Under which of the following conditions is an element subjected to stresses said to be in a state of triaxial stress?
Try it first: pick an option, then read the explanation.
Correct answer: B. When principal stresses act along three mutually perpendicular directions
Asked in SSC JE 06/06/2024 (Morning)
Detailed Explanation
States of stress are named by how many principal (normal) stresses are non-zero:
- Uniaxial: one principal stress (e.g. a bar in tension).
- Biaxial: two principal stresses, the third is zero (e.g. a thin plate).
- Triaxial: principal stresses act in all three mutually perpendicular directions (e.g. a body under hydrostatic pressure, or a soil specimen in a triaxial cell).
Why “When principal stresses act along three mutually perpendicular directions” Is Correct
Option (b) is the definition of a triaxial state of stress. In the soil triaxial test, the vertical principal stress is σ₁ and both horizontal principal stresses equal the cell pressure σ₃.
Why the Other Options Are Wrong
- A. When shear stresses act along three mutually perpendicular directions of the element: States of stress are classified by principal (normal) stresses, not by shear stresses.
- C. When normal stress acts along two mutually perpendicular directions and shear stress along the third direction: Two normal stresses plus shear in the third direction is not a standard definition; on principal planes there is no shear at all.
- D. When the stress acts along only one axis of the element: Stress along only one axis is uniaxial.
Key Point
Count the non-zero principal stresses: 1 = uniaxial, 2 = biaxial, 3 = triaxial.
Key Concepts for Students
- Principal planes carry zero shear stress.
- Hydrostatic pressure is a triaxial state with σ₁ = σ₂ = σ₃.
- In the triaxial test σ₂ = σ₃ (axisymmetric condition).
Practice more: this is question 6 in Shear Strength of Soils MCQs – Part 1. Try the whole set and check every answer instantly.