Contents: Bending Moment

Where [.]represent Dot product of a vector.

The Mathematical Relation between load intensity, Shear Force and Bending Moment

Relations: Let f = load intensity

    Q = Shear Force

    M = Bending Moment

The rate of change of shear force will give the intensity of the distributed load.

The rate of change of bending moment will give shear force at that point only.

Unit for Bending Moment

Bending moment has a unit similar to the couple as Nm.

Bending Moment of a Beam

Assuming a Beam AB having a certain length subjected to Bending Moment M, If the Top fiber of the beam, i.e., above the neutral axis, is in compression, then it is called Positive Bending Moment or Sagging Bending moment. Similarly, If the Top fiber of the beam, i.e., above the neutral axis, is in tension, it is called the Negative Bending Moment or Hogging Bending moment.

Bending Moment Sign Convention

There is a Specific Sign convention followed while determining Maximum Bending-moment and Drawing and BMDs.

1. If we start calculating Bending-Moment from the right side or right end of the beam, Clockwise Moment is taken as negative, and Counter-wise Moment is taken as Positive.
2. If we start calculating Bending-Moment from the Left side or Left end of the beam, Clockwise Moment is taken as Positive, and Counter Clockwise Moment is taken as Negative.
3. If we start calculating Shear Force from the right side or right end of the beam, Upward acting force is taken as Negative, and Downward acting Force is taken as Positive.
4. If we start calculating Shear Force from the Left side or Left end of the beam, Upward acting force is taken as Positive, and Downward acting Force is taken as Negative.

Shear Force and Bending Moment Diagram

Shear Force is the Algebraic sum of forces Parallel to cross-section over a particular cross-section of the beam due to action and reaction forces. Shear Force tries to shear off the beam’s Cross section perpendicular to the beam’s axis, and due to this, the developed shear stress distribution is Parabolic from the neutral axis of the beam. Bending moment is a sum of the moments over a particular cross-section of the beam due to Clockwise and Counter Clockwise Moments. This tries to bend the beam in the plane of the member, and due to transmission of it over a cross-section of the beam, the Developed Bending stress distribution is Linear from the neutral axis of the beam.

Shear Force Diagram is the Graphical representation of the variation of Shear Force Over the cross-section along the length of the beam. With the Shear Force Diagram’s help, we can identify Critical sections Subjected to Shear and design amendments to be made to avoid failure.

Similarly, Bending Moment Diagram is the Graphical representation of the Bending moment’s variation over the cross-section along the length of the beam. With the B. M Diagram’s help, we can identify Critical sections Subjected to bending and design amendments to be made to avoid failure. While constructing the Shear Force Diagram [S.F.D.], There is a sudden rise or sudden drop due to point load acting on the beam while constructing Bending moment Diagram [BMD]; there is a sudden rise or sudden drop due to couples acting on the beam.

Types of Supports and Loads

Fixed Support: It can offer three reactions in the plane of the member (1 Horizontal reaction, 1 Vertical reaction, 1 Moment reaction)

Pin Support: It can offer two reactions in the plane of the member (1 Horizontal reaction, 1 Vertical reaction)

Roller Support: It can offer only one reaction in the plane of the member (1 Vertical reaction)

Concentrated or point Load: In this, the entire intensity of load is restricted to a finite area or on a point.

Uniformly Distributed Load [U.D.L.]:  In this, the entire intensity of load is constant along the length of the beam.

Uniformly varying Load [U.V.L.]:  In this, the entire intensity of load is varying linearly along the length of the beam.

Shear Force Diagram and Bending Moment Diagram for a simply supported beam carrying point load only.

Consider the simply supported beam shown in the figure below carrying Point loads only. In a Simply supported beam, one end is pin supported while another end is roller support.

The value of the reaction at A and B can be calculated by applying Equilibrium conditions of

For vertical Equilibrium,

Taking Moment about A, Clockwise moment positive and Counter Clockwise moment is taken negative

Putting the value of R_B in [1], we get

Let X-X be the section of interest at a distance of x from end A

According to the Sign convention discussed earlier, if we start calculating Shear Force from the Left side or Left end of the beam, Upward acting force is taken as Positive, and Downward acting Force is taken as Negative.

Shear Force at Point A

We know that the Shear Force remains constant between points of application of Point Loads.

Shear force at C

Shear force at region X-X is

Shear Force at B

For Bending Moment Diagram, if we start calculating B.M from the Left side or Left end of the beam, Clockwise Moment is taken as positive. Counter Clockwise Moment is taken as Negative.

• at A = 0
• at B = 0
• at C

Shear Force [S.F.D] and Bending Moment Diagram [B.M.D] for a Cantilever beam with Uniformly Distributed load (U.D.L.) only.

Consider the Cantilever beam shown in the figure below U.D.L. only. In a Cantilever beam, one end is Fixed while another end is free to move.

The resultant load acting on the Beam Due to U.D.L. can be given by

W = Area of a rectangle

W = L * w

W=wL

Equivalent Point Load wL will act at the center of the beam. i.e., at L/2

Free Body Diagram of the Beam becomes

The value of the reaction at A can be calculated by applying Equilibrium conditions

For horizontal Equilibrium

For vertical Equilibrium

Taking Moment about A, Clockwise moment positive and Counter Clockwise moment is taken as negative

Let X-X be the section of interest at a distance of x from a free end

According to the Sign convention discussed earlier, if we start calculating Shear Force from the Left side or Left end of the beam, Upward acting force is taken as Positive, and Downward acting Force is taken as Negative.

Shear force at A is 

at region X-X is

Shear force at B is

The shear Force values at A and B states that the Shear force varies linearly from fixed end to free end.

For BMD , if we start calculating Bending Moment from the Left side or Left end of the beam, Clockwise Moment is taken as Positive and Counter-Clockwise Moment is taken as Negative.

B.M at A

B.M at X

B.M at B

4 Point Bending Moment Diagram and Equations

Consider a simply supported beam with two equal Loads W acting at a distance a from either end.

The value of the reaction at A and B can be calculated by applying Equilibrium conditions

For vertical Equilibrium

Taking Moment about A, Clockwise moment positive and Counter Clockwise moment is taken negative

From [ 1 ]we get

According to the Sign convention discussed earlier, if we start calculating Shear Force from the Left side or Left end of the beam, Upward acting force is taken as Positive, and Downward acting Force is taken as Negative. For BMD diagram plotting, if we start calculating Bending Moment from the Left side or Left end of the beam, Clockwise Moment is taken as Positive and Counter-Clockwise Moment is taken as Negative.

Shear force at A is

Shear force at C is

Shear force at D is

Shear force at B is

For Bending Moment Diagram

B. M at A = 0

B. M at C

B.M at D

B. M at B = 0

Question and Answer of Bending Moment

Q.1) What is the difference between moment and bending moment?

Ans: A Moment can be defined as the product of force and the length of the line passing through the point of support and is perpendicular to the force. A bending moment is a reaction induced inside a structural member when an external force or moment is applied to it, causing the member to bend.

Q.2) What is a bending moment diagram definition?

Ans: Bending Moment Diagram is the Graphical representation of the variation of B.M Over the cross-section along the length of the beam. With this Diagram’s help, we can identify Critical sections Subjected to bending and design amendments to be made to avoid failure.

Q.3) What is the Formula for Bending Stress?

Ans: Bending Stress can be defined as resistance induced due to Bending Moment or by two equal and opposite couples in the plane of the member. Its Formula is given by

Where, M = Applied bending moment over the cross-section of the beam.

I = Second area moment of Inertia

σ = Bending Stress-induced in the member

y = Vertical distance between the neutral axis of the beam and the desired fiber or element in mm

E = Young’s Modulus in MPa

R = Radius of Curvature in mm

To know about Strength of material click here

What is fluid mechanics?

The fluid mechanics can be elaborated as the study of fluid and fluid systems for their physical behaviour, governing laws, actions of different energies and different flow pattern.

The fluid is sub-divided into two types :

1. Liquid
2. Gas

The fluid mechanics is the subject of engineering which will be useful in many engineering discipline. The subject of fluid mechanic is important in mechanical engineering, civil engineering, chemical engineering and environment engineering etc.

Even the study of geology, geophysics, ocean and nano science also requires some knowledge of fluid mechanics and fluid dynamics.

It is interesting for you that some basic laws of fluid mechanics is involved in primary and secondary education, so it can be expected that it is familiar subject for you.

What are the fluid mechanics branches?

There are three branches of fluid mechanics based on forces and energy.

Hydrostatic:

The hydrostatics can be defined as fluid mechanics studying when the fluid or fluid element at rest. It means there is no fluid flow. There are no shearing stresses.

We can take an example of fluid at rest like a dam, pond etc.

The dam is very known example of hydrostatic branch. In holidays you might have visited some famous dam near you.

Kinematics:

The kinematics is the study of fluid mechanics about fluid motions like translation, rotary or deformation. Remember-> There is no consideration of forces and energy acting on fluid (Fluid in motion) in this study.

Here, the fluid is flowing so we can take example of flowing fluid in river, canal etc.

Dynamics:

The fluid dynamics is a complete study of flowing fluid. It studies velocity, acceleration, forces and energies acts on the fluid in motion.

Here, the study of flowing fluid (Fluid in motion) is carried out by considering forces and energy acts on it. The example of fluid dynamic are fuel flow inside diesel fuel injector, liquid flow inside pump, fluid flow inside turbine etc.

Fluid flow | What is fluid flow?

When gas or liquid is travelling or moving fluid from one point (destination) to another point, we can call it fluid flow.

Let’s understand in another word, the trend of continuous deformation of fluid is known as fluidity. The action of this continuous deformation is known as fluid flow.

For example flow of wind, flow in the river, waves in the sea, liquid flow in pipelines etc.

Classification of fluid

In common term, there are two types of fluid as given below,

1. Ideal fluid
2. Real fluid

What is the ideal fluid?

First, keep it in mind “there is no existence of ideal fluid in nature and it is imaginary fluid”. In practical purpose, we are considering water and air as an ideal fluid for many studies because of its lower viscosity.

