Strength of Materials/Introduction
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Solid Mechanics is the study of load carrying members in terms of forces, deformations, and stability. In this book, we take the continuum mechanics approach, where we take the material properties to be the same even when we consider infinitesimal areas and volumes. The alternative approach is to build up material properties from basic equations relating atomic forces and interactions, and extending it to larger sets of such entities (e.g., molecular dynamics). Other approaches include meso-scale theories like dislocations to explain behavior of materials, especially for plasticity. However, the approach in this book is applicable to a large variety of practical problems, where we deal with structural members, usually under elastic deformation.
The images on the right show a body which is acted upon by external forces 
, 
, etc. The supports provide reaction forces (
, 
) so that the body is stationary.
In addition to external forces, which act at points on the surface, we can also have forces which are body forces, i.e., they act on each point in the body. Gravity is an example of a body force.
Consider a body which has several external forces acting on it. If we take an imaginary section of the body, each of the parts should also be in equilibrium. Now, consider an elemental area dA in that section. Let the force acting on the elemental area so that the whole body is in equilibrium be dF. We can resolve this force in three mutually perpendicular directions. Let the component of the force normal to the surface be dFz. Let the components in the plane of dA be dFx and dFy respectively.
