Types of Stress: Longitudinal, Shearing and Volumetric

When a deforming force acts on a solid, the material develops internal forces to resist it. Stress is the measure of those internal forces: the internal force per unit area. It tells us what the material itself actually "feels," no matter how big or small the object is.

Stress matters because engineers design with it, not with raw force. A 1000 N pull is trivial for a thick steel cable but fatal for a thin wire. Depending on how the force is applied, stress comes in three types — and each can break a material in its own way.

Key Concepts

• Longitudinal stress: force perpendicular to the cross-section — tensile when pulling (bar lengthens), compressive when pushing (bar shortens).
• Shearing stress: force parallel to the surface, sliding one layer over another like a deck of cards.
• Volumetric stress: uniform pressure from all sides, as on a deep submarine; changes volume, not shape.
• Unit: newton per square metre (N/m²), the pascal (Pa); engineering stresses are often quoted in MPa.
• Stress vs pressure: pressure pushes on a surface from outside; stress is the internal force per unit area inside the body.

Formulas

Longitudinal stress σ = F ÷ A, with perpendicular force F in newtons and cross-sectional area A in square metres. Shearing stress uses the same formula, but F acts tangentially (parallel) to the area. Volumetric stress equals the applied uniform pressure p. All three share the unit N/m² = Pa, assuming the force spreads uniformly and deformations are small.

Worked Example

A steel cable of cross-section 5 × 10⁻⁶ m² carries a 2500 N load. The tensile stress is σ = 2500 ÷ (5 × 10⁻⁶) = 5 × 10⁸ Pa = 500 MPa. Structural steel breaks near 500 MPa, so this cable is at its limit — an engineer would choose a thicker cable. A bolt of the same area, joining plates that slide with 1000 N of tangential force, faces shearing stress 1000 ÷ (5 × 10⁻⁶) = 2 × 10⁸ Pa = 200 MPa, comfortably safe for steel.

Common Misconceptions

• "Stress is just force." The same force gives huge stress in a thin wire and tiny stress in a thick rod — which is why thin things snap first.
• "Tension and compression are unrelated." Same formula, opposite directions; concrete's weakness in tension is a material property, not a formula difference.
• "Stress points like a vector." Stress describes force per area on internal planes facing different directions; normal stress acts perpendicular to its plane.

Real-World Applications

• Cranes and elevators: cables are sized so tensile stress stays far below breaking stress, with a safety factor.
• Dams: the base endures enormous compressive stress from the water above — hence walls thickest at the bottom.
• Rivets and bolts: bridge and aircraft joints are designed against shearing where plates try to slide.
• Submarines: hulls withstand volumetric stress from water pressure on every square centimetre.

Stress is internal force per unit area — longitudinal when pulled or pushed, shearing when slid, volumetric when squeezed from all sides. Every safe structure is an exercise in keeping each type within what the material can bear.