Stress and Strain - Types of Stress and Corresponding Strain

When you deform a solid object (such as stretching a rubber band), it resists the deformation.

• Deforming Force: The external force applied to change the object's shape.
• Restoring Force: The internal force generated inside the object to bring it back to its original shape.

This happens when forces act along the length of a rod or wire.

I. Tensile (Stretching)

Fig. Tensile stress.

• Action: Pulling a rod outwards from both ends.
• Result: Length increases (ΔL).
• Analogy: A Tug-of-war rope being pulled taut.
  Tensile Stress (σ_t) = \[\frac{|\vec{F}|}{A}\]
  Tensile Strain (ε_t) = \[\frac{\text{Change in Length}}{\text{Original Length}} = \frac{\Delta L}{L}\]

II. Compressive (Squeezing)

Fig. Compressive stress.

• Action: Pushing a rod inwards from both ends.
• Result: Length decreases.
• Analogy: The pillars of a bridge support the road's weight.
  Compressive Stress (σ_c) = \[\frac{F}{A}\]
  Compressive Strain (ε_c) = \[\frac{\Delta L}{L}\]

This occurs when force is applied perpendicular to the entire surface area, such as when an object is submerged in water.

Fig. Volume stress.

• Action: Force presses in from all sides (Pressure).
• Result: Volume decreases, but shape remains the same.
• Real-Life Check: A submarine deep underwater or a balloon filled with air (pressure pushes walls out).

Hydraulic Stress (σ_v) = \[\frac{F}{A} = P \text{ (Pressure)}\]
Volume Strain (ε_v) = \[\frac{\text{Change in Volume}}{\text{Original Volume}} = \frac{\Delta V}{V}\]

This is the tricky one! It happens when force is applied parallel to the surface, while the bottom is fixed.

Fig. Tangential force produces shearing stress.

• Action: Pushing the top of a book while holding the bottom table.
• Result: The shape changes (it tilts), but the volume stays the same.
• Visual Guide: Imagine a cube turning into a slanted parallelogram.
• Analogy: Swiping the top card off a deck of cards.

Shearing Stress (σ_s) = \[\frac{\text{Tangential Force}}{\text{Area}} = \frac{F_t}{A}\]
Shearing Strain (θ) = \[\frac{\text{Relative Displacement}}{\text{Length}} = \frac{\Delta x}{L} = \tan \theta\]
(For small deformations, tan θ ≈ θ)

• The Balloon Paradox: When you blow up a balloon, the air pressure inside pushes the walls out. This creates Volume Stress in the rubber material. If this stress exceeds the balloon's "Elastic Limit," it explodes!
• Gas Cylinders: This is why heavy-duty gas cylinders are made of thick steel—to withstand the massive internal Hydraulic Stress without ripping apart.