The water is incompressible, so it is closer to an ideal fluid as compared to air.

Ideal fluid possess the following characteristics,

• Incompressible
• Non-viscous (Inviscid)
• No friction (Frictionless)
• No surface tension

The ideal fluid possesses no viscosity. It means that the friction does not exist in the fluid. The ideal fluid is our imagination of standard fluid with superior characteristics. In nature, there is always frictional resistance whenever any motion exists.

What is real fluid?

The all fluid in nature can be considered as real. Let’s see why?

It possesses most of the practical characteristics,

• Viscous
• Compressible
• Friction
• Surface tension

Principles of fluid dynamics

Some of the basics principles of fluid dynamics are enlisted below for your information. The study of each principle in detail with our next articles will take you in-depth of fluid dynamics.

• Conservation of mass, momentum and energy
• Newton’s law of viscosity
• Principles of continuity
• Momentum equation and energy
• Euler’s equation
• Bernoulli’s theorem
• Archimede’s principle
• Pascal’s law
• Laws of similarities and model
• Rayleigh’s method and Buckingham pi-theorem
• Navier stock equation
• Reynold and Darcy equation

These principles are helpful since many of the approaches and techniques of analysis used in fluid mechanics problems. It will be well understood when you come across real problems on fluid mechanics.

Fluid Mechanic applications

The fluid mechanics subject encircles numerous applications in domestic as well as industrial. Some of the applications are enlisted below,

• The water distribution channel network and pipelines in domestic and industrial.
• The hydraulics machinery and hydraulic structures are designed based on fluid mechanics.  Hydraulics Machinery: Turbines, pumps, valves, fluid couplings, actuators etc.

Hydraulic structures: Canal, dams, weirs, overhead tanks etc.

• The fundamental of fluid dynamics can be used to design supersonic aircraft, missiles, gas turbine, rocket engines, torpedo, submarine etc.
• The power plants like hydroelectric power, thermal (steam) power, gas turbine power uses fluid mechanics.

• The fluid mechanics have vast applications in measurement devices of pressure, velocity and flow measurement instruments.

Pressure measurement: Bourdon tube pressure gauge, vacuum gauge, manometer etc.

Velocity and flow measuring instruments: Pitot tube, current meter, venturi meter, orifice meter, rotameter etc.

• Some of the scientific subjects like oceanography, meteorology, geology etc. also require fluid dynamics.
• The pneumatics and hydraulic various fluid control devices
• Even if we consider blood flowing inside the human vein possess fluid dynamics

In nature, there are so many processes governed by fluid mechanics and fluid dynamics laws. Example: Rise of groundwater to top of the tree, rainwater cycle, wind flow and waves, ocean waves, weather patterns etc.

Let’s understand some practical applications of fluid dynamics, which will become very familiar with you.

You might have your automobile vehicle bike or car. You know that air is infiltrated inside vehicle tyres with pressure, so it possesses pressure laws.

Secondly, the shock absorber is filled with oil which absorbs jerk or shock. The oil will get pressurized and provide cushioning to your vehicle. There numerous day to day applications in your life that is totally or partially governed by fluid mechanics or dynamics.

Units and Dimensions

Since our subject is fluid mechanics, we will study a variety of fluid characteristics; it is a requirement to follow a system for indicating these attributes, both qualitatively and quantitatively.

The qualitative aspect describes to find the nature, or type, of the characteristics like length, time, stress, temperature, velocity and pressure on the next side the quantitative aspect indicates a value measure of the attributes.

A dimension can be defined as a description of measurable quantities or attributes of an object such as mass, length, temperature, pressure, time etc.

The understanding of unit can be considered as the standard for measuring the dimension or quality.

To understand the difference between units and dimensions, let’s take an example of the distance between Mumbai and Goa.

The term length is used to describe the qualitative concept of physical quantity.

The term unit indicates the magnitude of the distance between Mumbai and Goa in our example. This distance can be expressed in meter, kilometre or miles.

There are four fundamentals dimensions used in the physical dimensioning system. In the SI (standard international) system, the dimensions are mass, length, time and temperature. Let’s understand how it works?

International System (SI). In 1960, the 11^th General Conference organised on Weights and Measures, the international organization responsible for managing precise, systematic standards of measurements, properly accepted the International System of Units as the international standard. This system, generally termed SI, has been broadly accepted worldwide and is broadly used.

Mass (M)	Kilogram	kg
Length (L)	Meter	m
Time (T)	Second	s
Temperature (K)	Kelvin	K

These are the fundamental units of the SI system. Other all the units of any physical properties can be derived based on these four units. Let’s take some example to understand it better way.

Work

 You have heard about work. The unit of work is Joule. Now we expand its unit.

In other words, it is an energy transfer of any object when it moved from one place to another place. The force can be positive or negative.

Work = Force * Distance

The newton (N) is a unit of force, and the unit meter is a unit of distance. So the unit of work,

Unit of work = Newton* meter =N*m =Joule (J)

Density

The formula of density is given as below.

Density = mass per unit volume

Here, the unit of mass is kg, the unit of volume is m^3.

The unit of density is kg/m³

The density of water is considered 1000 or 997 kg/m³. The density of air is 1.225 kg/m³

Its means that water is considered standard dense and it is heavier than much other liquid. The air is significantly lighter, and it is a highly compressible fluid.

Power

The definition of power is given as the ability of doing work in unit time. Or we can say work done per unit time.

Power = Work done per unit time.

The unit of work is Joule (J) and the unit of time is second (s).

The unit of power is derived as J/s (Joule/second). The unit Joule/second is in general known as watt (w).

Questions and Answers

What are types of fluid according to state?

According to the state, there are two types of fluid.

1. Liquid
2. Gas

Give the name of fluid mechanics branches.

1. Hydrostatics
2. Fluid kinematics
3. Fluid dynamics

What is real fluid?

It possesses most of the practical characteristics,

1. Viscous
2. Compressible
3. Friction
4. Surface tension

Define: Dimension and unit

A dimension can be defined as a description of measurable quantities or attributes of an object such as mass, length, temperature, pressure, time etc.

The understanding of unit can be considered as the standard for measuring the dimension or quality.

Give four fundamental dimensions of SI (Standard International).

Mass (M)

Length (L)

Time (T)

Temperature (K)

What is SI (Standard International) System?

International System (SI). In 1960 the 11^th General Conference organized on Weights and Measures, the international organization responsible for managing precise, systematic standards of measurements, properly accepted the International System of Units as the international standard.

Enlist three applications of fluid mechanics.

• Design supersonic aircrafts
• The water distribution channel network
• The pneumatics and hydraulic various fluid control devices

What are the pressure measuring instruments?

• Bourdon tube pressure gauge
• Vacuum gauge
• Manometer

Give any three names of fluid mechanic principles.

• Bernoulli’s theorem
• Rayleigh’s method and Buckingham pi-theorem
• Archimede’s principle

MCQ on Articles

Choose the fluid mechanics branch; the study includes force and energy acts on moving fluid?

(a) Hydro statics               (b) Fluid kinematics         (c) Fluid dynamics            (d) None

In which of the following fluid mechanics branch, there is no shearing stress or fluid motion?

(a) Hydro statics               (b) Fluid kinematics         (c) Fluid dynamics            (d) None

An ideal fluid is known as the fluid which is________

(a) In-compressible          (b) Compressible             (c) Viscous          (d) None

A real fluid is one which possesses ________

(a) In-compressible          (b) Viscous             (c) Inviscid           (d) Frictionless

Which of the following is basic principle of fluid dynamics?

(a) Newton’s law of cooling         (b) Newton’s law of viscosity

(c) Law of gearing                            (d) Stefan-Boltzmann

Which of the following is the hydraulic machinery?

(a) Spiral gear    (b) Crank shaft  (c) Turbine          (d) drilling

Choose the name of hydraulic structure from the following choices.

(a) house beam                (b) Machine structure     (c) Dam (d) None

Which of the following is a flow measurement device?

(a) Rotameter   (b) Bourdon tube gauge (c) Manometer               (d) None

What is the unit of Power?

(a) J/s    (b) J       (c) Nm  (d) K

What is the unit of the density?

(a) kg      (b) m/s (c) kg/m³ (d) m²

Conclusion

This article is helpful to get the basic knowledge about fluid mechanics fundamental. The article includes an understanding of some basics terms like hydrostatics, fluid kinematics and fluid dynamics. The list of various fluid mechanics principle and applications are provided to get an idea about subject and future learning topics. In last, the dimension and unit definitions are given with detailed examples.

This article teaches you to visualize and remember applications of fluid mechanics in your day to day life. You have to collaborate with applications with fluid mechanic’s principles.

More topic related to fluid mechanics, please click here.

• When force transmits from one body to another, forces parallel to the surface are experienced by the body, such kind of forces produce shear stress.
• It is vital to know about the shear stresses acting on the material while designing the product. Shear failure is the most common failure which occurs due to inappropriate consideration of shear forces.

Shear Stress Definition

• When the applied force is parallel/tangential to the surface area of application, then the stress produced is known as shear stress.
• Here application of force is tangential to the surface of application.
•  A component of the stress tensor in the direction parallel to the area of application.
• Shear stress also occurs in axial loading, bending, etc.

Shear Stress Formula

 Shear Stress= Force imposed parallel to the area/ Area of cross-section

What is Shear Stress Units ?

Unit of shear stress is N/m² or Pa.

In industries, the unit used to measure shear stress is N/mm² or MPa (Mega Pascal)

Shear Stress Symbol | Shear Stress tau

The symbol used to represent shear stress is τ (Tau). It is also represented by T.

Shear Stress Diagram

Shear Stress Notation

• Symbol τ is used to represent shear stress.
• To show the applied force and direction of the application area, subscripts are used with the symbol τ as τ_ij.
• Where i represent the direction of the surface plane on which it is being applied (perpendicular to the surface), and j represents the applied force’s direction.
• Thus, τ_ij= Shear stress acting on the i-surface in j-direction.

          τ_ji= Shear stress acting on the j-surface in i-direction.

