Strength of Materials

Introduction to SOM Stress and Strain

Stress

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Stress

When an external force acts on a body, it tends to deform the body. To resist this deformation, internal resisting forces develop within the material. The internal resisting force per unit area is called stress.

Also, stress can be defined as the force intensity at a point, resisting separation or distortion of the material. It represents how the internal force is distributed through the material.

Stress is denoted by Greek letter sigma (\(\sigma\)).

Mathematical representation of stress

Mathematically stress is represented as internal force per unit area.

\[\sigma = \frac{F_{\text{internal}}}{A}\]

Where:

  • \(\sigma\) (sigma) = Stress
  • \(F\) = Force applied (N)
  • \(A\) = Cross-sectional area (\(m^2\))

Unit of Stress

The SI unit of stress is \( N/m^2 \) or Pascal (\( Pa \)).

But Pascal is a very small unit to solve real-world engineering problems; due to which megapascal (\( MPa \)) or gigapascal (\( GPa \)) are used.

\[ \begin{alignat*}{2} 1 \, \frac{N}{m^2} & = 1 \, Pa \\ 1 \, MPa & = 1 \, \frac{N}{mm^2} &&= 10^6 \, Pa \\ 1 \, GPa & = 10^9 \, Pa \end{alignat*} \]

Types of Stress

There are primarily three types of stress:

  1. Normal Stress (\(\sigma\)): Acts perpendicular to the area.
  2. Shear Stress (\(\tau\)): Acts parallel to the area
  3. Bearing Stress: Occurs in connections where one member presses against another.
  4. Torsion Stress: Stress occurred in beam due to equal and opposite torques or couples.
  5. Thermal Stress: The volume of body changes with change in temperature. If change in volume is restricted by an external force, stresses that are occurred in material are called thermal stress.
  6. Bending Stress: The stress occurred in beam due to bending moment called bending stress.
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