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Chapter 9: Elasticity and Fracture

Chapter 9: Elasticity and Fracture. Christopher Chui. Statics: Forces in Equilibrium. 1 st condition for equilibrium: The sum of all forces is zero: S F x = 0, S F y = 0, S F z = 0 2 nd condition for equilibrium: The sum of all torques is zero: St = 0. Problem Solving in Statics.

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Chapter 9: Elasticity and Fracture

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  1. Chapter 9: Elasticity and Fracture Christopher Chui Chapter 9: Elasticity and Fracture - Christopher Chui

  2. Statics: Forces in Equilibrium • 1st condition for equilibrium: The sum of all forces is zero: SFx = 0, SFy = 0, SFz = 0 • 2nd condition for equilibrium: The sum of all torques is zero: St = 0 Chapter 9: Elasticity and Fracture - Christopher Chui

  3. Problem Solving in Statics • Choose one body at a time for consideration, and make a careful free-body diagram to show all forces acting on it • Choose a coordinate system and resolve the forces into their components • Using letters to represent unknowns, write down the equation for SFx = 0, SFy = 0, SFz = 0 • For St = 0 equation, choose any axis perpendicular to the xy plane. Pay attention to the sign of the torque • Solve these equations for the unknowns Chapter 9: Elasticity and Fracture - Christopher Chui

  4. Stability and Balance • If an object is displaced slightly, 3 possible outcomes: 1) the object returns to its original position—stable equilibrium; 2) the object moves even farther—unstable equilibrium; 3) the object remains in its new position—neutral equilibrium • A body whose CG is above its base of support will be stable if a vertical line projected downward from the CG falls within the base of support Chapter 9: Elasticity and Fracture - Christopher Chui

  5. Elasticity, Stress and Strain • Hooke’s law: DL is proportional to applied force • There is a limit of elasticity; plasticity follows; and finally breaking • DL =(1/E)(F/A)Lo E is elastic or Young’s modulus • Stress = force / area = F/A • Strain = change in length / original length = DL / Lo • E = stress / strain Chapter 9: Elasticity and Fracture - Christopher Chui

  6. Three Types of Stresses • Tensile stress • Compressive stress • Shear stress • Shear strain DL = (1/G)(F/A) Lo where G is shear modulus = ½ to 1/3 of the elastic modulus • DV/Vo= -(1/B) DP, where B is the bulk modulus Chapter 9: Elasticity and Fracture - Christopher Chui

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