STRESS_IV - STRESS TRANSFORMATIONS AND MOHRS CIRCLE...

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1 STRESS TRANSFORMATIONS AND MOHR’S CIRCLE MECH320-SPRING 08

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2 OUTLINES Principal Stresses Maximum Shear Stress Mohr's Circle
3 Principal stresses Consider the traction vector on the x-face as shown. For this entire stack we will make an important limitation on our stress state, namely that it is 2-Dimensional . The traction vector shown lies in the x-y plane, and we will change the orientation of the block by rotating about the z-axis only.

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4 We know that the traction vector on a given surface depends on the orientation of the surface. We might ask if we can find an orientation such that the traction vector is parallel to the normal. Principal stresses (Cont.)
5 Principal stresses (Cont.) The normal component, σ x' is equal in magnitude to the traction vector and the shear vanishes. Such stress components are very important since they turn out to be the maximum and minimum normal components, and so we give them a special name: Principal Stresses. To calculate such stress components it is necessary to determine the proper block orientation. For this we will need the stress transformation equation for shear.

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Principal stresses (Cont.) By definition, the principal stresses occur on planes for which the shear stress vanishes. Therefore, we can use this equation to solve for the θ for which τ x'y' = 0. The algebra is not difficult, and we can obtain the relation between the principal orientation angle and the basic stress components as shown. Find
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This note was uploaded on 02/07/2011 for the course MECH 320 taught by Professor D.a during the Spring '09 term at American University of Beirut.

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STRESS_IV - STRESS TRANSFORMATIONS AND MOHRS CIRCLE...

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