2009+15-3+StressStrain

2009+15-3+StressStrain - Introduction to Solid Mechanics...

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1 SJTU Introduction to Solid Mechanics -Vm211 Chapter 15 SRESS AND STRAIN TRANSFORMATION Chapter 15 Stress and Strain Transformation SJTU Introduction to Solid Mechanics -Vm211 ± A point in a body subjected to a general 3-D state of stress will have a normal stress and 2 shear-stress components acting on each of its faces. ± We can develop stress-transformation equations to determine the normal and shear stress components acting on ANY skewed plane of the element. 15.5 ABSOLUTE MAXIMUM SHEAR STRESS SJTU Introduction to Solid Mechanics -Vm211 ± It is possible to determine the unique orientation of an element having only principal stresses acting ± These principal stresses are assumed to have maximum, intermediate and minimum intensity: σ max int min . 15.5 ABSOLUTE MAXIMUM SHEAR STRESS SJTU Introduction to Solid Mechanics -Vm211 ± Assume that orientation of the element and principal stress are known, thus we have a condition known as triaxial stress. The transformation of stress for 3-D (is beyond the scope of this course?) can be done in Appendix B . 15.5 ABSOLUTE MAXIMUM SHEAR STRESS SJTU Introduction to Solid Mechanics -Vm211 ± Viewing the element in 2D ( y’-z’, x’-z’,x’-y’ ) we then use Mohr’s circle to determine the maximum in-plane shear stress for each case. 15.5 ABSOLUTE MAXIMUM SHEAR STRESS SJTU Introduction to Solid Mechanics -Vm211 ± As shown, the element have a 45 ° orientation and is subjected to maximum in-plane shear and average normal stress components. 15.5 ABSOLUTE MAXIMUM SHEAR STRESS
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2 SJTU Introduction to Solid Mechanics -Vm211 ± Comparing the 3 circles, we see that the absolute maximum shear stress is defined by the circle having the largest radius. ± This condition can also be determined directly by choosing the maximum and minimum principal stresses: max abs τ () 13 - 5 1 2 min max max abs σ = 15.5 ABSOLUTE MAXIMUM SHEAR STRESS SJTU Introduction to Solid Mechanics -Vm211 ± Associated average normal stress 14 - 5 1 2 min max avg + = 15.5 ABSOLUTE MAXIMUM SHEAR STRESS SJTU Introduction to Solid Mechanics -Vm211 ± It can be proved by theory of elasticity that regardless of the orientation of the plane, specific values of shear stress τ on the plane is always less than absolute maximum shear stress found from Eq. 15-13. 15.5 ABSOLUTE MAXIMUM SHEAR STRESS 13 - 5 1 2 min max max abs = SJTU Introduction to Solid Mechanics -Vm211 ± It is also proved that the normal stress acting on any plane will have a value lying between maximum and minimum principal stresses, max min .
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2009+15-3+StressStrain - Introduction to Solid Mechanics...

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