2009+15-1+StressStrain

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 , 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 ² the magnitude and direction of each stress component, and ² the orientation of the area upon which each component acts. 15.1 PLANE-STRESS TRANSFORMATION
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2 SJTU Introduction to Solid Mechanics-Vm211 Procedure for Analysis ± If state of stress at a point is known for a given orientation of an element of material, then state of stress for another orientation can be determined 15.1 PLANE-STRESS TRANSFORMATION SJTU Introduction to Solid Mechanics-Vm211 Procedure for Analysis 1. Section element as shown. 2. Assume that the sectioned area is A , then adjacent areas of the segment will be A sin θ and A cos . 3. Draw free-body diagram of segment, showing the forces that act on the element. (Tip: Multiply stress components on each face by the area upon which they act) PLANE-STRESS TRANSFORMATION SJTU Introduction to Solid Mechanics-Vm211 Procedure for Analysis 4. Apply equations of force equilibrium in the x ’ and y directions to obtain the two unknown stress components σ x , and τ x’y .
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This note was uploaded on 08/09/2011 for the course EE 211 taught by Professor Liuxila during the Summer '09 term at Shanghai Jiao Tong University.

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

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