• We can write it as:

Shear Stress Direction

In 2 Dimensions:

• In the vector form, shear stress is the ratio of a parallel component of force applied to the unit normal vector of area.

                  τ= F_‖ / A

In 3 Dimensions:

• In naming xy, which is in the subscript form (subscript convention), index x represents the direction of a vector perpendicular to the application area, and y represents the direction of applied force.
• In the following figure, it is represented for all three axes.

Any of the shear stress can be represented as follow:           

Shear Stress Sign Convention

When the shear stress is applied on a surface along the principal axis, the adjacent perpendicular axis experiences the equal amount of shear stress in the opposite direction known as complementary shear stress as shown in the figure:

• Shear stress is positive if the shear force applied along the x-axis is in the right direction or clockwise.

Similarly, Shear stress is positive if the shear force applied along the y-axis is in an upward direction or it is counterclockwise.

• Shear stress is negative if the shear force applied along the x-axis is in the left direction or in counterclockwise.

Similarly, Shear stress is negative if the shear force applied along the y-axis is in a downward direction or it is clockwise.

• Half arrowheads are used to represent shear stress.

Shear Strain

• When the shear stress is applied on a surface, deformation is produced in the material. So, the ratio of deformation to the original length perpendicular to the member’s axes is known as shear strain. It is denoted by γ.
• It is also defined as the tangent of the strain angle ө.
• Shear Strain= del l/ h = tangent(Ө)

Shear Stress and Shear Strain

• It is noted that shear strain is dependent on shear stress. The relation is expressed as

Modulus of Rigidity | Shear Stress Modulus | Shear Modulus of Rigidity

• The proportionality constant G is known as Modulus of Rigidity or Shear Stress Modulus or Shear Modulus of Rigidity.
• Thus,

     Modulus of Rigidity = Shear Stress/ Shear Strain

• In most of the metals, G is about 0.4 times of Young’s Modulus of Elasticity.

For isotropic materials, Modulus of Rigidity and Modulus of Elasticity is related to each other according to

      Y = 2*G* (1+ ʋ)

Where, Y= Modulus of Elasticity

             G= Modulus of Rigidity

             ʋ= Poisson’s Ratio

Shear Strength

• Shear strength is the maximum value of shear stress that can resist failure due to shear stress.
• It is a significant parameter while designing and manufacturing machines.
• Example: While designing bolts and rivets, it is indispensable to know about the material’s shear strength.

Shear Stress vs Normal Stress

	Shear Stress	Normal Stress
1.	Force applied is parallel to the surface on which it is being applied	Force applied is perpendicular to the surface on which it is being applied.
2.	Force vector and area vector are perpendicular to each other	Force vector and area vector are parallel to each other.

 Shear Stress from Torque | Shear Stress Due to Torsion

• Torque is a rotational form of force which makes the object to rotate around an axis. When this torque is applied on a deformable body, it generates shear stress in that body, making that body twist around an axis, known as torsion.
• This type of stress is significant in shafts. The stresses or deformations induced in the shaft due to this torsion are shear kinds of stresses.
• The shear strain produced in the following shaft of radius r is represented as follows:

γ= rdө/dz

Thus, the shear stress produced is represented by

Shear Stress Fluid

• Shear stress produced in any material is due to relative movement of planes on each other.
• When it comes to fluid, shear stress is produced in the fluids due to relative movement of fluid layers on one another. It is the viscosity which causes shear stress in the fluid.
• Due to shear stress, fluid cannot be held in one place.
• Thus, the shear stress produced in the fluid is equal to the  

Where μ= Dynamic Viscosity

             u= Flow Velocity

             y= Height above the boundary

• This equation is also known as Newton’s Law of Viscosity.

Read more about Shear Strain and All important facts

Shear Rate

• Shear rate is the rate at which one layer of fluid passes on another adjacent layer of fluid; this can find out by both using geometry and speed of the flow.
• The viscosity of fluid mainly depends upon the shear rate of the fluid.
• This parameter is very important while designing fluid products like syrups, sunscreen cream, body lotion, etc.

Shear Stress vs Shear Rate

• The shear rate is defined as the rate of change of velocity of layers of fluid on one another. For all Newtonian fluids, the viscosity remains constant when there is a change in shear rate, and the shear stress is directly proportional to the shear rate. 
• Following is a graphical representation of shear stress vs shear for a different type of fluid:

Shear Stress in Beams

• If a cantilever beam of diameter d is twisted on its free end, if torsion of magnitude T is applied on its free end, then the shear stress produced in the beam.
• This shear stress is represented as follows  

Shear Stress due to Bending

• For an ideal case, shear stress does not produce due to bending, but in real condition, shear stress occurs in the bending conditions.
• A varying bending moment along the length of the beam causes movement of one plane on another because shear stress gets produced in the beams.

Read more about Shear modulus and Modulus of rigidity

Shear Stress in Bolts

• Bolts are mainly used to fix two different assembly bodies like joints, two different metal sheets, two different pipes of an assembly etc.
• The bolt experiences shear load or shear force due to the presence of two different loadings acting in the different directions this causes one plane of the bolt to slip on another plane of the bolt.
• ; This causes shear failure in joints like cotter joint, knuckle joint, etc. so, while selecting material for different mechanisms, it is essential to know its shear stress.
• Double shear stress is calculated in bolts.

Shear Stress Steel

• Steel is one of the most applicable metals in all types of industries. From constructions to machines, steel is used everywhere. Therefore the maximum shear stress value of steel is a significant parameter while designing.
• It is determined using the ultimate tensile strength of the steel. Von Misses factor is used to determine maximum shear stress. It states that maximum shear stress is 0.577 times of the ultimate tensile strength.
• In many cases, it is considered as 0.5 times of ultimate tensile strength of the steel. 

Read more about How to calculate shear strain

Shear Stress Problems

Subjective Questions

What is Shear Stress?

  Ans.: When the applied force is parallel to the surface/area of application, then the stress produced is known as shear stress. Shear stress is a component of the stress tensor in the direction parallel to the area of application.

What is complementary shear stress?

Ans.: When the shear stress is applied on a surface along the principal axis the adjacent perpendicular axis experiences the equal amount of shear stress in the opposite direction known as complementary shear stress

What are the sign conventions for shear stress? | How to decide sign of shear stress?

Ans.: Shear stress is positive if the shear force applied along the x-axis is in the right direction or clockwise.

Similarly, Shear stress is positive if the shear force applied along the y-axis is in an upward direction or it is counterclockwise.

Shear stress is negative if the shear force applied along the x-axis is in the left direction or in counterclockwise.

Similarly, Shear stress is negative if the shear force applied along the y-axis is in a downward direction or it is clockwise.

What is the sign for shear stress?

Symbol τ is used to represent shear stress. To specify the directions of applied force and direction of the application area, subscripts are used with the symbol τ as τij.

What are examples of shear?

When a piece of paper is cut with the scissor.

A bolt and nut tightly fixed with plates.

Rubbing palm on each other

Any friction leads to the production of shear.

What’s an example of shear stress?

Painting walls using colour.

Chewing food under the teeth.

In cotter and knuckle joints, cotter and knuckle experiences shear stress.

How do you solve shear stress?

Shear Stress= Force imposed parallel to the area/ Area of cross Section

What causes shear stress?

When force transmits from one body to another, forces parallel to the surface are experienced by the body, such kind of forces produce shear stress.

What is the difference between shear stress and shear force?

Shear force is the force applied parallel or tangential to the plane’s surface, whereas shear stress is the shear force experienced by the plane’s surface per unit area.

What is the difference between shear stress and shear rate?

When the applied force is parallel to the surface area of application, then the stress produced is known as shear stress whereas the shear rate is the rate at which one layer of fluid passes on another adjacent layer of fluid.   

What is a positive shear force?

Shear stress is positive if the shear force applied along the x-axis is in the right direction or clockwise. Similarly, Shear stress is positive if the shear force applied along the y-axis is in an upward direction or it is counterclockwise.

What is average shear stress?

Actual shear stress is never uniform; it is different for the different unit cross-sectional area. So, to calculate this shear stress, the considered shear stress is the average shear stress.

Average shear stress is always lesser than maximum shear stress for the given area of cross-section.

What is Shear Strain?

When the shear stress is applied on a surface, deformation is produced in the material. So, the ratio of deformation to the original length perpendicular to the member’s axes is known as shear strain. It is denoted by γ.

Is shear strain in radian?

No. shear strain is the tangent value of del l and h, which is a unitless quantity.

Objective Questions:

A block of a material with a shear modulus of rigidity G = 90 KPa is bonded to two rigid horizontal plates. The lower plate is fixed, while the upper plate is subjected to a horizontal force P. knowing that the upper plate moves through 0.04 cm under the force’s action if the height of the block is 2cm, determine the average shearing strain in the material.

1. 0.04 rad
2. 0.02 rad
3. 0.01 rad
4. 0.08 rad

Solution: Option 2. Is the answer.                

A block of a material with a shear modulus of rigidity G = 90 KPa is bonded to two rigid horizontal plates. The lower plate is fixed, while the upper plate is subjected to a horizontal force P. knowing that the upper plate moves through 0.04 cm under the force’s action if the height of the block is 2cm, find the force P exerted on the upper plate.

1. 180
2. 360
3. 720
4. 90

Solution: Option 1. is the answer.

Find the value of shear stresses developed in the pin A for the bell crank mechanism shown in the figure? Find the safe diameter of the pin if the allowable shear stresses for the pin material is180 MPa.

1. 3mm
2. 4mm
3. 4.5mm
4. 5mm

Solution: Answer is option 4.

                   Stresses developed in pin are shear stress and bearing stress.

                   Force at B= 5*0.1/0.15= 3.33KN

Considering double shear at A

The safe diameter of pin is more significant than 4.6mm.

Which of the following basic assumption is not considered while deriving torsion equation for a circular member?

1. The material must be homogenous and isotropic.
2. A plane perpendicular to the axis remains plane also after the torque application.
3. Shear strain varies linearly from the central axis in a circular member when subjected to a torque.
4. The material does not obey Hooke’s law

Solution: Option 4.

