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# Stress and strain

## Symbols and units

The table below identifies the symbols and units used in the calculation of stress and strain.

 Description Symbol Name Units Direct stress σ Sigma N/m² and N/mm² Direct strain ε Epsilon None Shear stress τ Tau N/m² and N/mm² Young’s modulus of elasticity E N/m² and N/mm²

Note: 1N/mm²  =  10⁶N/m² = 1MN/m²
And 1kN/mm² = 1GN/m²
The alternative for stress is the pascal (pa)which equals 1 N/m²

Two effects may be identified, when the force acts on a solid material which remains stationary.

The material will:-

• Exert an internal resisting force known as a state of stress;
• Experience dimensional changes

This behaviour is typical of stressed engineering components but the dimensional changes are usually small are not normally seen with the naked eye.

## Direct forces

One end of a bar may be subjected to push or pull.  Now, if a bar remains stationary, a pull on one end must result in an equal and opposite pull on the other end, and the bar is said to be in tension.  Similarly, a push on one end is accompanied by a push on the other end, and the bar is in compression.

The forces which are producing a tension or compression are called direct forces.

Also, direct forces are called either tensile (A pull) or compressive (A push).

Tensile forces cause a bar to stretch and compressive forces cause a bar to contract.

Fig 1

Fig 1 Illustrates a bar acted upon by a tensile force at either end causing the bar to stretch.

F = The applied force
A = Cross sectional area of the bar
L = Original length of the bar
x = Change in length produced by the applied force, F

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