1 / 35

Chapter 11

Chapter 11. Equilibrium and Elasticity. Equilibrium. Two Conditions for Equilibrium. To motivate these, recall:. Defining Equilibrium. Equilibrium = no net external force or torque = no change in translation or rotation) your text says L =0; others allow nonzero L :.

shauna
Télécharger la présentation

Chapter 11

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 11 Equilibrium and Elasticity

  2. Equilibrium

  3. Two Conditions for Equilibrium • To motivate these, recall:

  4. Defining Equilibrium • Equilibrium= no net external force or torque = no change in translation or rotation) • your text says L=0; others allow nonzero L:

  5. Defining Static Equilibrium • ‘Static’ Equilibrium= the special case of no translation or rotation at all

  6. Two Conditions for Equilibrium • When applying these, we must consider all external forces • But the gravitational force is rather subtle

  7. Center of Gravity (cg) • Gravity acts at every point of a body • Let t = the torque on a body due to gravity • Can find t by treating the body as a single particle (the ‘cg’)

  8. Center of Mass (cm) • it can be shown: if g = constant everywhere, then: • center of gravity =center of mass

  9. Using the Center of Gravity Pressent some more explanatory notes

  10. SolvingEquilibrium Problems

  11. Two Conditions for Equilibrium • From now on, in this chapter/lecture: • center of mass = center of gravity • ‘equilibrium’ means ‘static equilibrium’ • write: SF and St for SFext and Stext

  12. First Conditionfor Equilibrium

  13. Second Condition for Equilibrium

  14. Exercise 11-11 Work through Exercise 11-11

  15. Exercise 11-14 Work through Exercise 11-14

  16. A different version of Example 11-3 The ‘Leaning Ladder’ Problem Work through the variation the the text’s leaning ladder problem

  17. Problem 11-62 ‘Wheel on the Curb’ Problem Work through Problem 11-62

  18. Elasticity

  19. Elasticity • Real bodies are not perfectly rigid • They deform when forces are applied • Elastic deformation: body returns to its original shape after the applied forces are removed

  20. Stress and Strain • stress: describes the applied forces • strain: describes the resulting deformation • Hooke’s Law: stress = modulus × strain • modulus: property of material under stress • (large modulus means small deformation)

  21. Hooke’s Law and Beyond • O to a : • small stress, strain • Hooke’s Law:stress=modulus×strain • a < b : • stress and strain areno longer proportional

  22. Units • stress = modulus × strain • stress (‘applied force’): pascal= Pa=N/m2 • strain (‘deformation’): dimensionless • modulus: same unit as stress

  23. Types of Stress and Strain • Applied forces are perpendicular to surface: • tensile stress • bulk (volume) stress • Applied forces are parallel to surface: • shear stress

  24. Tensile Stress and Strain • tensile stress = F/A • tensile strain = Dl/l0 • Young’s modulus = Y

  25. Tensile Stress and Strain Work through Exercise 11-22

  26. Compression vs. Tension • tension (shown): pull on object • compression: push on object(reverse directionof F shown at left) • Ycompressive = Ytensile Work through Exercise 11-26

  27. Tension and Compression at once

  28. Bulk Stress and Strain • pressure: p=F/A • bulk stress = Dp • bulk strain = DV/V0 • bulk modulus = B

  29. Bulk Stress and Strain • B > 0 • negative sign above:Dp and DV have opposite signs Work through Exercise 11-30

  30. Shear Stress and Strain

  31. Shear Stress and Strain • shear stress = F7/A • shear strain = x/h = tanf • shear modulus = S

  32. Shear Stress and Strain Do Exercise 11-32

  33. Regimes of Deformation • O to a : • (small stress, strain) • stress=modulus×strain • elastic, reversible • a < b : • elastic, reversible • but stress and strainnot proportional

  34. Regimes of Deformation • From point O to b : • elastic, reversible • from point b to d: • plastic, irreversible • ductile materials havelong c–d curves • brittle materials haveshort c–d curves

  35. Demonstation Tensile Strength and Fracture

More Related