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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

Illistrates a bar acted upon by a tensile force at either end, causing the bar to stretch.

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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