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Understanding Stability, Elasticity, and Fracture in Statics Concepts

Learn about equilibrium, stability, deformation, Hooke’s Law, stress, strain, modulus, fractures in objects under stress, and more in statics.

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Understanding Stability, Elasticity, and Fracture in Statics Concepts

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  1. Section 9-4:Stability & Balance • STATICS (Equilibrium) ∑F = 0 and ∑τ = 0 • Now:A body initially at equilibrium. Apply a small force & then take that force away. The body moves slightly away from equilibrium. 3 Possible Results: 1. Object returns to the original position.  The original position was aSTABLE EQUILIBRIUM. 2.Object moves even further from the original position.  The original position was anUNSTABLE EQUILIBRIUM. 3.Object remains in the new position.  The original position was aNEUTRAL EQUILIBRIUM.

  2. Usually: Interested in maintaining a Stable Equilibrium “BALANCE”. • General: Object with Center of Gravity (CG) below its support point is in Stable Equilibrium. • CG above base of support? Stable as long as remains above base. Unstable if displaced so CG is no longer above base. Critical point = point where CG is just above edge of base.

  3. Stable(BALANCED): Vertical line from CG falls within support base. • Unstable: Vertical line falls outside support base. • Critical point in changing from stable to unstable = point where CG is above edge of support base.

  4. Stability: A relative concept. 4 legged animals are more stable than humans.

  5. Section 9-5: Elasticity, Stress, Strain One effect of forces on objects: DEFORMATION= Change of size or shape. Suppose force F pulls on object. Find (L0 >> L) F  L . Write: F = kL “Hooke’s Law” (small forces only!) k = constant which depends on material

  6. Hooke’s “Law” F = kL holds only for small L! For larger L, material will permanently deform & possibly break.

  7. Elastic Modulus • F = kL. Ldepends on applied force & also on material composition. • The constant k can be written to account for this. Experiment: Object, cross sectional area A pulled by force F (L << L0) Write: F  EA(L/L0)  k L E  “Elastic Modulus” (Young’s Modulus) (Depends on material) • Another form (fractional length change or strain): (L/L0) = (1/E)(F/A) F/A = Force/area (Stress). Strain  Stress

  8. (L/L0) = (1/E)(F/A)

  9. Strain & Stress • (L/L0) = (1/E)(F/A)  Strain  Stress • External force  Internal stress (tension) This is tensile stress (tension)

  10. 3 Types of Stress

  11. Shear Modulus • Object under shear stress is not in equilibrium. A net torque exists. ∑τ 0 Shear modulus G.

  12. Bulk Modulus • Object subjected to inward forces from all sides  Volume decreases. (Ch. 10: Object submersed in a fluid). Initial volume V0. Change in volume V. • Write: (V/V0)  -(1/B) (F/A) = -(1/B) P B  Bulk modulus. P = F/A = pressure - sign indicates volume shrinks under pressure

  13. Section 9-6: Fracture • If stress is too great, object breaks or cracks = “Fractures”

  14. Section 9-6: Fracture

  15. Example 9-11 • Beam sagging under its own weight:

  16. Conceptual Example 9-12 • Tragic substitution!

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