Stress

Force and stress

Force can be described as two distinctive actions: push and pull. A body reacts to exerted force by changing its velocity based on the force’s magnitude and direction. According to Newton’s third law of motion, for every unit of force exerted by one body on another, an equal magnitude of force will be exerted back to it in the opposite direction. Take a restrained girder, as shown in Fig. 2.1, as an example, where supports 1 and 2 are, in fact, two bodies in contact with the girder.

When force is exerted on the girder, it is transmitted throughout the body. When the force is transferred to the point of contact with any of the restrain, Newton’s third law of motion will come into play and a reaction force will be exerted by the support to the girder.

Force is transmitted throughout the body via particles. At the microscopic level, particles will change their velocity from zero (at rest) to a certain value. The moving particles will fill the void between them and because of the attraction force, the nearby particles are pushed or pulled as well. In short, particles will experience an internally developed force in every direction.

By cutting the solid and inspecting the sectional plane, one can find such internal forces acting on that plane. The concept of stress, which is the average of the resultant internal forces distributed over that sectional plane, is introduced.

In engineering, two main types of force are concerned: normal force and shear force. Therefore, normal stress and shear stress are two fundamental types of stress discussed in solid mechanics. Normal stress is developed by a normal force acting perpendicularly to a plane (Fig. 2.2) while shear stress is developed by a shear force acting parallelly to a plane (Fig. 2.3).

where

F is the normal force;

A is the area of sectional plane.

where

V is the shear force;

A_v is the area of the shear plane.

FIGURE 2.1 Girder subjected to point loads.

FIGURE 2.2 Girder subjected to normal force.

FIGURE 2.3 Girder subjected to shear force.