THE IMPORTANCE OF MANUFACTURING ENGINEERING

If we carefully think about human civilization, one shall notice an wonderful fact about human beings. The thing that made us different from other hominids is the skill to manufacture tools. We just triumphed due to our ability to make primitive tools out of stone and metals during the dawn of the civilizations. Since then much time has passed and we have entered into a Machine Era and man has been still continuously engaged in converting the natural resources into useful products by adding value to them through machining and other engineering activities applying on the raw materials. Manufacturing is the sub branch of Engineering which involves the conversion of raw materials into finished products.

The conversion of natural resources into raw materials is normally taken care of by two sub branches of engineering viz. Mining and Metallurgy Engineering. The value addition to the raw materials by shaping and transforming it to final products generally involves several distinct processes like castings, forming, forging, machining, joining, assembling and finishing to obtain a completely finished product.

Understanding Manufacturing Engineering largely based upon three engineering activities and they are Designing,  Production and Development of new more efficient techniques.

At the Design stage, engineering design mainly concentrates on the optimization of engineering activities to achieve most economical way to manufacture a goods from raw materials. It also chooses the raw materials and impart the requisite engineering properties of materials like hardness, strength, elasticity, toughness by applying various heat treatment to them.

During the production stages, the selection of the important process parameters to minimize the idle time and cost, and maximizing the production and its quality is very important.

The New Technologies must be implemented to adapt to the changing scenarios of the markets and demands to make the sales competitive and sustainable.

QUESTIONS BANK 5 : FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

 

QUESTIONS BANK 4 : FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

QUESTIONS BANK 3 : FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

 

QUESTIONS BANK 2: FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

1)      Explain the principle of Super-position.

Ans: The principle of superposition states that “The effect of a force on a body does not change and remains same if we add or subtract any system which is in equilibrium.”

In the fig 4 a, a force P is applied at point A in a beam, where as in the fig 4 b, force P is applied at point A and a force system in equilibrium which is added at point B. Principle of super position says that both will produce the same effect.

2)      What is “Force-Couple system?”

Ans: When a force is required to transfer from a point A to point B, we can transfer the force directly without changing its magnitude and direction but along with the moment of force about point B.

As a result of parallel transfer a system is obtained which is always a combination of a force and a moment or couple. This system consists of a force and a couple at a point is known as Force-Couple system.

      In fig 5 a, a force P acts on a bar at point A, now at point B we introduce a system of forces  in equilibrium (fig 5 b), hence according to principle of superposition there is no change in effect of the original system. Now we can reduce the downward force P at point A and upward force P at point B as a couple of magnitude Pxd at point B (fig 5 c).

3) What do you understand by Equivalent force systems?

Ans: Two different force systems will be equivalent if they can be reduced to the same force-couple system at a given point. So, we can say that two force systems acting on the same rigid body will be equivalent if the sums of forces or resultant and sums of the moments about a point are equal.

4)      What is orthogonal or perpendicular resolution of a force?

Ans: The resolution of a force into two components which are mutually perpendicular to each other along X-axis and Y-axis is called orthogonal resolution of a force.

If a force F acts on an object at an angle θ with the positive X-axis, then its component along X-axis is F_x = Fcosθ, and that along Y-axis is F_y = Fsinθ

5) What is oblique or non-perpendicular resolution of a force?

Ans: When a force is required to be resolved in to two directions which are not perpendiculars to each other the resolution is called oblique or Non-perpendicular resolution of a force.

   
       F_OA = (P sin β)/ sin (α +β)

 F_OB = (P sin α)/ sin (α +β)

QUESTION BANK 1: FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

QUESTION BANK: ENGINEERING MECHANICS

by Er. Subhankar Karmakar

Unit: 1 (Force System)

VERY SHORT QUESTIONS (2 marks):

1)      What is force and force system?

