Strength of Materials - Stress

Summary

This video introduces the fundamental concept of stress in the study of materials. The instructor begins by explaining the role of external loads in causing deformation in materials, highlighting the difference between elastic and plastic deformation. The video then defines stress as the internal resistance per unit area that a material offers to deformation. The instructor also discusses the mathematical formula for stress and its units, explaining the relationship between Newtons, Pascals, and other measurements commonly used in engineering. The video sets the stage for deeper exploration of different types of stresses in future episodes.

Takeaways

• 📚 The subject of strength of materials is introduced, focusing on understanding stresses and strains.
• 🔍 Stress is defined as the fundamental topic in materials science that needs to be understood to grasp the subject.
• 📐 The concept of 'load' is central to understanding stress; it's the external force applied to a body causing deformation.
• 🔨 Deformation is undesirable in engineering as it implies a change in the shape or size of the material, categorized into elastic and plastic deformation.
• 🧱 Stress is the resistance per unit area provided by the material to resist deformation, symbolized by the Greek letter Sigma (Σ).
• 📉 The formula for stress is mathematically expressed as the ratio of the resisting force (ΣFR) to the area (a), i.e., Σ = ΣFR / a.
• ⚖️ The body under stress is in static equilibrium, meaning the internal resistive forces are equal to the external load (P = ΣFR).
• 🔢 The SI unit for stress is Newtons per square meter (N/m²), which is equivalent to Pascal (Pa).
• 📏 In engineering, due to the smaller scales involved, the unit of stress is often given in Newtons per square millimeter (N/mm²), which is 1 Megapascal (MPa).
• 🔑 The understanding of stress involves recognizing it as an internal resistive force per unit cross-sectional area of a body under load.
• 🚀 The video promises to explore different types of stresses corresponding to different kinds of loads in the next installment of the series.

Q & A

What is the fundamental concept in the subject of Strength of Materials introduced in this video?

The fundamental concept introduced is stress, which is crucial to understanding the entire subject of Strength of Materials.

How is stress related to the concept of load in materials?

Stress is produced when an external load is applied to a body, causing deformation. Stress is the resistance per unit area that the material provides against this deformation.

What happens to a material when an external load is applied?

When an external load is applied, the material undergoes deformation. This deformation is resisted by the internal forces of the material, leading to the development of stress.

How is stress mathematically defined?

Stress is mathematically defined as the internal resistive force per unit cross-sectional area of a body. It is represented by the Greek letter Sigma (σ) and can be calculated using the formula σ = F/A, where F is the internal resistive force and A is the cross-sectional area.

What is the significance of static equilibrium in the context of stress?

Static equilibrium is important because it indicates that the sum of the internal resistive forces in the material equals the external load applied to it, ensuring that the body remains stationary and stress is distributed evenly.

What units are used to measure stress, and how are they related?

Stress is measured in units of Newtons per square meter (N/m²) in SI units, also known as Pascals (Pa). In engineering, stress is often measured in Newtons per square millimeter (N/mm²), which is equivalent to Megapascals (MPa). 1 N/mm² is equal to 1 MPa or 1 million Pascals.

Why is it important to understand the conversion between meters and millimeters when calculating stress?

Understanding the conversion between meters and millimeters is important because mechanical engineering often deals with components measured in millimeters. Knowing that 1 meter equals 1000 millimeters helps in accurately converting and calculating stress in practical applications.

What are the two types of deformation mentioned, and how do they differ?

The two types of deformation mentioned are elastic deformation and plastic deformation. Elastic deformation is temporary and reversible, meaning the material returns to its original shape after the load is removed. Plastic deformation, on the other hand, is permanent and irreversible, meaning the material remains deformed even after the load is removed.

How does the internal structure of a material resist applied loads?

The internal structure of a material resists applied loads through the collective action of its fibers. These fibers generate internal resistive forces that counteract the external load, preventing deformation or minimizing it.

What is the practical significance of understanding stress in engineering?

Understanding stress is crucial in engineering because it helps in designing materials and structures that can withstand external loads without undergoing undesirable deformations. It ensures the safety, durability, and reliability of engineering components and structures.

Outlines

00:00

💪 Introduction to Stress in Materials

The video series begins by introducing the concept of stress in the subject of strength of materials. Stress is the foundational topic necessary to understand the entire subject. The explanation starts with the concept of load, particularly external load, which leads to deformation in materials. The speaker explains that deformation is undesirable for engineers and introduces the ideas of elastic and plastic deformation, which will be discussed in later videos. Stress is defined as the resistance per unit area that a material offers to deformation. The video uses a simple diagram to illustrate how an external load causes internal resistance within a material, leading to the concept of stress, represented mathematically by the Greek letter Sigma.

