Chapter 11: Equilibrium and Elasticity

Students learn the two essential equilibrium conditions that must be satisfied for static equilibrium: the vector sum of all external forces must equal zero to prevent translational motion, and the net external torque about any axis must equal zero to prevent rotational motion. The concept of center of gravity emerges as a critical tool for analyzing equilibrium problems, representing the point where an object's total weight effectively acts and coinciding with the center of mass in uniform gravitational fields. The chapter develops systematic problem-solving strategies for equilibrium analysis, including construction of free-body diagrams, strategic selection of reference axes, and identification of forces that produce torque. Material mechanics introduces the relationship between stress and strain through Hooke's law, establishing that stress is proportional to strain within the elastic limit of materials. Three fundamental elastic moduli characterize material responses: Young's modulus governs tensile and compressive deformation, shear modulus describes resistance to parallel forces, and bulk modulus quantifies volumetric changes under pressure. The distinction between elastic and plastic behavior reveals critical material limits, including the proportional limit where linear stress-strain relationships end, the elastic limit beyond which permanent deformation occurs, and the ultimate breaking stress that causes material failure. Elastic hysteresis demonstrates energy dissipation during loading and unloading cycles, commonly observed in biological materials like tendons and synthetic materials like rubber, providing insight into real-world material behavior under repeated stress applications.