Principal Plane Stress Quiz and Flashcards for Soil Mechanics

Study Notes

Principal Stresses

At any stressed point, there exist three orthogonal planes with zero shear stresses, known as principal stress planes.
The normal stresses acting on these planes are called principal stresses: major principal stress (𝜎􏰑), minor principal stress (𝜎􏰧), and intermediate stress (𝜎􏰝).
The major principal stress is the largest, and the minor principal stress is the smallest.

Geostatic Stresses

When stresses in the ground are geostatic, the horizontal plane through a point is a principal plane, as are all vertical planes through the point.
When 𝑘 = 􏰫􏰬 (𝑘 ≠ 1), the situation is reversed.

Mohr Circle

The Mohr circle deals with stresses in two dimensions, specifically the state of stress in a plane containing the major and minor principal stresses (𝜎􏰑, 𝜎􏰧).
Stresses are considered positive when compressive.
The Mohr circle equation is: 𝜏 = (𝜎􏰑 - 𝜎􏰧) sin²(𝜃/2)

Finding Stresses using Mohr Circle

To find the stresses, there are two methods: by drawing or using equations.
To find the normal and shear stresses on any plane:
- Draw the stress state on the Mohr circle.
- Find the origin of planes (Op) by selecting 𝜎􏰑 or 𝜎􏰧.
- Draw a line parallel to the plane on which the stresses are needed, and find the point of intersection on the Mohr circle.

Origin of Planes (Op)

Op is a point on the Mohr circle with the property that a line through Op and any point (A) on the Mohr circle is parallel to the plane on which the stresses given by point A act.
If the plane and Op are known, the line parallel to the plane passes through Op and intersects the Mohr circle, giving the point that acts on that plane.

Description

Learn about principal stresses in soil mechanics and how they are related to the major, minor, and intermediate principal stresses. Understand the concept of zero shear stresses on orthogonal planes known as principal stress planes.