Chapter 6 - COMPLEX STRESS.pdf - CHAPTER 6 COMPLEX STRESS INTRODUCTION • The most general state of stress at a point may be represented by 6


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2 INTRODUCTION The most general state of stress at a point may be represented by 6 components, , , : (Note stresses shearing , , stresses normal , , xz zx zy yz yx xy zx yz xy z y x Same state of stress is represented by a different set of components if axes are rotated. 9.1 Plane Stress Transformation In practice, approximations and simplifications are done to reduce the stress components to a single plane.
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3 Plane Stress Plane Stress state of stress in which two faces of the cubic element are free of stress. For the illustrated example, the state of stress is defined by . 0 , , and xy zy zx z y x State of plane stress occurs in a thin plate subjected to forces acting in the midplane of the plate. State of plane stress also occurs on the free surface of a structural element or machine component, i.e., at any point of the surface not subjected to an external force. 9.1 Plane Stress Transformation
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4 Plane Stress Transformation The material is then said to be subjected to plane stress. For general state of plane stress at a pt, we represent it via normal-stress components, x , y and shear-stress component xy . Transforming stress components from one orientation to the other is similar in concept to how we transform force components from one system of axes to the other. Note that for stress-component transformation, we need to account for - the magnitude and direction of each stress component, and - the orientation of the area upon which each component acts. 9.1 Plane Stress Transformation
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5 Procedure of Analysis (Method of Equilibrium) If state of stress at a pt is known for a given orientation of an element of material, then state of stress for another orientation can be determined. 9.1 Plane Stress Transformation
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Transformation of Plane Stress consider the stress element has rotated through an angle θ as shown. As linear equations, the transformed stresses are given by 145
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7 Sign Convention Positive normal stresses, x and y , acts outward from all faces Positive shear stress xy acts upward on the right-hand face of the element.
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