CONCLUSION 

In this article all the concepts related to shear stress are discussed in detail. It is very important to know about shear stress while designing any product.

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When a deformable material is stretched in a particular direction, its length increases in that direction, and thickness reduces in the lateral one. Similarly, the material is compressed in a specific direction and, its length decreases in that direction, and thickness increases in the lateral one. Poisson’s ratio is a parameter that relates these deformations, which is useful in material selection and application.

Poisson’s Ratio Definition | Poisson’s Ratio Equation

When we apply tensile stress on the material, there is elongation in the direction of applied force and shrinkage in the transverse/lateral movement. Thus the strain gets produced in both directions. The ratio of strain produced in the transverse direction to the strain produced in the direction of tensile stress application is known as Poisson’s ratio.

Its symbol is ʋ or μ.

The ratio obtained has a negative sign, as the ratio obtained is always negative.

Thus,

        Poisson’s Ratio= Transverse Strain/ axial Strain

                           ʋ= -(ε_x/ε_y)

Similarly, if compressive stress is applied to the material, there is shrinkage in the direction of applied force and thickening in the transverse/ lateral direction. Thus, the strain gets produced in both directions. The ratio of strain produced in the transverse direction to the strain produced in the direction of compressive stress application is also known as Poisson’s ratio.

Generally, it ranges from 0 to 0.5 for engineering materials. Its value increases under tensile stress and decreases under compressive stress.

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Poisson’s Ratio of Steel

• The value of Poisson’s ratio for steel ranges from 0.25 to 0.33.
• The average value of Poisson’s ratio for steel 0.28.
• It depends on the steel type used.

Following is the list of Poisson’s ratio for different steels

Steel Type	Poisson’s Ratio
High Carbon Steel	0.295
Mild Steel	0.303
Cast Steel	0.265
Cold Rolled Steel	0.287
Stainless Steel 18-8	0.305( 0.30-0.31)

Poisson’s Ratio of Aluminum

• The value of Poisson’s ratio for aluminum ranges from 0.33 to 0.34.
• The average value of Poisson’s ratio for aluminum is 0.33 and for aluminum alloy 0.32.
• It depends on the type of aluminum or aluminum alloy used.

Following is the list of Poisson’s ratio for different aluminum

Aluminum Type	Poisson’s Ratio
Aluminum Bronze	0.30
Rolled Aluminum	0.337/0.339
Rolled Pure Aluminum	0.327

 Poisson’s Ratio of Concrete

• The value of Poisson’s ratio for concrete ranges from 0.15 to 0.25.
• Its general value is taken as 0.2.
• It depends on the type of concrete (wet, dry, saturated) and loading conditions.
• Its value for high strength concrete is 0.1, and for low strength concrete, it is o.2.

Poisson’s Ratio of Copper

• The value of Poisson’s ratio ranges from 0.34 to 0.35.
• Its general value is taken as 0.355.
• It depends on the type of copper or copper alloy used.

Following is the list of Poisson’s ratio for different copper

Copper Type	Poisson’s Ratio
Normal Brass	0.34
Brass, 70-30	0.331
Brass, cast	0.357
Bronze	0.34

Poisson’s Ratio of Rubber

• The value of Poisson’s ratio for rubber is from 0.48 to 0.50.
• For most of the rubbers, it is equal to 0.5.
• Its value for natural rubber is 0.5.
• It has the highest value of Poisson’s Ratio. 

Poisson’s Ratio of Plastic

• The Poisson’s ratio of plastics generally increases with time, strain, and temperature and decreases with strain rate.
• Following is the list of Poisson’s ratio for different plastics

Plastic Type	Poisson’s Ratio
PAMS	0.32
PPMS	0.34
PS	0.35
PVC	0.40

Poisson’s Ratio and Young’s Modulus

The materials for which elastic behavior does not vary with the crystallographic direction are known as elastically isotropic materials. Using Poisson’s ratio of the material, we can obtain a relation between Modulus of Rigidity and Modulus of Elasticity for isotropic materials as follows.

                                  Y= 2*G*(1+ʋ)

Where, Y= Modulus of Elasticity

             G= Modulus of Rigidity

             ʋ= Poisson’s Ratio

Questions and Answers

What is meant by Poisson’s ratio?

 When we apply tensile stress on the material, there is elongation in the direction of applied force and shrinkage in the transverse/lateral direction. Thus the strain gets produced in both directions. The ratio of strain produced in the transverse direction to the strain produced in the direction of tensile stress application is known as Poisson’s ratio.

What does a Poisson ratio of 0.5 mean?

Poisson’s ratio of precisely 0.5 means the material is perfectly incompressible isotropic material deformed elastically at small strains.

How is Poisson’s ratio calculated?

        Poisson’s Ratio= Transverse Strain/ axial Strain

                           ʋ=-εx/εy

What is the Poisson’s ratio for steel?

The value of Poisson’s ratio for steel ranges between 0.25 to 0.33.

The average value of Poisson’s ratio for steel 0.28.

What is Poisson’s ratio for aluminum?

The value of Poisson’s ratio for aluminum ranges between 0.33 to 0.34.

The average value of Poisson’s ratio for aluminum is 0.33 and for aluminum alloy 0.32.

What is Poisson’s ratio for concrete?

The value of Poisson’s ratio for concrete ranges between 0.15 to 0.25.

Its general value is taken as 0.2.

It depends on the type of concrete (wet, dry, saturated) and loading conditions.

Its value for high strength concrete is 0.1, and for low strength concrete, it is 0.2.

What is the relation between Poisson’s Ratio and Young’s Modulus of Elasticity?

                                  Y= 2*G*(1+ʋ)

Where, Y= Modulus of Elasticity

             G= Modulus of Rigidity

             ʋ= Poisson’s Ratio

Which parameters affect the Poisson’s Ratio of Polymers?

The Poisson’s ratio of polymeric materials like plastic generally increases with time, strain, and temperature and decreases with strain rate.

What if Poisson’s ratio is zero?

If the Poisson’s ratio is zero, the material is not deformable; hence, it is a rigid body.

Which material has the highest Poisson’s ratio?

Rubber has the highest Poisson’s Ratio, almost equal to 0.5.

Why is Poisson’s ratio always positive?

Poisson’s ratio is the negative of the ratio of lateral strain to axial strain. The ratio of lateral strain to axial strain is always negative because elongation causes contraction in diameter, which ultimately makes the ratio negative .similarly, compression causes elongation in diameter, which makes the ratio negative.

Is Poisson’s ratio constant?

For the stresses in the elastic range, Poisson’s ratio is almost constant.

Does Poisson’s ratio dependent on temperature?

Yes. With the increasing temperature, Poisson’s ratio decreases.

Objective Questions

Tensile stress is applied along the longitudinal axis of a cylindrical brass rod with a diameter of 10mm. Determine the magnitude of the strain produced in the transverse direction where the load is required to produce a 2.5 *10^-3 change in diameter if the deformation is entirely elastic. Poisson’s ratio of brass is 0.34.

1. 3.5*10-3
2. 5.5*10-3
3. 7.35*10-3
4. 1.0*10-3

Solution: Answer is option 3.

A wire of length 2 m is loaded, and an elongation of 2mm is produced. If the wire’s diameter is 5 mm, find the change in the diameter of the wire when elongated. Poisson’s ratio of the wire is  0.35

Solution: L= 2m

                 Del L= 2mm

                 D= 1mm

                 ʋ= 0.24

                Longitudinal Strain= 2*10^-3/2=10^-3

                Lateral Strain= Poisson’s Ratio*Longitudinal Strain

                                        = 0.35*10^-3

                Lateral Strain= Change in diameter/ Original Diameter=0.35*10^-3

                                                                             Change in Diameter=0.35*10^-3*5*10^-3

                                                                                                                = 1.75*10^-6

                                                                                                                =1.75*10^-7 

                 Thus, the Change in diameter is 1.75*10^-7mm.

A wire of steel having a cross-sectional area of 2 mm2 is stretched by 20 N. Find the lateral strain produced in the wire. Young’s Modulus for steel is 2*1011N/m2, and Poisson’s ratio is 0.311.

Solution: A= 2mm2= 2*10-6mm2

                 F= 20N

                                                 Y= Longitudinal Stress/ Longitudinal Strain

                                                   =F/ (A*Longitudinal Strain)

                 Longitudinal Strain= F/(Y*A)

                                                   =20/ (1*10^-6*2*10¹¹) = 10^-4

              Poisson’s Ratio= Lateral Strain/ Longitudinal Strain

              Lateral Strain= Poisson’s Ratio*Longitudinal Strain

                                    = 0.311*10^-4

              Lateral Strain=0.311*10^-4

Conclusion

In this articles, all the important concepts related to Poisson’s Ratio are discussed in detailed . Numerical and subjective type of questions are added for practice.

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Nanofluids have emerged as a promising solution for enhancing heat transfer in various applications. By incorporating nanoparticles into conventional heat transfer fluids, nanofluids exhibit improved thermal properties that can significantly enhance heat transfer efficiency. In this section, we will explore the definition and composition of nanofluids, as well as their application in heat transfer enhancement.

Definition and Composition of Nanofluids

Nanofluids can be defined as suspensions of nanoscale particles in a base fluid, typically water or oil. These nanoparticles, which are usually metallic or non-metallic, are dispersed uniformly in the base fluid, creating a stable colloidal mixture. The size of the nanoparticles used in nanofluids typically ranges from 1 to 100 nanometers.

The composition of nanofluids plays a crucial role in determining their heat transfer properties. The choice of nanoparticles and base fluid depends on the specific application requirements. Metallic nanoparticles, such as copper, aluminum, and silver, are commonly used due to their high thermal conductivity. Non-metallic nanoparticles, such as carbon nanotubes and graphene, are also gaining attention for their unique properties.

To ensure the stability of nanofluids, various techniques are employed to prevent particle agglomeration. Surface modification of nanoparticles, such as coating them with surfactants or polymers, helps to maintain the stability and prevent sedimentation. Additionally, ultrasonication and magnetic stirring are used during the synthesis process to disperse the nanoparticles evenly in the base fluid.

