Imagine pulling on a rubber band. As you stretch it, you feel a resistance. This resistance comes from internal forces within the rubber band that are fighting your pull. Stress is simply a way to measure these internal forces.

Specifically, stress is the internal force acting over a specific area inside a material. It’s not just about how much force is applied, but how concentrated that force is. A 10-pound weight resting on a needle tip creates enormous stress, while the same weight spread across a large wooden plank creates very little.

We calculate stress (represented by the Greek letter sigma, $\sigma$) by dividing the force ($F$) by the cross-sectional area ($A$) it acts on.

The standard unit for stress is the Pascal (Pa), which is one Newton of force per square meter. In the imperial system, you'll often see pounds per square inch (psi).

Stress isn't a one-size-fits-all concept. It depends on the direction of the force relative to the surface it's acting on. This gives us two main types of stress: normal stress and shear stress.

Normal stress happens when the force acts perpendicular (or "normal") to the surface. Think of it as a direct push or pull.

• Tensile Stress: This pulls the material apart, stretching it. A cable holding up a bridge is under tension.
• Compressive Stress: This squeezes the material, compacting it. A pillar holding up a roof is under compression.

Shear stress, on the other hand, occurs when the force acts parallel to the surface. Imagine pushing the top of a thick book sideways. The pages slide past each other. That sliding action is due to shear stress. Scissors don't cut paper by pulling it apart; they create high shear stress that slices the material.

We represent shear stress with the Greek letter tau, $\tau$. The calculation is the same as normal stress, but the force $F$ is parallel to the area $A$.

When an object is subjected to stress, it changes shape. It might stretch, shrink, or twist. Strain is the measurement of this deformation. Crucially, strain isn't about the total change in shape, but the relative change. A one-inch stretch is significant for a rubber band but negligible for a 100-foot cable.

Like stress, strain also comes in two main types.

Normal strain measures how much an object stretches or compresses. We calculate it (using the Greek letter epsilon, $\epsilon$) by dividing the change in length ($\Delta L$) by the original length ($L_0$).

Since it's a ratio of length to length (e.g., meters/meters), normal strain is a dimensionless quantity. It's often expressed as a percentage.

Shear strain measures the distortion caused by shear stress. Instead of a change in length, it measures a change in angle within the object. Imagine that square-shaped book you pushed on earlier. As the top slides, the sides tilt. The shear strain (represented by the Greek letter gamma, $\gamma$) is the measure of that change in angle.

Stress and strain are two sides of the same coin. You can't have one without the other. Applying a stress causes a strain, and creating a strain induces a stress. To visualize this fundamental relationship for a given material, engineers use a stress-strain diagram.

By pulling on a material sample and measuring the stress and strain at many points, we can create a graph. Stress is typically plotted on the vertical axis (y-axis) and strain on the horizontal axis (x-axis). The shape of the resulting curve tells us a lot about the material's mechanical properties, though we won't dive into those details here.

This diagram is the foundation of materials science and engineering. It allows us to understand how a material will behave under a load, which is critical for designing everything from airplane wings to medical implants.

Understanding these core concepts is the first step in analyzing how forces affect the objects all around us.