When we talk about stress in materials that twist, things can get pretty complicated if there are other forces acting on them too.

Let’s imagine a structural piece, like a rod or beam, that is twisting. It mainly deals with something called shear stress. This is sort of like how much force is trying to slide one part of the material over another. The formula to calculate shear stress looks like this:

$\tau = \frac{T \cdot r}{J}$

In this formula:

• $\tau$ is the shear stress,
• $T$ is the torque (or twisting force) applied,
• $r$ is the distance from the center,
• and $J$ is a measure of how the material can resist twisting.

But, if there are other forces at play, like pulling or bending, things become a lot more complex.

1. Axial Loads: When a pulling force (or axial load) is applied along with the twisting, it adds more stress in the direction of that pull. We can calculate this normal stress using:

$\sigma = \frac{F}{A}$

Here:

• $\sigma$ is the normal stress,
• $F$ is the force applied,
• and $A$ is the area that the force is acting on.

This pulling stress works together with the shear stress from twisting, which can make the total stress higher than what the material can handle without breaking.

2. Bending Moments: If something also bends while it’s twisting, that adds another layer of stress. We can find this bending stress with:

$\sigma_b = \frac{M \cdot c}{I}$

In this formula:

• $M$ is the bending moment,
• $c$ is how far the bending force is from the center,
• and $I$ is a measure of the beam’s resistance to bending.

This bending stress can make the shear stress even worse, creating a mix of stresses that can make the material fail sooner than expected.

In short, when a structure faces multiple stresses like twisting, pulling, and bending all at once, it's really important to think about all these stresses together. Understanding how they interact helps engineers make sure that things stay safe and don’t break down unexpectedly.