1.4 Decomposition of Shear Stress
Imagine a nasty shear stress acting on your material. This evil stress wants to tear your material apart! But don't panic, we can outsmart it!
First, we conjure up a coordinate system. The x-axis points boldly in the direction of the surface normal, i.e. perpendicular to the surface. The other two axes, y and z, just chill next to it.
Now comes the trick: We decompose the mean shear stress into its individual parts! This makes it much weaker and we can easily defeat it.
Just like a team consists of different players, the shear stress consists of two "partial stresses":
- Shear stress in y-direction: This is the stress that wants to tear the surface in the direction of the y-axis.
- Shear stress in z-direction: This is the stress that wants to tear the surface in the direction of the z-axis.
This way we can understand and calculate the stress much better. And it's also much more fun to play with two small stresses than with one big, evil one.
It shows you how the shear stress is decomposed into its two parts. Look at the arrows:
- The green arrow \(\tau_{xy}\) shows the shear stress in y-direction and
- the green arrow \(\tau_{xz}\) shows the shear stress in z-direction.
The evil shear stress is defeated! We have decomposed it into two harmless parts, which we can now easily calculate.
With a little imagination and coordinate systems, we can defeat even the nastiest stresses.
Important: Shear stress is not as easy to understand as normal stress. But don't worry, we'll go through it step by step. In the next sections you will learn everything you need to know about shear stress.