Ans: A force is a physical quantity having magnitude as well as direction. Therefore, it is a   vector quantity. It is defined as an "external agency" which produces or tends to produce or destroys or tends to destroy the motion when applied on a body.

Its unit is Newton (N) in S.I. systems and dyne in C.G.S. system.

When two or more forces act on a body or particle, it is called force system. Therefore, a force system is a collection of two or more forces.

2)      What is static equilibrium? What are the different types of static equilibrium?

Ans: A body is said to be in static equilibrium when there is no change in position as well as no rotation exist on the body. So to be in equilibrium process, there must not be any kind of motions ie there must not be any kind of translational motion as well as rotational motion.

We also know that to have a linear translational motion we need a net force acting on the object towards the direction of motion, again to induce an any kind of rotational motion, a net moment must exists acting on the body. Further it can be said that any kind of complex motion can be resolved into a translational motion coupled with a rotating motion.

“Therefore a body subjected to a force system would be at rest if and only if the net force as well as the net moment on the body is zero.”

There are three types of Static Equilibrium

1.      Stable Equilibrium

2.      Unstable Equilibrium

3.      Neutral Equilibrium

3)      What are the characteristics of a force?

Ans: A force has four (4) basic characteristics.

·         Magnitude: It is the value of the force. It is represented by the length of the arrow that we use to represent a force.

·         Direction: A force always acts along a line, which is called as the “line of action”. The arrow head we used to represent a force is the direction of that force.

·         Nature or Sense: The arrow head also represent the nature of a force. A force may be a pull or a push. If a force acts towards a particle it will be a push and if the force acts away from a point it is pull.

·         Point of Application: It is the original location of a point on a body where the force is acting. 

4)      What are the effects of a force acting on a body?

Whenever a force acts on a body or particle, it may produce some external as well as internal effects or changes.

·         A force may change the state or position of a body by inducing motion of the body. (External effect)

·         A force may change the size or shape of an object when applied on it. It may deform the body thus inducing internal effects on the body.

·         A force may induce rotational motion into a body when applied at a point other than its center of gravity.

·         A force can make a moving body into an equilibrium state at rest.

5)      What is composition and resolution of forces?

Ans: Composition of forces: Composition or compounding is the procedure to find out single resultant force of a force system

Resolution of forces: Resolution is the procedure of splitting up a single force into number of components without changing the effect of the same.

6)      What is Resultant and Equilibrant?

Ans: Resultant: The resultant of a force system is the Force which produces same effect as the combined forces of the force system would do. So if we replace all components of the force by the resultant force, then there will be no change in effect.

The Resultant of a force system is a vector addition of all the components of the force system. The magnitude as well as direction of a resultant can be measured through analytical method.

Equilibrant: Any concurrent set of forces, not in equilibrium, can be put into a state of equilibrium by a single force. This force is called the Equilibrant. It is equal in magnitude, opposite in sense and co-linear with the resultant. When this force is added to the force system, the sum of all of the forces is equal to zero.

7)      Explain the principle of Transmissibility?

Ans: The principle of transmissibility states “the point of application of a force can be transmitted anywhere along the line of action, but within the body.”

The fig 3 a shows a force F acting at a point of application A and fig 3 b, the same force F acts along the same line of action but at a different point of action at B and both are equivalent to each other.

STRESS, STRAIN AND YOUNG'S MODULUS

STRESS:

When a material is subjected to an external force, it will either totally comply with that force and be pushed away, like a liquid or powder, or it will set up internal forces to oppose those applied from outside. Solid materials generally act rather like a spring – when stretched or compressed, the internal forces come into play, as is easily seen when the spring is released.

A material subjected to external forces that tend to stretch it is said to be in tension, whereas forces which squeeze the material put it in compression.

An important aspect is not so much the size of the force, as how much force is applied per unit of cross-sectional area. The term ‘stress’, symbol σ (Greek letter sigma), is used for the force per unit area, and has the units of pascals (Pa) with 1Pa being one newton per square metre.

