To figure out torque when looking at forces in structures, we need to know what torque means.

Torque (or moment of force) is similar to a force but instead of pushing in a straight line, it causes things to rotate. We can find torque with this simple formula:

$$\tau = r \times F$$

Here’s what the letters mean:

• $\tau$ is the torque,
• $r$ is the distance from the pivot point (where things rotate) to where the force is applied,
• $F$ is the force applied straight out from the pivot point.

How to Calculate Torque:

1. Find the Pivot Point: This is the point that will stay still when things rotate. It is usually where the structure is supported, like where a beam rests.

2. Measure the Distance: Check how far ($r$) the force is from the pivot point, making sure it's measured straight out from the pivot.

3. Apply the Force: Know both how strong the force is and the direction it is pushing on the structure.

4. Calculate Torque: Put those values into the formula $\tau = r \times F$. If the force isn’t straight out, only use the part of it that goes straight out from the pivot.

Example:

Let’s say a force of 100 N is applied 2 meters away from the pivot point, and it pushes straight out (at a 90-degree angle). Then the torque would be:

$$\tau = r \times F = 2 \, \text{m} \times 100 \, \text{N} = 200 \, \text{N}\cdot\text{m}$$

Why Torque is Important in Structures:

• Balance: For a structure to be balanced, all the torques on it must add up to zero. This is called the principle of moments:

$$\sum \tau = 0$$

• Safety: Knowing how to calculate and use torque helps engineers create strong structures that won't break easily. This keeps everyone safe and makes sure buildings can stand strong.