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Material Joining and Beam Bending

Material Joining and Beam Bending. Lab 7. F. δ. Beam Deflection. Every object acts as a spring – it will deflect when a force is applied Extent of deflection ( δ ) depends on: Force applied Object geometry Material properties. Object Geometry: Moments of Inertia.

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Material Joining and Beam Bending

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  1. Material Joining and Beam Bending Lab 7 Autumn Quarter

  2. F δ Beam Deflection • Every object acts as a spring – it will deflect when a force is applied • Extent of deflection (δ) depends on: • Force applied • Object geometry • Material properties Autumn Quarter

  3. Object Geometry: Moments of Inertia • A larger moment of inertia means that the beam will be more resistant to deflection • Area Moments of Inertia (I) depends on object shape h h2 h1 b b2 b1 Autumn Quarter

  4. Although the beams have the same cross-sectional area, the moments of inertia are different Because the moments of inertia are different, the beams deflect different amounts Differences in Deflection - Geometry Autumn Quarter

  5. Strain: Stress: (lb/inch2) L (original length) F (applied force) A (cross-sectional area) d (deflection from original length) Stress and Strain: Simple Definitions Autumn Quarter

  6. Material Property: Young’s Modulus (E) Strain: Stress: (lb/inch2) Young’s modulus (or the modulus of elasticity) is the ratio of stress to strain in a material: units: Note that Young’s modulus does not depend on the geometry of the object. Autumn Quarter

  7. Strain: Stress: Stress, Strain, and Young’s Modulus Stress vs. Strain Curves: Linear Portion (Hooke’s Law): Young’sModulus (slope of curve or material stiffness) Autumn Quarter

  8. dial indicator δ F s L Cantilever Beam Bending Equation • In this lab, you will measure the deflection δ for various loads F. Compare experimental deflection to theoretical for each case. Theoretical deflection: Autumn Quarter

  9. Welding • Consists of heating the joints and adding a filler material • Different from brazing and soldering • Alternative to fasteners like nuts and bolts • More permanent way to join materials Autumn Quarter

  10. Material Joining • The final product will form a ‘T’ shape Autumn Quarter

  11. Things to Consider: • How will joining the beams through welding affect the overall stiffness? • Is there any advantage to choosing a more flexible material such as aluminum over a stiffer material such as steel? • Hypothetically, if you were to design a 9x9” robot spring quarter, which materials do you feel would be most suited for use? • Which shapes would form a stiffer chassis? Autumn Quarter

  12. Lab Reports • Individual lab report • Include sketch of experimental set-up • Detailed lab-specific requirements not given: determine what is appropriate based on write-up and data gathered. Autumn Quarter

  13. Questions ? Autumn Quarter

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