Application of Nanofluids in Heat Transfer Enhancement

The use of nanofluids in heat transfer applications has gained significant interest due to their ability to enhance thermal conductivity and convective heat transfer. The incorporation of nanoparticles into the base fluid increases the effective thermal conductivity of the nanofluid, resulting in improved heat transfer rates.

Nanofluids find applications in various heat transfer systems, including heat exchangers, electronics cooling, and solar thermal systems. In heat exchangers, nanofluids can enhance the overall heat transfer coefficient, leading to improved system performance. The increased heat transfer efficiency of nanofluids allows for smaller heat exchanger designs, reducing space and cost requirements.

In electronics cooling, nanofluids offer a solution to dissipate heat generated by electronic devices more effectively. By using nanofluids as coolants, the heat transfer rate from the electronic components to the cooling system can be significantly improved, ensuring optimal device performance and reliability.

Furthermore, nanofluids have shown promise in solar thermal systems, where they can enhance the absorption and transfer of solar energy. The improved heat transfer properties of nanofluids enable more efficient conversion of solar radiation into usable heat, making them a potential solution for sustainable energy applications.

Heat Transfer Enhancement in Nanofluids

Overview of Heat Transfer Enhancement in Nanofluids

Nanofluids, a combination of base fluids and nanoparticles, have gained significant attention in recent years due to their ability to enhance heat transfer. These nanofluids exhibit improved thermal properties compared to traditional fluids, making them a promising solution for various heat transfer applications. In this section, we will explore the concept of heat transfer enhancement in nanofluids and delve into the underlying mechanisms that contribute to their superior performance.

Nanofluids are engineered by dispersing metallic or non-metallic nanoparticles, typically in the range of 1-100 nanometers, into a base fluid such as water, oil, or ethylene glycol. The addition of nanoparticles alters the thermal conductivity, viscosity, and convective heat transfer characteristics of the base fluid, leading to enhanced heat transfer rates.

One of the key factors that contribute to the improved heat transfer in nanofluids is the significantly higher thermal conductivity of nanoparticles compared to the base fluid. The presence of nanoparticles in the fluid creates a conductive network that facilitates the transfer of heat. This increased thermal conductivity allows for more efficient heat dissipation, resulting in enhanced heat transfer rates.

Importance of Thermal Conductivity in Nanofluids

Thermal conductivity plays a crucial role in determining the heat transfer performance of nanofluids. The ability of a material to conduct heat is quantified by its thermal conductivity coefficient. In the case of nanofluids, the thermal conductivity is significantly enhanced due to the presence of nanoparticles.

The high thermal conductivity of nanoparticles allows for better heat conduction within the nanofluid, enabling faster heat transfer. This property is particularly beneficial in applications where heat dissipation is critical, such as heat exchangers or electronic cooling systems. By utilizing nanofluids with enhanced thermal conductivity, the overall efficiency of these systems can be greatly improved.

Moreover, the increased thermal conductivity of nanofluids also leads to a higher heat transfer coefficient. The heat transfer coefficient represents the rate at which heat is transferred between a solid surface and a fluid. In the case of nanofluids, the higher thermal conductivity results in a larger heat transfer coefficient, indicating a more efficient heat transfer process.

In addition to thermal conductivity, the convective heat transfer characteristics of nanofluids are also influenced by the presence of nanoparticles. The nanoparticles alter the fluid dynamics within the nanofluid, promoting better heat transfer through convection. This enhanced convective heat transfer further contributes to the overall heat transfer enhancement in nanofluids.

Methods to Increase Heat Transfer

Heat transfer is a crucial process in various industrial applications, ranging from cooling electronic devices to optimizing the efficiency of power plants. Enhancing heat transfer is essential to improve the overall performance and effectiveness of these systems. In recent years, researchers have been exploring innovative methods to increase heat transfer, including the use of nanofluids. Nanofluids, which are a combination of nanoparticles and base fluids, have shown great potential in enhancing heat transfer due to their unique thermal properties. In this section, we will explore different ways to enhance heat transfer and delve into the fascinating world of nanofluid technology.

Before we delve into the ways to enhance heat transfer, let’s first understand the fundamental equation that governs heat transfer. The heat transfer equation, also known as Fourier’s law, describes the rate at which heat is transferred through a material. It states that the heat transfer rate is directly proportional to the temperature gradient and the thermal conductivity of the material, and inversely proportional to the thickness of the material. Mathematically, it can be represented as:

q = -k * A * (dT/dx)

Where:
– q is the heat transfer rate
– k is the thermal conductivity of the material
– A is the cross-sectional area through which heat is transferred
– dT/dx is the temperature gradient across the material

Understanding this equation is crucial as it forms the basis for exploring methods to enhance heat transfer.

Ways to Enhance Heat Transfer

Now that we have a basic understanding of the heat transfer equation, let’s explore some ways to enhance heat transfer. These methods can be broadly categorized into two main approaches: improving thermal conductivity and optimizing convective heat transfer.

Improving Thermal Conductivity

One way to enhance heat transfer is by improving the thermal conductivity of the working fluid. Thermal conductivity refers to the ability of a material to conduct heat. By incorporating high thermal conductivity nanomaterials, such as metallic or carbon-based nanoparticles, into the base fluid, the overall thermal conductivity of the nanofluid can be significantly enhanced. These nanoparticles, due to their small size and large surface area, facilitate efficient heat transfer by increasing the number of heat transfer pathways within the fluid.

Optimizing Convective Heat Transfer

Convective heat transfer, which occurs when a fluid flows over a solid surface, is another area where heat transfer enhancement can be achieved. By using nanofluids, researchers have observed improvements in convective heat transfer due to the unique properties of nanoparticles. The presence of nanoparticles in the fluid alters its flow behavior, leading to enhanced heat transfer. The nanoparticles act as disruptors, breaking up the thermal boundary layer near the solid surface and promoting better heat transfer between the fluid and the surface.

To optimize convective heat transfer, researchers have explored various parameters, such as nanoparticle concentration, particle size, and flow velocity. By carefully tuning these parameters, it is possible to achieve significant improvements in heat transfer performance. Additionally, the use of advanced heat exchangers and fluid dynamics techniques can further enhance convective heat transfer in nanofluids.

Comparison of Various Nanofluids

Overview of Nanofluid Thermal Conductivity Dependence on Metallic Particle Properties

Nanofluids, which are colloidal suspensions of nanoparticles in a base fluid, have gained significant attention in recent years due to their potential for enhancing heat transfer in various applications. Metallic nanoparticles, such as copper, silver, and aluminum, are commonly used in nanofluids due to their high thermal conductivity and stability.

The thermal conductivity of nanofluids is influenced by several factors, including the properties of the metallic nanoparticles. The size, shape, and concentration of the nanoparticles play a crucial role in determining the thermal conductivity enhancement of the nanofluid.

Size: The size of the nanoparticles affects the thermal conductivity enhancement of the nanofluid. Smaller nanoparticles have a larger surface area-to-volume ratio, which promotes better heat transfer. As the particle size decreases, the phonon scattering at the nanoparticle-fluid interface increases, leading to enhanced thermal conductivity.

Shape: The shape of the nanoparticles also impacts the thermal conductivity of the nanofluid. Nanoparticles with a higher aspect ratio, such as nanorods or nanowires, exhibit better thermal conductivity enhancement compared to spherical nanoparticles. The elongated shape provides a larger contact area, facilitating efficient heat transfer.

Concentration: The concentration of metallic nanoparticles in the nanofluid affects the thermal conductivity enhancement. As the nanoparticle concentration increases, the interparticle interactions and clustering can occur, leading to a decrease in thermal conductivity. However, at lower concentrations, the nanoparticles disperse more uniformly, resulting in enhanced thermal conductivity.

Comparison of Different Nanofluids for Heat Transfer Enhancement

Numerous studies have been conducted to compare the heat transfer enhancement capabilities of different nanofluids. These studies have focused on various factors, including the type of nanoparticles, base fluid, and experimental conditions. Let’s take a look at some of the key findings:

1. Metallic Nanoparticles: Nanofluids containing metallic nanoparticles, such as copper, silver, and aluminum, have shown significant heat transfer enhancement compared to pure base fluids. The high thermal conductivity of these metallic nanoparticles facilitates efficient heat transfer, making them suitable for applications in heat exchangers and cooling systems.

2. Carbon-Based Nanoparticles: Carbon-based nanoparticles, such as graphene and carbon nanotubes, have also demonstrated excellent heat transfer enhancement properties. These nanoparticles have high thermal conductivity and unique structural properties, enabling efficient heat dissipation. However, challenges related to dispersion and stability need to be addressed for practical applications.

3. Oxide Nanoparticles: Nanofluids containing oxide nanoparticles, such as alumina and titania, have been extensively studied for heat transfer enhancement. These nanoparticles offer good stability and have the potential to enhance convective heat transfer. However, their lower thermal conductivity compared to metallic nanoparticles limits their overall heat transfer enhancement capabilities.

4. Hybrid Nanofluids: Hybrid nanofluids, which combine different types of nanoparticles, have also been investigated for heat transfer enhancement. These nanofluids aim to leverage the unique properties of multiple nanoparticles to achieve enhanced heat transfer performance. However, further research is needed to optimize the nanoparticle combination and concentration for maximum heat transfer enhancement.

Applications of Nanofluids in Heat Transfer

Nanofluids, which are suspensions of nanoparticles in a base fluid, have gained significant attention in recent years due to their remarkable thermal properties. These unique fluids have found numerous applications in various heat transfer systems, ranging from electronic cooling to solar thermal devices. Let’s explore some of the key applications of nanofluids in heat transfer.

Use of Nanofluids in Electronic Cooling

Electronic devices generate a substantial amount of heat during operation, which can lead to performance degradation and even failure if not properly managed. Nanofluids offer a promising solution for efficient electronic cooling. Two commonly used techniques for electronic cooling are the vapor chamber and jet impingement methods.

