---
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.
> $$
> 100 MPa = 100 M\frac{N}{m^2} = 100\frac{10^6 N}{10^6 mm^2} = 100 \frac{N}{mm^2}
> $$

---

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))

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:

$σ = \frac{F}{A}$

And for strain:

$ϵ = \frac{δ l}{l_{0}}$

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 $σ$ while shear stress is denoted by $τ$ .

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

[!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 $σ_{b}$ .

Shear stress

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

Shear stress example

Units

In SI unit, stress is expressed as $N / m^{2}$ or pascals. However, in practical world these values are very small. Hence $k P a$ , $M P a$ , or $G P a$ are more commonly used.

In US Imperial unit, force is expressed as pounds ( $l b$ ) or kilopond ( $k i p$ ) and the cross-sectional area is expressed as square inches ( $i n^{2}$ ). The stress is expressed as pounds per square inch ( $p s i$ ) or kilopond per square inch ( $k s i$ ),

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

References: