Physics · Ch 8 — Mechanical Properties of Solids
Introduction
Introduction
8.1 Introduction
In Chapter 6, we studied the rotation of bodies and saw that motion depends on how mass is distributed within the body. That analysis was restricted to rigid bodies — objects that do not change shape under any force. A rigid body, in the ideal sense, is a hard solid object with a definite shape and size that remains unchanged regardless of the forces applied.
But real solids are not perfectly rigid. Even a steel bar, which we think of as extremely stiff, can be deformed when a sufficiently large external force is applied. This means that every solid body, no matter how hard, can change its shape or size under load.
Deformation and the Need for Force
A solid has a definite shape and size. To change either — to stretch it, compress it, bend it, or twist it — a force is required. Consider a helical spring. If you gently pull its ends, the length of the spring increases slightly. The spring has been deformed. Now release the ends — the spring snaps back to its original size and shape. This behaviour is not unique to springs; it is a general property of many solid materials.
Elasticity and Elastic Deformation
The property of a body by virtue of which it tends to regain its original size and shape when the applied force is removed is called elasticity. The deformation produced during the action of the force is called elastic deformation.
Elastic deformation is reversible — the body returns to its original configuration once the load is taken off. The spring example is a perfect illustration: the extension disappears when you let go.
Plasticity and Plastic Deformation
Not all materials behave this way. Take a lump of putty or mud and squeeze it. When you remove your hand, the putty does not spring back — it stays deformed. Such substances show no gross tendency to regain their previous shape. They are called plastic materials, and this property is called plasticity. Putty and mud are close to ideal plastics — they undergo permanent deformation under even small forces.
Do not confuse elasticity with plasticity. In elastic deformation, the body returns to its original shape after the force is removed. In plastic deformation, the change is permanent — the body does not recover.
Why Elasticity Matters in Engineering
The elastic behaviour of materials is not just a textbook curiosity — it is central to engineering design. When a building is designed, the engineer must know the elastic properties of steel, concrete, and other materials to ensure the structure can bear loads without collapsing or deforming permanently. The same is true for bridges, automobiles, ropeways, and virtually every load-bearing structure.
Consider these questions that engineers face:
- Can we design an aeroplane that is very light but sufficiently strong?
- Can we design an artificial limb that is lighter but stronger than existing ones?
- Why does a railway track have a particular shape — like the letter I?
- Why is glass brittle while brass is not?
The answers to all these questions begin with the study of how relatively simple kinds of loads or forces act to deform different solid bodies. Understanding the relationship between force and deformation — the elastic behaviour of materials — is the first step toward answering them.
What This Chapter Covers
In this chapter, we shall study the mechanical properties of solids — how solids respond to external forces, the concepts of stress and strain, Hooke's law, elastic moduli, and the elastic behaviour of materials. The introduction sets the stage: solids are not perfectly rigid; they deform under load, and the nature of that deformation — elastic or plastic — determines how we use them in the real world.
The key distinction to carry forward: elasticity means the body returns to its original shape after the force is removed; plasticity means the deformation is permanent. Most real materials show some of both — they are elastic up to a certain limit, and plastic beyond it. That limit is crucial in design.