Vapor Chamber

Vapor chambers are heat pipes that utilize the evaporation and condensation of a working fluid to transfer heat. By incorporating nanofluids as the working fluid, the heat transfer performance can be significantly enhanced. The high thermal conductivity of nanoparticles improves the overall heat transfer rate, allowing for more efficient cooling of electronic components.

Jet Impingement

Jet impingement cooling involves directing a high-velocity fluid jet onto the surface of a heated object. Nanofluids can be employed in this process to enhance convective heat transfer. The presence of nanoparticles in the fluid increases the heat transfer coefficient, resulting in improved cooling efficiency. This makes nanofluids an excellent choice for cooling high-power electronic devices.

Application of Nanofluids in Radiators for Engine Cooling

Efficient cooling is crucial for the proper functioning of internal combustion engines. Traditional coolants, such as water or ethylene glycol, can be enhanced by adding nanoparticles to form nanofluids. These nanofluids exhibit superior thermal conductivity compared to conventional coolants, leading to improved heat dissipation from the engine.

By utilizing nanofluids in radiators, the heat transfer rate can be significantly increased. This translates to better engine performance, reduced fuel consumption, and lower emissions. Moreover, nanofluids offer enhanced stability and reduced corrosion, making them an attractive option for engine cooling applications.

Utilization of Nanofluids in Solar Thermal Devices

Solar thermal devices, such as parabolic solar collectors, harness the energy from the sun to generate heat. Nanofluids can play a vital role in enhancing the efficiency of these devices. By incorporating nanoparticles into the heat transfer fluid, the thermal conductivity is improved, resulting in more effective heat absorption and transfer.

The use of nanofluids in solar thermal devices allows for higher operating temperatures and increased energy conversion efficiency. This, in turn, leads to improved performance and reduced costs in solar power generation. Nanofluids have the potential to revolutionize the field of solar energy by maximizing the utilization of available sunlight.

Nanofluid Application in Transformer Cooling

Transformers are essential components in electrical power systems, and efficient cooling is crucial to ensure their reliable operation. Nanofluids offer a promising solution for transformer cooling due to their excellent thermal properties. By using nanofluids as the cooling medium, the heat transfer rate can be significantly enhanced.

Nanofluids provide improved thermal conductivity and heat transfer coefficients compared to traditional cooling fluids. This allows for more efficient heat dissipation from the transformer, reducing the risk of overheating and extending its lifespan. The application of nanofluids in transformer cooling systems can lead to enhanced reliability and reduced maintenance costs.

Other Applications of Nanofluids in Cooling and Heat Transfer Systems

In addition to the aforementioned applications, nanofluids have found use in various other cooling and heat transfer systems. Some notable examples include:

• Heat exchangers: Nanofluids can be employed in heat exchangers to enhance heat transfer efficiency and reduce energy consumption.
• Fluid dynamics: Nanofluids have been studied extensively to understand their flow behavior and optimize their performance in different applications.
• Nanotechnology: The field of nanotechnology has benefited greatly from the development of nanofluids, as they offer unique opportunities for heat transfer enhancement at the nanoscale.
• Nanofluid synthesis: Researchers continue to explore new methods for synthesizing nanofluids with improved stability and enhanced thermal properties.
• Nanofluid properties: The study of nanofluid properties, such as viscosity, density, and thermal conductivity, plays a crucial role in optimizing their performance in various heat transfer systems.

Feasibility and Future Scope of Nanofluids

Nanofluids, a suspension of nanoparticles in a base fluid, have gained significant attention in recent years due to their potential for enhancing heat transfer in various applications. In this section, we will explore the feasibility of nanofluids as thermal fluids, discuss their importance in increasing equipment efficiency, and highlight the future prospects and research opportunities in this exciting field.

Feasibility of Nanofluids as Thermal Fluids

Nanofluids offer several advantages over traditional heat transfer fluids. The addition of nanoparticles to the base fluid enhances its thermal conductivity, which is crucial for efficient heat transfer. The high surface area-to-volume ratio of nanoparticles allows for better heat dissipation, leading to improved thermal performance.

Moreover, nanofluids exhibit unique properties at the nanoscale, such as enhanced convective heat transfer and altered fluid dynamics. These properties make them suitable for a wide range of applications, including heat exchangers, cooling systems, and thermal management in electronic devices.

To ensure the feasibility of nanofluids, researchers have focused on studying their stability, flow characteristics, and thermal properties. Stability is a critical factor as nanoparticles tend to agglomerate, affecting the overall performance of the nanofluid. By employing suitable surfactants and dispersants, scientists have made significant progress in stabilizing nanofluids and preventing particle aggregation.

Importance of Nanofluids in Increasing Equipment Efficiency

The use of nanofluids can significantly enhance the efficiency of various equipment and systems. By improving heat transfer, nanofluids can reduce the energy consumption of heat exchangers, leading to cost savings and environmental benefits. The enhanced heat transfer coefficient and heat transfer rate of nanofluids ensure that heat is efficiently transferred between the solid surface and the fluid.

Additionally, the unique properties of nanofluids, such as their ability to alter fluid dynamics, enable the design of more compact and efficient heat exchangers. This, in turn, leads to space savings and increased performance in a wide range of applications, including automotive cooling systems, power plants, and electronic devices.

Future Prospects and Research Opportunities in Nanofluids

The field of nanofluids holds immense potential for future advancements and research opportunities. As nanotechnology continues to evolve, researchers are exploring novel nanomaterials and nanoparticles that can further enhance the thermal properties of nanofluids. By tailoring the size, shape, and composition of nanoparticles, scientists can optimize their heat transfer capabilities for specific applications.

Moreover, understanding the underlying heat transfer mechanisms in nanofluids is crucial for their successful implementation. Ongoing research aims to elucidate the fundamental mechanisms responsible for the enhanced heat transfer observed in nanofluids. This knowledge will enable the development of predictive models and simulations, facilitating the design and optimization of nanofluid-based systems.

Furthermore, the application of nanofluids extends beyond heat transfer enhancement. Researchers are exploring the use of nanofluids in areas such as energy storage, solar thermal systems, and biomedical applications. The versatility of nanofluids opens up new avenues for innovation and cross-disciplinary collaborations.

Frequently Asked Questions

1. How does nano heat transfer differ from traditional heat transfer?

Nano heat transfer refers to the study and application of heat transfer at the nanoscale, involving the transfer of heat between objects or systems at the nanometer level. Traditional heat transfer, on the other hand, deals with heat transfer at macroscopic scales. Nano heat transfer takes into account unique phenomena and properties that arise at the nanoscale, such as quantum effects and surface interactions.

2. What is heat transfer enhancement using nanofluids?

Heat transfer enhancement using nanofluids involves the incorporation of nanoparticles into conventional heat transfer fluids to improve their thermal properties. By adding nanoparticles, such as metal or oxide particles, to the base fluid, the thermal conductivity and convective heat transfer characteristics of the fluid can be enhanced, leading to improved heat transfer rates in various applications.

3. How can heat transfer be increased using nanofluids?

Heat transfer can be increased using nanofluids by exploiting the enhanced thermal conductivity and convective heat transfer properties of the nanoparticles suspended in the fluid. The nanoparticles facilitate better heat transfer by increasing the effective thermal conductivity of the fluid and promoting convective heat transfer through improved fluid dynamics. This results in higher heat transfer rates compared to conventional fluids.

4. What are the techniques for heat transfer enhancement using nanofluids?

There are several techniques for heat transfer enhancement using nanofluids, including altering the nanoparticle concentration, controlling the particle size and shape, optimizing the fluid flow conditions, and utilizing surface modifications to enhance the interaction between the nanoparticles and the fluid. These techniques aim to maximize the thermal properties and convective heat transfer characteristics of the nanofluid, leading to improved heat transfer rates.

5. How does nanotechnology contribute to heat transfer enhancement?

Nanotechnology plays a crucial role in heat transfer enhancement by enabling the synthesis and manipulation of nanomaterials and nanoparticles with unique thermal properties. Through nanotechnology, researchers can design and engineer nanofluids with enhanced thermal conductivity and convective heat transfer characteristics, thereby improving heat transfer rates in various applications, such as heat exchangers and thermal management systems.

6. What is the role of nanofluid flow in heat transfer enhancement?

Nanofluid flow plays a significant role in heat transfer enhancement as it affects the convective heat transfer characteristics of the fluid. By optimizing the flow conditions, such as flow rate, velocity, and turbulence, the interaction between the nanoparticles and the fluid can be maximized, leading to improved heat transfer rates. Proper understanding and control of nanofluid flow dynamics are essential for effective heat transfer enhancement.

7. How does nanofluid stability impact heat transfer enhancement?

Nanofluid stability is crucial for heat transfer enhancement as it ensures the uniform dispersion and suspension of nanoparticles in the base fluid. Stable nanofluids prevent particle agglomeration and sedimentation, which can hinder the convective heat transfer process. By maintaining nanofluid stability, the nanoparticles can effectively enhance the thermal conductivity and convective heat transfer properties of the fluid, leading to improved heat transfer rates.

8. What are the heat transfer mechanisms in nanofluids?

The heat transfer mechanisms in nanofluids involve three main processes: conduction, convection, and radiation. Conduction refers to the transfer of heat through direct particle-to-particle contact, while convection involves the transfer of heat through the movement of the nanofluid. Radiation, on the other hand, occurs when heat is transferred through electromagnetic waves. The combination of these mechanisms contributes to the overall heat transfer enhancement in nanofluids.

9. What are the applications of nanofluids in heat transfer?

Nanofluids find various applications in heat transfer, including heat exchangers, electronics cooling, solar thermal systems, and automotive cooling systems. The enhanced thermal properties and convective heat transfer characteristics of nanofluids make them suitable for improving heat transfer rates in these applications. Nanofluids offer potential benefits in terms of increased energy efficiency and improved thermal management.

10. How are nanofluids synthesized for heat transfer enhancement?

Nanofluids can be synthesized through various methods, including one-step and two-step processes. One-step synthesis involves directly dispersing nanoparticles into the base fluid, while two-step synthesis involves the separate synthesis of nanoparticles followed by their dispersion into the fluid. The choice of synthesis method depends on factors such as nanoparticle material, desired concentration, and stability requirements.

