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2009+15-1+StressStrain - Introduction to Solid...

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1 SJTU Introduction to Solid Mechanics-Vm211 Chapter 15 STRESS AND STRAIN TRANSFORMATION Chapter 15 Stress and Strain Transformation SJTU Introduction to Solid Mechanics-Vm211 CHAPTER OUTLINE 1. Plane-Stress Transformation 2. General Equations of Plane Stress Transformation 3. Principal Stresses and Maximum In-Plane Shear Stress 4. Mohr’s Circle – Plane Stress 5. Absolute Maximum Shear Stress 6. Plane Strain 7. General Equations of Plane-Strain Transformation 8. Mohr’s Circle Plane Strain 9. Strain Rosettes 10. Material-Property Relationships SJTU Introduction to Solid Mechanics-Vm211 Stress state at a point State of plane stress at a point on surface of airplane fuselage. SJTU Introduction to Solid Mechanics-Vm211 15.1 PLANE-STRESS TRANSFORMATION General state of stress at a point is characterized by six independent normal and shear stress components. In practice, approximations and simplifications are done to reduce the stress components to a single plane. SJTU Introduction to Solid Mechanics-Vm211 The material is then said to be subjected to plane stress . For general state of plane stress at a point, we represent it via normal-stress components, σ x , σ y and shear-stress component τ xy . Thus, the state of plane stress at the point is uniquely represented by three components acting on an element that has a specific orientation at that point. 15.1 PLANE-STRESS TRANSFORMATION SJTU Introduction to Solid Mechanics-Vm211 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. 15.1 PLANE-STRESS TRANSFORMATION
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