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### 1.3 Stress & Strain Relationship of Hooke’s Law.ppt

• 1. UNIT 1.3 Stress & Strain Relationship of Hooke’s Law, Elastic Moduli, Stress–Strain Diagram Department of Physics
• 2. Restoring force or recovering force per unit area is called stress. Stress is expressed in or Pascal. Types of Stress •Normal stress •Tangential stress -2 Nm Department of Physics Stress Restoringforce F Stress= = Area A
• 3. Canyon Bridge, Los Alamos, NM o s = F A Simple compression Here compressive structure member (s < 0 here). OTHER COMMON STRESS STATES Ao Balanced Rock, Arches National Park Department of Physics
• 4. Ratio of the change in dimension produced by an external force to its original dimension is known as strain. Strain Change in volume Volumetric strain= Original volume Change in length Longitudinal strain= Original length Shearing strain=Angular displacement of the plane perpendicular to the fixed surface Department of Physics
• 5. Stress and Strain Stress refers to the cause of a deformation, and strain refers to the effect of the deformation. stress is the force strain is the elongation Department of Physics The downward force F causes the displacement x
• 6. Types of Modulus 1. Young’s Modulus (Y) 2. Bulk Modulus (K) 3. Rigidity Modulus (n) Department of Physics
• 7. Longitudinal Stress and Strain L DL A A F For wires, rods, and bars, there is a longitudinal stress F/A that produces a change in length per unit length. In such cases: F Stress A = L Strain L D = Young’s Modulus ' longitudinal stress Young s modulus longitudinal strain = / / F A FL Y L L A L = = D D Department of Physics
• 8. Shearing Stress and Shearing Strain A F F f l d A shearing stress alters only the shape of the body, leaving the volume unchanged. F F f l d A F Stress A = The strain is the angle expressed in radians d Strain l f = = Shearing Modulus The shearing modulus Units are in Pascal. F A S f = Department of Physics F
• 9. Bulk Modulus Volume stress F A K Volume strain V V  = = D Since F/A is generally pressure P, we may write: / P PV K V V V   = = D D Unit is Pascal Department of Physics
• 10. • When a spring is stretched, there is a restoring force that is proportional to the displacement. • Within the elastic limit, the ratio of the stress to the strain is constant (E). • E is the modulus of elasticity. Hooke’s Law Department of Physics 2 Stress strain Stress E Strain Stress E Nm Strain   =  =
• 11. Poisson’s Ratio (σ) Lateral strain σ = ------------------------------- = Longitudinal strain β = a constant α Department of Physics l d F D
• 12. Department of Physics Elastic Limit Maximum stress a body can experience without becoming permanently deformed. Fatigue If a body is continuously subjected to Stress or Strain, it gets fatigued (weak), called Elastic Fatigue.
• 13. 10 m steel wire stretches 3.08 mm due to the 200 N load. What is the longitudinal strain? Srain 3 Data Given : L 10m; L 3.08 10 m  = =  -3 ΔL 3.08 10 Strain = = L 10m m  -4 Longitudinal strain = 3.08×10 Department of Physics
• 14. Young’s modulus for brass is 8.96 x 1011Pa. A 120N weight is attached to an 8 m length of brass wire; the diameter is 1.5 mm. Find the increase in length. . Area of the wire Department of Physics -3 ΔL= 0.6×10 m 11 Y= 8.96 10 Pa, F=120N  -6 2 L=8m A=1.77×10 m 2 -3 2 -6 2 A=πr = 3.14×(0.75×10 m) =1.77×10 m -6 11 1 FL Increase in Length ΔL = AY 120N 8m = (1.77 10 )m (8.96 10 )Nm    
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