05:02

📏 Mathematical Definition and Units of Stress

This paragraph delves deeper into the mathematical representation of stress, highlighting that stress is the internal resistive force per unit cross-sectional area of a body. The formula \( \sigma = \frac{P}{A} \) is introduced, where \( \sigma \) (Sigma) represents stress, \( P \) is the external load, and \( A \) is the cross-sectional area. The concept of static equilibrium is explained, indicating that the internal resistive forces are equal to the external load when the body is in equilibrium. The paragraph also discusses the SI units of stress, explaining that stress is measured in Newtons per square meter (Pa or Pascal). Additionally, it explains how these units are converted into more practical engineering units, such as megapascals (MPa) and gigapascals (GPa), for mechanical engineering applications, where dimensions are often in millimeters.

Keywords

💡Stress

Stress is a fundamental concept in the strength of materials. It refers to the internal resistance offered by a material to the external load applied to it, measured per unit area. In the video, stress is introduced as the key concept that must be understood to grasp the subject of material strength. The video explains that stress is produced when a load causes deformation in a material, and this resistance to deformation is what stress measures.

💡Load

Load refers to the external force applied to a material or structure. This is a crucial starting point in understanding stress because it is the load that causes deformation in a material. The video emphasizes that to understand stress, one must first understand load, particularly external load, as it is the source of deformation that leads to stress.

💡Deformation

Deformation is the change in shape or size of a material when an external load is applied. Engineers generally aim to minimize deformation, as it can compromise the integrity of a structure. In the video, deformation is categorized into two types: elastic and plastic, which are discussed later in the series. Deformation is the result of stress, and understanding it is key to managing material strength.

💡Elastic Deformation

Elastic deformation is the temporary change in shape or size of a material under load, which is fully recoverable once the load is removed. The video hints at this concept, explaining that some deformations are not permanent, meaning the material returns to its original shape after the load is removed. This concept is crucial in materials science for designing materials that can withstand loads without permanent damage.

💡Plastic Deformation

Plastic deformation refers to the permanent change in shape or size of a material when subjected to a load beyond its elastic limit. Unlike elastic deformation, plastic deformation does not reverse when the load is removed. The video indicates that plastic deformation will be discussed in later stages, emphasizing its importance in understanding material failure and design limits.

💡Internal Resistance

Internal resistance is the force generated within a material to counteract an applied load, preventing deformation. The video describes how the material’s internal fibers resist being pulled apart by the load, and this resistance is what we measure as stress. This concept is essential to understand how materials behave under stress and maintain structural integrity.

💡Cross-Sectional Area

Cross-sectional area refers to the area of a material's section perpendicular to the applied load. The video explains that stress is calculated as the internal resistance force divided by the cross-sectional area, highlighting its importance in determining the material's ability to withstand loads. A larger cross-sectional area typically means the material can resist more stress.

💡Equilibrium

Equilibrium in this context refers to a state where the internal resistive forces within a material are equal to the external load applied, resulting in no net movement or deformation. The video states that when a body is in static equilibrium, the stress formula (P/A) can be applied, emphasizing its importance in ensuring that structures remain stable under load.

💡Pascal (Pa)

Pascal (Pa) is the SI unit of stress, equivalent to one Newton per square meter (N/m²). The video explains how stress is measured in Pascals and how this unit is commonly used in engineering applications. Understanding Pascals is vital for quantifying stress in a material and comparing it to the material's strength limits.

💡Sigma (σ)

Sigma (σ) is the symbol used to represent stress in engineering and physics. The video mentions that stress is denoted by the Greek letter Sigma, which is central to the mathematical representation of stress. Recognizing this symbol is important for interpreting stress-related equations and understanding discussions of material strength.

Highlights

Introduction to the subject of Strength of Materials, starting with simple stresses and strains.

Explanation of the term 'stress' as a fundamental concept necessary for understanding the entire subject.

Discussion on the concept of 'load' and its importance in producing stress in materials.

Distinction between external load and its impact on the deformation of a body.

Introduction to the concepts of elastic deformation and plastic deformation, which will be explored later in the series.

Definition of stress as the resistance per unit area provided by a material when an external load is applied.

Use of a diagram to explain the concept of stress and the internal resistive forces within a material.

Introduction of the mathematical formula for stress, denoted by the Greek letter Sigma (σ).

Explanation of the body under static equilibrium, where the internal resistive forces equal the external load.

Clarification that stress is not simply P/A (load divided by area), but rather the result of internal forces resisting deformation.

Explanation of the units of stress in SI terms, specifically Newton per square meter (N/m²), also known as Pascal (Pa).

Discussion on the use of millimeters in engineering applications and the conversion between meters and millimeters.

Conversion of stress units from Newton per square millimeter (N/mm²) to megapascals (MPa).

Introduction to larger units of stress, including gigapascals (GPa).

Teaser for the next video in the series, which will cover the different kinds of stresses corresponding to different types of loads.