Following contents are explained in this articles:

• Nanofluid definition | what is nanofluid?
• What is base fluid?
• How do you make a Nanofluid?
• What is hybrid nanofluid?
• Uses of nanofluid | applications of nanofluid
• Types of nanofluid & Its Poperties

Nanofluid definition | What is nanofluid?

Nanofluid is fluid that consists of a base fluid with nanosized particles (1–100nm) suspended in it. Nano particles used in this type of studies are made of a metal or metal oxide, increase conduction and convection, allowing for more heat transfer. In the past few years, high-speed advancement in nanotechnology has made emerging of new generation coolants called nanofluid.

Let’s take example, check figure below. The CuO (metal oxide) nanoparticles are added to make nanofluid with a volume fraction of 0.25% CuO. The nanoparticle is dispersed in distilled water (base fluid). The surfactant sodium dodecyl sulfate (SDS) is added to the nanofluid for the stability of nanoparticles.

What is base fluid?

The nanoparticles are suspended in some ordinary liquid coolant like distilled water, ethylene glycol, oil, refrigerants, etc. This widely used ordinary coolant is known as base fluid.

You might have noticed while mechanic changing or pouring coolant in your car radiator. Do you remember its color? Yes, it’s green. That green colored fluid (coolant) is ethylene glycol.

Let’s know about base fluid oil. You might have noticed mechanic changing oil from your car or bike. It is lubrication and transmission system oil. This type of oil can be base fluid for nanofluid preparation.

How do you make a Nanofluid?

                The preparation of nanofluid can be possible by following two widely used methods. It is prepared by dispersing nanoparticles in base fluid with a magnetic stirrer and sonicator, as shown in figure “Preparation of nanofluid : Sonicator”.

                There are two types of stirrer used to disperse particles into basefluid, one is the magnetic and another is mechanical. The another lab instrument called ultrasonic sonicator is also required for proper dispersion.

Two-step method

The two-step procedure is the most widely used method for preparing nanofluid. The chemical and physical peocesses are used to produce dry powder of nanoparticles.

The powder of particles is added into the base fluid. The second step could be intensive magnetic force agitation or ultrasonic agitation. The two-step procedure is the economic procedure to produce nanofluid on  bulk because the nano fluid requirements are raising with new applications.

Use of surfactant in nanofluid

The nanoparticles have large surface area and surface activity which lead to aggregate. The use of surfactant is convenient method to get good stability. However, the surfactants’ functionality under high temperatures is also a big issue, especially for high-temperature applications.

One-step method

Eastman suggested a one-step method of vapor condensation. It is used prepare Cu/ethylene glycol (EG) nanofluid to limit the agglomeration of nanoparticles.

The use of one-step preparation method avoid spreading the particles in the fluid. There are some function not needed in this method. This method eliminates drying of particles, storage of material, and spreading. Agglomeration is limited in one -step method. it also increases stability of nanofluid.

Vacuum method – SANSS

 (full form Submerged -arc -nanoparticle -synthesis- system)

It is one of the preparation method of nanofluid with good efficiency. Different dielectric fluid are used in this method

The shape of nanoparticles are like different different type. The procedure avoids the undesired particle aggregation reasonably well. There are some disadvantages of this method. There is some reactant remain present in nanofluid.

What is a hybrid nanofluid?

A hybrid material is a combination of physical and chemical properties of two or more materials. The two or more nanoparticles are dispersed in a base fluid to achieve desired properties for individual applications. The making of nanofluid with two or more similar or different nanoparticles is popular as hybrid nanofluid. The work on hybrid nanofluid is not extensively done.

There are many experimental studies on hybrid nanofluid is still left to be done. The generally used hybrid nanofluids are Al₂O₃/Cu, Al₂O₃/CNT, Cu/TiO₂, CNT/Fe₃O_4, etc.

The hybrid nanofluid is a new research area for thermal engineering researcher to obtain enhanced cooling system.

Usage of nanofluid

                Nanofluid can be utilized for various different applications. These uses not affecting energy transfer thoroughly, they may be reduce the basic need for conventional fuel, electrical energy, or gas. Let’s read some important application of nanofluids

Electronic devices cooling

               The research going on the electronics suggests that the use of nanofluid can perform superior heat transfer. The vapour chamber is utilizing nanofluid in it for better heat transfer.

Jacket-water fluid in electricity generator

               The management of machinery space is main problem in all automobile vehicle. The size of component (cooling) can be reduced only if we improve heat transfer performance of parts. The nanofluid is the one of the option to improve performance of part and develop compactness.

Solar energy – thermal energy system

                To absorb solar radiation, the working fluid is passes through solar thermal energy system. The energy absorbed by fluid is sent to heat exchanger for other purposes.The solar energy absorbed by working fluid is generally transferred to the heat exchanger for other applications.

Cooling oil in Transformer

                The transformer is power transmission electrical equipment. The generated heat in transformer is absorbed by oil. If we add nanoparticle in cooling oil. The performance of transformer can be improved.

Other usage of nanofluid in the field of heat transfer enhancement:

Refrigeration process

                The refrigeration process is working on different thermodynamic cycles.  The working fluid in this process is refrigerant. The thermal properties of some refrigerant can be improved by use of nanoparticle.

Cooling system of nuclear energy

                The huge amount of heat is produced in the nuclear fission. It is required to arrange proper cooling to system. The nano fluid is advance fluid which can be utilized in nuclear cooling system.

Types of nanofluid

The types of nanofluid are dependent on the use of different types of nanoparticles and base fluids. There are three types of nanoparticles, like pure metal, metal oxide, and carbide-based nanoparticles. These particles are dispersed in various choices of base fluids like water, water/ethylene glycol, oil, ethylene glycol, etc.

Pure Metal	Metal oxides	Carbide
Al	Al2O3	Diamond
Cu	CuO	Graphite
Fe	Fe2O3, Fe3O4	Single wall nanotube
Ag	Ag2O	Multiwall nanotubes
Zn	ZnO
Ti	TiO2

Properties of nanofluid

Thermal conductivity is one of the vital property related to heat transfer for nanofluid. It is high thermal conductivity compared to standard cooling liquid, it is an essential characteristic for many applications. Use of copper nanoparticles with ethylene glycol results in an increase in thermal conductivity by 40% compared to the base fluid.

All processes indicates that thermal conductivity basic for proper cooling system in any devices. In the cooling system, a large surface area and high thermal conductivity are attributed to this heat transfer improvement.

The ratio of surface area and volume is main criteria for thermal conductivity improvement. This ration can be increased by using small size nanoparticles. The thermal conductivity is raised by using higher concentration of the particles.

The properties like density, viscosity, specific heat, thermal conductivity are well known for base fluid. The properties of nanofluid can be calculated theoretically by correlations suggested by various researchers. These properties also can be measured with multiple instruments experimentally in the lab.

The density of nanofluid can be calculated using correlation as  

Where ρ_pand ρ_bfare the nanoparticles’ densities and base fluid, respectively, and фis the volume concentration (% w/w) of nanoparticles dispersed in the base fluid. As per the idea of the strong fluid combination, the specific heat of nanofluid is given by the accompanying:

Where cp_pand cp_bf, are the specific heat of the nanoparticles and base fluid, respectively. The viscosity of nanofluid can be obtained from the following equation:

Credit Einstein 1906

 a is constant in viscosity equation and its  value is 14.4150 to  calculate viscosity. This formula is basically given for Brownian motion of particle in fluid. One well-known formula for computing the thermal conductivity of nanofluid is the Kang model which is expressed in the following form :

Credit Hamilton and Crosser (1962)

Question and Answers

What is nanofluid?

It is an advance fluid. It is prepared by dispersing nanoparticles in the base fluid.

What is base fluid?

 The base fluid is conventional coolant liquid. It is used to prepare nanofluid.

Give the examples of some commonly used nanoparticles to prepare nanofluid.

The commonly used nanoparticles are Copper (Cu), Aluminium (Al), Iron (Fe), Aluminium Oxide (Al₂O₃), Copper Oxide (CuO)_, Titanium Oxide (TiO₂ ) etc.

What are widely used preparation methods of nanofluid?

There are two methods widely used mentioned as below:

1. Two-step method
2. One-step method

What is the stability of nanofluid?

The stability can be stated as how long the particle keep dispersed in the base fluid. Technically, The higher stable nanofluid is one who has less sedimentation.

What is the use of surfactant in preparation of nanofluid?

The surfactant is used in nanofluid to increase its stability. The commonly used surfactant is sodium dodecyl sulfate (SDS).

Why hybrid nanofluid became a new research topic?

The individual application needs the desired properties of the material. To get likely properties in nanofluid, more than one nanoparticles are added in the base fluid.

Why the use of nanofluid results enhanced heat transfer?

The nanofluid is an advanced fluid with a higher thermal conductivity as the nanosized particles provide more surface area to conduct heat transfer.

How can nanofluid reduce the size of the heat exchanger?

The convention coolant used in heat exchanger shows less heat transfer as compared to nanofluid. The use of nanofluid requires proportionally less sized heat exchanger as compared to the conventional coolant.

Conclusion

                This article is about basic introduction of nanofluid, preparation of nanofluid, application of nanofluid and properties of nanofluid. Recently, it is advance coolant in heat transfer applications. The scope of nanofluid is vast in present nanotechnology world. The nanofluid and its applications can be a good topic for students and researcher for project work.

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More topic related to Nanofluid and heat transfer, please click here

There are two types of body: rigid body and deformable-body. Distance between any two points remains constant with force applied on a body is known as a rigid body and the body in which this distance change is known as a deformable body. Strength of material is the study of deformable bodies.  In this, we study the different properties of materials by applying force on it. Study of the strength of materials helps to select material for different applications according to their properties. Strength of Material is also referred as Mechanics of Material. Strength of Material includes stress, strain, stress-strain curve etc.