Because the reference area is so large, it is normally necessary to use high multiples such as the megapascal (MPa = 10⁶ Pa) and gigapascal (GPa = 10⁹ Pa). However, when we bear in mind that, in electronics, the area over which forces are applied is generally very much smaller, it is useful to keep in mind that one MPa is equivalent to a force of 1 newton applied on a square millimetre of area.



STRAIN:

A material in tension or compression changes in length, and the change in length compared to the original length is referred to as the ‘strain’, symbol ε (Greek letter epsilon). Since strain is a ratio of two lengths it has no units and is frequently expressed as a percentage: a strain of 0.005 corresponds to a ½% change of the original length.



HOOKE'S LAW:

As you know from a spring, if you gradually stretch it, the force needed increases, but the material springs back to its original shape when the force is released. Materials which react in the same way as a spring are said to be ‘elastic’. Typically if we measure the extension of different forces and plot the graph of this, we will find that the extension is proportional to the force applied. Materials that obey Hooke’s Law exhibit a linear relationship between the strain and the applied stress (Figure 1).

Figure 1: Stress-strain graph for an elastic solid

Many metals follow Hooke’s Law until a certain level of stress has been applied, after which the material will distort more severely. The point at which straight line behaviour ceases is called the limit of proportionality: beyond this the material will not spring back to its original shape, and is said to exhibit some plastic behaviour (Figure 2). The stress at which the material starts to exhibit permanent deformation is called the elastic limit or yield point.

Figure 2: Stress-strain graph for a typical metal

 
As Figure 2 shows, if the stress is increased beyond the yield point the sample will eventually break. The term (ultimate) tensile strength is used for the maximum value of tensile stress that a material can withstand without breaking, and is calculated at the maximum tensile force divided by the original cross-sectional area.

Note that there may be substantial differences between the stress at the yield point and on breaking – for example, one source quotes the ‘ultimate tensile strength’ for AISI304 stainless steel as 505 MPa, and the ‘yield tensile strength’ as 215 MPa. For most engineering purposes, metals are regarded as having failed once they have yielded, and are normally loaded at well below the yield point.

With some materials, including mild steel, the stress/strain graph shows a noticeable dip beyond the elastic limit, where the strain (the effect of the load) increases without any need to increase the load. The material is said to have ‘yielded’, and the point at which this occurs is the yield point. Materials such as aluminium alloys on the other hand don’t show a noticeable yield point, and it is usual to specify a ‘proof’ test. As shown in Figure 3, the 0.2% proof strength is obtained by drawing a line parallel to the straight line part of the graph, but starting at a strain of 0.2%.

Figure 3: Stress-strain graph for an aluminium alloy

YOUNG'S MODULUS:

As you will appreciate from the shapes of Figure 2 and Figure 3, the slope of the stress/strain graph varies with stress, so we generally take only the slope of the initial straight-line portion. The stress/strain ratio is referred to as the modulus of elasticity or Young’s Modulus. The units are those of stress, since strain has no units. Engineering materials frequently have a modulus of the order of 10⁹Pa, which is usually expressed as GPa. 

CENTROID OF A COMPOSITE LINE

In the figure, a composite line A-B-C-D is made of three straight lines AB, BC, CD as shown in the figure. If the coordinate of point A is (5,5), find the centroid of the composite line.


Solution: At first, the composite line is divided into three parts.








