Determine the stress components for an element rotated 25° clockwise. (b) Determine the principal stresses, maximum in-plane shear, and the principal angle. s Hide Text 7 This is the result for σ x '. (a) Determine the stress components for an element rotated 25° clockwise.
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