Engineering Stress

• Instantaneous load or force applied per unit original area of cross-section (Before any deformation) is known as engineering stress.
•  It is denoted by σ (sigma). SI unit of engineering stress is N/m² or Pascal (Pa).

Engineering Stress= (Force Applied)/ (Original Area)

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Classification of Stress

Generally following engineering stresses are classified in strength of materials studies.

Normal Stress

• When the applied force is perpendicular to the given cross-section of the specimen (axial load), then the corresponding stress produced in the material is known as normal stress.
•  Many times force applied on the surface is not uniform; in that case, we take an average of the applied force.

Normal Stress= (Perpendicular component of Applied Force)/ Area

Tensile Stress

When the applied force is away from the material, then the Stress produced is known as tensile stress.

Compressive Stress

When the applied force is in towards the object, then the Stress produced is known as compression stress.

Bending Stress

• When force is applied on the beam-shaped material, the material’s top surface undergoes a compressive type of stress, and the bottom surface undergoes tension-type of Stress and middle of the beam remains neutral. Such stress is known as bending Stress.
•  It is also known as flexural Stress.

Shear Stress

When the applied force is parallel to the area on which it is applied, the Stress is known as shear stress.

Shear Stress Formula

Shear Stress= (Force imposed parallel to the upper and lower faces) / Area.

Tensile Stress vs Shear Stress

Tensile Stress	Shear Stress
The applied force is perpendicular to the surface.	The applied force is parallel to the surface.
It is denoted by σ.	It is denoted by τ.

Combined Stress Equation

While studying strength of materials in real-life examples, we can have cases in which more than one type of Stress is acting on the material, in that case, we need to have an equation which can combine different type of stresses

Following is the equation which combines shear and tensile stresses.

Where,

f_x= tensile or compressive stress in the x-direction

f_y= tensile or compressive stress in the y-direction

f_s= shear stresses acting on the faces in x and y-direction

f₁= maximum principle Stress

f₂= minimum tensile Stress

q= maximum shear stress

Stress Concentration Factor

• In the studies of Strength of Materials, many times the material on which we are applying Stress is not uniform. It may have some irregularities in its geometry or within the structure formed due to nicks, scratches holes, fillets, grooves, etc., which causes the concentration of stress to be very high at some point on the material known as stress concentration or stress riser/raiser.
• The degree of this concentration is expressed as the ratio of maximum Stress to reference Stress, where reference stress is total Stress within an element under the same loading conditions, without any concentration or discontinuity.

Stress Concentration Factor Formula:

Stress Concentration= maximum Stress / Reference Stress

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Factor of Safety

• While studying strength of Materials, there are always some uncertainties in the measured values of stresses; therefore, the stress that we are going to consider for our use known as working stress (σ_w) is always less than the experimental value of stress. In most of the applications, we consider yield strength (σ_y).
• Working Stress is determined by reducing the yield strength by a factor; that factor is known as the factor of safety. So, the factor of safety is a ratio of yield strength to working stress. Its symbol is N. It is a unitless quantity.

            Factor of Safety= Yield Strength/ Working Stress

Engineering Strain

• Change in length at some instant of the material per unit original length (Before any application of force) is known as engineering strain.
•  It is denoted by ε (Epsilon) or γ (Gamma). It’s a unitless quantity.

              Engineering Strain= (Change in length)/ (Original Length)

Poisson’s Ratio

• When tensile stress is applied to the material, there is elongation along the applied load axis and shortening along with perpendicular directions to the applied Stress. Thus, the strain produced in the applied stress direction is known as axial strain and the strain produced in the perpendicular direction the applied Stress is known as lateral strain or transverse strain.
• The ratioof the lateral strain and axial strain is known as Poisson’s Ratio. It is denoted by ʋ (nu). It is a very important constant for a given material.

            Poisson’s Ratio= – (Lateral Strain/ Axial Strain)

Let the applied load is in z-direction and strain produced in that direction is ε_x  and  material is isotropic and homogeneous ( ) then Poisson’s ratio is

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Stress-Strain Curve

• Plotting of stress to strain gives a considerable number of properties of the material in strength of materials study.
• The stress-strain curve is stress versus strain curve in which strain is on independent axis i.e., x-axis and stress is on dependent i.e. y-axis. It is an important characteristic of the material.
• On the load application, two types of deformation occur in the material depending upon the strain value, first is elastic deformation and second is plastic deformation.

True Stress-Strain Curve

It is a stress-strain curve in which true Stress is plotted against true strain. Both Stress and strain are based on instantaneous measurement. Hence, the instantaneous cross-section area is considered instead of original cross-section, and instantaneous length is considered instead of the original length.

Elastic Deformation

• Elastic deformation is the deformation in which material regains its original shape on the removal of the force.
• This region has a proportional limit, elastic limit, upper yield point and lower yield point.

Modulus of Elasticity | Hooke’s Law

• When this type of deformation occurs, the strain in the metal piece is nearly proportional to the stress; therefore, this deformation occurs as a straight line in Stress versus strain plot except for some materials like grey cast iron, concrete and many polymers.
• Stress is proportional to the strain through this relationship.

• This is known as Hooke’s Law, where Y the proportionality constant is known as Young’s Modulus or Modulus of Elasticity. It is also denoted by E. It is the slope of the stress-strain curve in the elastic limit. It is one of the most important law in the studies of strength of material.

Modulus of Elasticity Formula

Its value is slightly higher for ceramics than metals and value is slightly lower for polymers than metals. Or most structures are required to have deformation only in the elastic limit; therefore, this region is quite important.

Plastic Deformation

• If the applied force is removed in this region, then the material does not regain its original shape.
• The deformation in the material is permanent.
• In this region, Hooke’s law is not valid.
• This region has ultimate tensile strength of materials and breaking point.

• There are some points on the curve around which type of deformation changes. These points are very important as they tell us about the limitations and ranges of material which are ultimately useful in material’s application.

Proportional Limit

• It is the point in the curve up to which Stress is proportional to the strain.
• When the material is stretched beyond the proportionality limit, stress is not proportional to the strain, but still, it shows elastic behaviour.

Elastic Limit

• It is the point in the curve up to which material shows elastic behaviour.
• After this point, plastic deformation in the material begins.
• Beyond the elastic limit, Stress causes the material to flow or yield.

Yield Point

It is the point where yielding of the material occurs; hence plastic deformation of material begins from this point.

What is Yield Strength?

• Stress corresponding to the yield point is known as yield strength—its resistance to its plastic deformation.
• Many times it is not possible to locate it precisely. The elastic-plastic transition is well-defined and very abruptly, termed as yield point phenomenon.

• Upper Yield Point: It is the point in the graph at which maximum load or Stress required to initiate the plastic deformation of the material.

• Lower Yield Point: It is a point at which minimum Stress or load is required to maintain the material’s plastic behavior.

• The upper yield point is unstable, but lower yield point is stable, so we use a lower yield point while designing the components.

Ultimate Strength Definition | Ultimate Stress Definition

• After yielding, as plastic deformation continues, it reaches a maximum limit known as ultimate Stress or ultimate strength.
• It is also known as Ultimate Tensile Strength (UTS) or tensile strength. It is the maximum stress that can be sustained by material in tension.
• All deformation up to this point is uniform, but at this maximum stress, small narrowing of material begins to form, this phenomenon is termed as ‘necking’.

Rupture Point | Fracture Point | Breaking Point

• Stress necessary to continue plastic deformation starts to decrease after ultimate strength and eventually breaks the material at a point known as rupture point or fracture point.
• The stress of the material at rupture point is known as ‘rupture strength’.

Stress-Strain curve for Brittle material

Stress-Strain Curve for Ductile Material

 Ref. – Stress-Strain

Important Questions and Answer related to Strength of Materials

What is engineering stress?

Instantaneous load or force applied per unit original area of cross-section (Before any application of force) is known as engineering stress.

It is denoted by σ (sigma). SI unit of engineering stress is N/m2 or Pascal (Pa).

What is Engineering Strain?

Change in length at some instant of the material per unit original length (Before any application of force) is known as engineering strain.

It is denoted by ε (Epsilon) or γ (Gamma). It’s a unitless quantity.

What is Tensile Stress?

When the applied force is away from the material, then the Stress produced is known as tensile stress.

What is Compressive Stress?

When the applied force is in towards the object, then the Stress produced is known as compressive stress.

What is Shear Stress?

When the applied force is parallel to the area on which it is applied, the Stress is known as shear stress.

What is Factor of Safety?

There are always some uncertainties in the measured values of stresses; therefore, the stress that we are going to consider for our use known as working Stress (σw) is always less than the experimental value of Stress. In most of the applications, we consider yield strength (σy).

Working Stress is determined by reducing the yield strength by a factor; that factor is known as the factor of safety. So, the factor of safety is a ratio of yield strength to working stress. Its symbol is N. It is a unitless quantity.

What is True Stress-Strain Curve?

It is a stress-strain curve in which true Stress is plotted against true strain. Both Stress and strain are based on instantaneous measurement hence instantaneous area of the cross-section is considered instead of original cross-section and instantaneous length is considered instead of the original length.

What is Breaking Point?

Stress necessary to continue plastic deformation starts to decrease after ultimate strength and eventually breaks the material at a point known as breaking point.

What is Ultimate Tensile Strength?

After yielding, as plastic deformation continues, it reaches a maximum limit known as ultimate Stress or ultimate strength, it is also known as Ultimate Tensile Strength (UTS)

What is Hooke’s Law? | Explain Hooke’s Law

When this type of deformation occurs, the strain in the metal piece is nearly proportional to the stress; therefore, this deformation occurs as a straight line in Stress versus strain plot except for some materials like grey cast iron, concrete and many polymers. Stress is proportional to the strain through this relationship.

This is known as Hooke’s Law, where Y the proportionality constant is known as Young’s Modulus.

It is one of the most important law in the studies of Strength of Materials.

CONCLUSION

In this articles important terminology of strength of materials are explained in detailed such as engineering stress, strain, stress-strain curve for both ductile and brittle materials, young modulus, Poisson’s ratio etc. Strength of materials is also known as mechanics of materials.

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