Page 172 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 13

Elasticity

STRESS AND STRAIN

The stress on a body acted on by a deforming force is equal to F/A, the magnitude of the force F divided by
the cross-sectional area A over which it acts. The unit of stress in SI units is newtons per square meter, which is
known as the pascal (Pa). In the British system it is customary to use pounds per square inch. The three categories
of stress—tension, compression, and shear—are illustrated in Fig. 13-1. The unstressed shape is shown by the
dashed lines, and the stressed shape by the solid lines.

Fig. 13-1

Therelativechangeinthesizeorshapeofabodyduetoappliedstressiscalledstrain.Strainisadimensionless
quantity; for instance, the longitudinal strain that tension produces in a body is L/L 0 , its change in length L
divided by its original length L 0 , which is a pure number.

ELASTICITY
The elastic limit of a material is the maximum stress that can be applied to a body without causing a permanent
deformation. For stresses below the elastic limit, the material exhibits elastic behavior: when the stress is removed,
the body returns to its original size and shape.
Below the elastic limit, strain is found to be proportional to stress. This relationship is known as Hooke’s law.
In the case of tension, for example, doubling the applied force on a body will double the amount by which the
body stretches. The modulus of elasticity of a material subjected to a particular kind of stress below its elastic
limit is defined by the relationship
stress
Modulus of elasticity =
strain
The ultimatestrength of a material is the greatest stress it can withstand without rupture. In many materials
the ultimate strength considerably exceeds the elastic limit. When a stress greater than its elastic limit but less
than its ultimate strength is applied to such a material, the result is a permanent deformation. Bending a piece of
metal is an example.
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