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Created: 2024/04/29 01:49
Materials: "[[Lec 01.pdf]]"
---
# Introduction

Stress is the reactive force per unit area of a section for the forces applied. And strain is the deformation experienced by the body in the direction of the force applied.

The formula for *stress* is:

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

And for strain:

$$
\epsilon = \frac{\delta l}{l_0}
$$

# Types of Stress

Stress can be compressive stress, tensile stress, or shear stress. The first two is known as normal stress. There is also a stress called bearing stress that is a derivative of compressive stress.

> [!Note] Know
> Normal stress is denoted by the Greek letter $\sigma$ while shear stress is denoted by $\tau$.

For solving problems related to stress, area $A$ is the cross section of the area likely to be torn.

## Normal stress

Stress produced as result of axial loading (force normal to cross section) is known as normal stress. In the figure below, `A` is experiencing tensile stress.

![Tensile stress example](../../../Resources/Pasted%20image%2020240506005400.png)

>[!Note] Convention
>Positive sign is used to indicate tensile stress while negative sign indicates compressive stress.

### Bearing stress

Compressive stress can sometimes be expressed as bearing stress when one body is supported by another. It is denoted by the $\sigma_b$.

## Shear stress

Stress produced as a result of forces applied parallel to the cross section is known as shear stress.

![Shear stress example](../../../Resources/Pasted%20image%2020240506010254.png)

# Units

In SI unit, stress is expressed as $N/m^2$ or pascals. However, in practical world these values are very small. Hence $kPa$, $MPa$, or $GPa$ are more commonly used.

In US Imperial unit, force is expressed as pounds ($lb$) or kilopond ($kip$) and the cross-sectional area is expressed as square inches ($in^2$). The stress is expressed as pounds per square inch ($psi$) or kilopond per square inch ($ksi$),

> [!Note] Convention
> $MPa$ is commonly expressed as $Nmm^{-2}$ and vice-versa.
> $$
> 100 MPa = 100 M\frac{N}{m^2} = 100\frac{10^6 N}{10^6 mm^2} = 100 \frac{N}{mm^2}
> $$

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References:

- [Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (byjus.com)](https://byjus.com/physics/stress-and-strain/)
- [Stress (mechanics) - Wikipedia](https://en.wikipedia.org/wiki/Stress_(mechanics))