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Understanding Elasticity and Fracture in Statics

Chapter 9 of Christopher Chui's text delves into the principles of elasticity and fracture. It explores key concepts like equilibrium, stress, strain, and the conditions for stability in physical systems. The chapter emphasizes the importance of free-body diagrams in problem-solving and introduces Hooke's law, which relates elastic deformation to applied force. Various types of stresses, including tensile, compressive, and shear, are discussed alongside their corresponding strains and moduli. This comprehensive overview serves as a fundamental guide for students studying mechanics.

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Understanding Elasticity and Fracture in Statics

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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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