Principal Plane Stress Quiz and Flashcards for Soil Mechanics

What are the planes on which there are zero shear stresses called?

Which stress is considered to be the smallest among the principal stresses?

In geostatic conditions, what type of plane is a principal plane?

What is the condition when the shear stresses on orthogonal planes must be numerically equal?

What is the Mohr circle concerned with in terms of stresses?

Which point on the Mohr circle has the property that any line through it and a point A on the Mohr circle will be parallel to the plane on which the stresses given by point A act?

How can the normal and shear stresses on any plane be determined?

What does the point denoted by OP represent in the stress analysis process?

What is the significance of intersecting a line from OP with Mohr Circle?

Why is drawing stresses on Mohr circle preferred over using equations?

What does drawing a line parallel to a specific plane from OP help determine?

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.

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.