engineering core courses

Solid Mechanics I
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Solid Mechanics I
 Course homepage
C7: Stress Transformation
7.1 Equations of Plane-Stress Transformation
- Theory - Example
7.2 Principal σ and τmax in-plane
- Theory - Example
7.3 Mohr’s Circle
- Theory - Example - Question 1 - Question 2
7.4 3D Mohr's Circle and τabs-max
- Theory - Example - Question 1 - Question 2

C7.4 3D Mohr's Circle and τabs-max

So far we’ve only looked at 2D plane-stress scenarios, but in the real world stresses act in a 3D manner, with a general state-of-stress that looks like:


stress element with 3D state-of-stress

The full-blown transformation for this scenario is not within the scope of this course (phew…). But we will be looking at a simple 3D scenario: zero-stress in the 3rd direction:

C7.4 3D Mohr's Circle and τabs-max

So far we’ve only looked at 2D plane-stress scenarios, but in the real world stresses act in a 3D manner, with a general state-of-stress that looks like:


stress element with 3D state-of-stress

The full-blown transformation for this scenario is not within the scope of this course (phew…). But we will be looking at a simple 3D scenario: zero-stress in the 3rd direction:

3D stress element with zero z-stress

In this case, all we have to do is to add a 3rd point of Z(0,0) in our existing 2D Mohr’s circle. We then draw our 3D Mohr’s circle which allows us to calculate our absolute maximum shear stress τabs-max.

Here’s some possible configurations of our 3D Mohr’s circle:


3D Mohr's circle configurations

Doesn’t seem too difficult to draw does it? Let’s look at an example now.

3D stress element with zero z-stress

In this case, all we have to do is to add a 3rd point of Z(0,0) in our existing 2D Mohr’s circle. We then draw our 3D Mohr’s circle which allows us to calculate our absolute maximum shear stress τabs-max.

Here’s some possible configurations of our 3D Mohr’s circle:


3D Mohr's circle configurations

Doesn’t seem too difficult to draw does it? Let’s look at an example now.

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