 # Fundamental Concepts in Solid Mechanics

## 1.1       Solid

A material is called solid if in addition to normal force it can also support substantial shear force in a static condition. On the other hand, fluids cannot support shear force and have continuous deformation on the application of shear.

## 1.2       Force

It is an action that tends to maintain or alter the motion of a body or to distort it. The concept of force is commonly explained in terms of Newton’s three laws of motion set forth in his Principia Mathematica (1687). Force has both magnitude and direction, and thus, it is a vector quantity.

## 1.3       Deformation

Deformation refers to any change in the shape and size of the object due to an applied force or a change in temperature. Deformations could be elastic, where the object regains its shape on removal of the external force, or, could be plastic when the object is not able to regain its shape on removal of the external force.

## 1.4       Strain

Strain describes relative deformation or change in shape and size of elastic and plastic materials under applied forces.  It is expressed as the ratio of total deformation to the initial dimension of the material body in which the forces are being applied.

## 1.5       Stress

Stress is the internal resistance offered by the material to the distorting effects of an external force. Stress is defined as the force across a “small” boundary per unit area of that boundary. If the body reaches the state of equilibrium then this resistance is equal to the applied load.  Thus, stress becomes equal to the applied force divided by the area.

## 1.6       Principal Stresses

Principal stresses are the extreme values of the normal stresses possible in the material. These are the maximum normal stress and the minimum normal stress possible for a specific point on a structural element. Maximum normal stress is called major principal stress while minimum normal stress is called minor principal stress. Shear stress is zero where principal stress occurs.

## 1.7       Principal Strain

The principal strain is the extreme values of the normal strain possible in the material. These are the maximum normal strain and the minimum normal strain possible for a specific point on a structural element. The maximum normal strain is called major principal strain while minimum normal strain is called minor principal strain. Shear strain is zero where principal strain occurs.

## 1.8       Failure

Failure is the loss of load carrying capacity of the member. It could be due to fracture or permanent deformation beyond the operational range due to the yielding of the member. Failure theory is the science of predicting the conditions under which solid materials fail under the action of external loads.

## 1.9       Factor of Safety (FS)

It is the ratio of the Failure Load to the Working Load of the material unit. The purpose of using a factor of safety is to design the member in such a way that it can take FS times the load for which it is designed. Essentially, the factor of safety is how much stronger the system is than it usually needs to be for an intended load. This takes care of the uncertainties in the assessment of loads while designing the member.