Stress and Strain:-

Introduction

Many materials, when in service, are subjected to forces or loads; examples include the aluminum alloy from which an airplane wing is constructed and the steel in an automobile axle. In such situations it is necessary to know the characteristics of the material and to design the member from which it is made such that any resulting deformation will not be excessive and fracture will not occur. The mechanical behavior of a material reflects the relationship between its response or deformation to an applied load or force. Important mechanical properties are strength, hardness, ductility, and stiffness.

Normal Stress

To introduce the concepts of stress and strain, we begin with the relatively simple case of a straight bar undergoing axial loading, as shown in Fig1. In this section we consider the stress in the bar.
Equal and opposite forces of magnitude P acting on a straight bar cause it to elongate, and also to get narrower, as can be seen by comparing Figs. la and lb. The bar is said to be in tension. If the external forces had been applied in the opposite sense, that is, pointing toward each other, the bar would have
shortened and would then be said to be in compression

Definition of Normal Stress:

In mechanics, the term stress is used to describe the
distribution of a force over the area on which it acts and is expressed as force intensity, that is,
the stress define as the applied force per unit surface area.
Stress = apllied force / surface area

The units of stress are units of force divided by units of area. In the International System of units (SI), stress is specified using the basic units of force (Newton) and length (meter) as Newtons per meter squared (N/m2).
This unit, called the Pascal (1 Pa = 1 N/m2),
is quite small, so in engineering work stress is normally expressed in kilopascals (1 kPa = 103 N/m2), megapascals (1 MPa = 106 N/m2),
or gigapascals (1 GPa = 109 N/m2).



There are two types of stress, called normal stress and shear stress.
The sign convention for normal stress is as follows:
•?A positive value for ( ? ) indicates tensile stress, that is, the stress due to a force (?F) that pulls on the area on which it acts.

•?A negative value for( ?) indicates compressive stress.

Engineering strain:
Engineering strain is defined as the change in lenght on original lengh