Strength of Materials - Stress
Summary
TLDRThis 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
💪 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.
📏 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.
Mindmap
Keywords
💡Stress
💡Load
💡Deformation
💡Elastic Deformation
💡Plastic Deformation
💡Internal Resistance
💡Cross-Sectional Area
💡Equilibrium
💡Pascal (Pa)
💡Sigma (σ)
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
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