Transcripts

hi friends and welcome to this video

series on the subject of strength of

materials in this subject we'll start

understanding the entire thing by simple

stresses and strains and in this

particular video I will introduce the

term stress to you now stress is the

most fundamental of the topic to be

understood in order to understand the

entire subject okay let's get to it now

I have written a very uh big word over

here which is load so to understand what

is stress or how the stress is produced

we must understand what is load okay and

more importantly we have

to talk about the external load which is

applied externally onto the body okay so

when you apply external load onto a body

what happens what is the result of this

external load the result of this

external

load is

deformation now deformation to Engineers

is not a very good thing to happen

because every engineer would not want

its material to be deformed so it'll

categorize this deformation into two

parts we'll talk about the elastic

deformation and we'll talk about the

plastic deformation at the later stages

in this video series but this video

will'll focus on understanding stress

okay so in a very high level

understanding you apply external load

onto a body that body gets deformed now

no body wants to be deformed it resists

that deformation so that resistance per

unit area that resistance is provided by

the material of the body okay that

resistance per unit area is called

stress so if you look at it uh you know

in a diagrammatical fashion and then

we'll write down the uh

mathematical relation for it so let us

say this is one section of the body this

is the other section of the

body okay so we have just cut the body

into half okay let us say we have a

external load

P acting at two ends of the body

now after understanding stresses we need

to understand the types of loads right

now I'm just telling you that load is

something which produces deformation the

deformation can be of the size the the

deformation can be of the shape okay or

both so we'll go into those details one

by one right now let's understand this

you have a body which is being applied

by these two loads or this load at the

two ends of the body okay now what

happens is this load on the left side

it's it tends to pull the body towards

this side and this load will tend to

pull this side onto the right side okay

now this body will not want to be pushed

in or to be pulled in both the

directions so what will happen the

internal fibers of this material will

start

resisting this load so all these fibers

are actually trying to resist this

pulling Force onto this side also you'll

have the

fibers putting up a resistance to resist

this pulling Force toward the right okay

so let us say if I take the summation of

all these Elementary forces you will get

summation F FR that is the resistance

force that is the sum of the internal

resistance forces similarly I'll have

the summation over here also Sigma FR FR

so Sigma F FR is the summation of these

small Elementary resistance forces

produced by the material fibers to these

external loads all right

so the

mathematical formula for stress which I

denote by a Greek letter Sigma so stress

is always denoted by Sigma remember this

so Sigma is this resistance force per

unit crosssection of this body so this

would be equal to Sigma F

FR by a so this is how you will

calculate the value of Sigma now if you

look at this entire body it is under

equilibrium it is under static

equilibrium it is not going

anywhere it is staying put equilibrium

okay this means that this load or more

importantly let's start with the other

way around this summation of the

internal resistive forces are equal to

this external load this means that P

will be equal to Sigma F

FR so I can put Sigma frr equal to P so

this will become P by a now this is the

formula that you will find in almost

every book

but this is how you understand it this

is Sigma is not P by a p by a is the

resultant of this entire body being in

static equilibrium so the formal

definition of the stress is that it is

the internal resistive

forces per unit cross-section area of

the body okay so this is how we denote

and we Define

stress so p is equal to Sigma so this is

the uh you know formula that you would

see in almost every textbook so it is

not P by a it is actually Sigma F by a

where this body being in static

equilibrium creat such situation like

this so that we can put P by a okay so

this is how we mathematically Define

stress now more importantly when you are

talking about a quantity and this being

a quantity stress a physical quantity it

has to have some units the units of

stress if you look at this we'll be

dealing with uh we'll Define the units

in SI terms and then because we are

talking in the engineering term we'll

have to Define it into the metric terms

the metric system okay so Sigma is equal

to P by a p has a unit of load which is

Newtons area has a unit of M Square so

these units or the SI units of Sigma are

Newton per M Square Now 1 Newton per M

Square this is equal

to 1 Pascal

okay now we don't deal in units of meter

when we talk about engineering

applications because uh very seldom you

have mechanical engineering components

in the length of meters unless and until

you are a civil engineer okay when where

you actually deal with beams of um you

know meter of spans so in mechanical

engineering terms this

length is more importantly

millimet okay so we need a conversion

unit so 1 m is equal to 1000 mm you need

to understand this and remember this

1

m is equal to 1000 mm or 10 ^ 3 mm I'm

using 1 M Square so 1 M squ becomes 10^

6 mm

Square so if I

replace the M Square quantity by mm

Square quantity I would get 1 nton upon

10^ 6 mm²

is equal to 1

Pascal now let's bring this 10 ^ 6 onto

the right hand side this would give you

1 Newton per

mm² is equal to 10^ 6 pascals now what

is 10 ^ 6 of anything it is Mega so 10 ^

6 Pascal is 1 MEAP Pascal so 1 Newton

per mm Square which is how you'll be

given the stress in the engineering term

so 1 Newton per mm square is equal to 1

MPA or 1 MEAP Pascal so 1 Newton per

mm² is equal

to 1 MEAP Pascal if you go into the

gigap Pascal so 1 gigap pascals 1 Mega

is equal to 10 the power 1 Giga is equal

to 10^ 3 mega so this becomes 1

Kon per mm square of stress so this is

how you understand Define and

mathematically denote the quantity of

stress now in the next video we'll talk

about the kinds of stresses

corresponding to the kinds of load now

let's move on to the next video