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Stress Analysis

Stress Analysis. Mechanics: Stress and strain. Topics. Free Body Diagrams (Review) Stress Strain Deformation Hooke’s Law Stress-Strain Diagrams Design: The Safety Factor. Free Body Diagrams. Shows all external forces acting on the body Procedure Identify the isolated body and draw it

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Stress Analysis

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  1. Stress Analysis Mechanics: Stress and strain Stress and Strain

  2. Topics • Free Body Diagrams (Review) • Stress • Strain • Deformation • Hooke’s Law • Stress-Strain Diagrams • Design: The Safety Factor Stress and Strain

  3. Free Body Diagrams • Shows all external forces acting on the body • Procedure • Identify the isolated body and draw it • At all force locations draw the vectors • Supports • Connections • Contacts • Add the Weight force • Label forces with their value or a letter for unknowns • Add a coordinate system • Add geometric data (Lengths, angles, … ) Stress and Strain

  4. Examples 1 Stress and Strain

  5. Examples 2 Stress and Strain

  6. Examples 3 Stress and Strain

  7. Stress • Internal Forces • Reaction to external forces • Distributed throughout volume of material • Stress • Normal stress • Acts at right angles to a selected plane • The axial direction in a rod or cable • Shear stress: stays in the selected plane(advanced topic: Strength of materials course) • Can a structure withstand the forces applied to it? Stress and Strain

  8. Stress 2  = P/A (Pascals) : Average stress P: Applied force A: Cross section area Tension / Compression Stress and Strain

  9. Strain • Strain: deformation due to stress  =  / L : Normal strain : Change in length L: Original (unstressed) length Stress and Strain

  10. Hooke’s Law • SpringsF = kx F: Applied Force k: Spring constant x: displacement • Stress-Strain = E : Stress E: Modulus of Elasticity  : Strain • Using = P / A and  =  / L Stress and Strain

  11. Stress-Strain Diagram Stress and Strain

  12. Example 6 • 200 kg engine block • Cables • 0.7 m long • 4 mm diameter • E = 200 GPa • Find • Normal Stress • Axial Deformation Fac Fab Weight F = 200 kg * 9.8 m/sec2 F = 1960 newtons Stress and Strain

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