Part -1 : The line AB : Let the centroid of the line be G₁(X₁,Y₁)

length, L₁ = 40 mm;                  


X₁ = 4 + (40*cos 60⁰)/2 = 14  
Y₁ = 4 + (40*sin 60⁰)/2 = 21.32








Part -2 : The line BC : Let the centroid of the line be G₂(X₂,Y₂)


length, L₂ = 15 mm; 


X₂ = 4 + (40*cos 60⁰) + 15/2 = 31.5 
Y₂ = 4 + (40*sin 60⁰) = 38.64




Part -3 : The line CD : Let the centroid of the line be G₃(X₃,Y₃)


length, L₃ = 20 mm; 

X₃ = 4 + (40*cos 60⁰) + 15 = 39 
Y₃ = 4 + (40*sin 60⁰) - 20/2 = 28.64



If the centroid of the composite line be G  (X_g,Y_g)

X_g = (∑L_iX_i)/(∑L_i) 

    = (L₁X₁ + L₂X₂ + L₃X₃)/(L₁ + L₂ + L₃)
    = (40 x 14 + 15 x 31.5 + 20 x 39)/(40 + 15 + 20) 
    = 24.17
     

Y_g = (∑L_iY_i)/(∑L_i) 

    = (L₁Y₁ + L₂Y₂ + L₃Y₃)/(L₁ + L₂ + L₃)
    = (40 x 21.32 + 15 x 38.64 + 20 x 28.64)/(40 + 15 + 20) 
    = 26.74

Mechanical Engineering Lecture Notes: IC Engines and Compressors

• IC ENGINES AND COMPRESSORS:

Internal Combustion Engines are the basis of human transportation and without them human civilization will come to halt. The main characteristics of an IC engines is its combustion chamber where fuel is burnt at elevated temperature and pressure to develop rotational kinetic energy.

IC engines, or internal combustion engines, are a type of heat engine that convert the heat generated by the combustion of fuel into mechanical energy. This mechanical energy is used to power a vehicle or machine. IC engines can be categorized into two types: spark ignition engines and compression ignition engines. In spark ignition engines, a spark is used to ignite the fuel-air mixture, while in compression ignition engines, the fuel-air mixture is compressed until it spontaneously ignites.

Compressors, on the other hand, are mechanical devices that are used to increase the pressure of a gas. They are commonly used in a variety of applications, such as in air conditioning and refrigeration systems, as well as in the compression of natural gas and other gases for transport or storage. There are several types of compressors, including positive displacement compressors and dynamic compressors. Positive displacement compressors work by trapping a fixed amount of gas and then compressing it, while dynamic compressors use a rotating impeller to increase the velocity of the gas and then convert that velocity into pressure.

While IC engines and compressors have some similarities in terms of their use of internal combustion, they are fundamentally different types of devices with different applications and operating principles.

Compressors are mechanical devices that are used to increase the pressure of a gas. There are several types of compressors, each with its own unique characteristics and applications. Here are some of the most common types of compressors and their functions:

• Types of Compressors and Functions:

Reciprocating compressors: This type of compressor uses a piston and cylinder to compress the gas. The piston moves back and forth within the cylinder, creating a vacuum that draws in the gas, which is then compressed as the piston moves back up.

Rotary screw compressors: These compressors use two interlocking screws to compress the gas. The screws rotate in opposite directions, drawing in the gas and compressing it as it moves through the screw threads.

Centrifugal compressors: Centrifugal compressors use a rotating impeller to increase the velocity of the gas, which is then converted into pressure by a diffuser. This type of compressor is commonly used in high-flow, low-pressure applications.

Axial compressors: Axial compressors use a series of rotating blades to compress the gas. The blades are arranged in a row, with each row of blades increasing the pressure of the gas as it moves through the compressor.

Scroll compressors: Scroll compressors use two interleaved spirals to compress the gas. One spiral remains stationary while the other moves in a circular motion, trapping and compressing the gas as it moves through the spirals.

The function of a compressor is to increase the pressure of a gas, which can then be used for a variety of purposes, such as powering tools and machinery, refrigeration, air conditioning, and gas transport and storage. Compressors are used in a wide range of industries, including manufacturing, healthcare, energy, and transportation.

• Reciprocating compressors: and its functions:

Reciprocating compressors are a type of positive displacement compressor that use a piston and cylinder to compress a gas. The piston moves back and forth within the cylinder, creating a vacuum that draws in the gas, which is then compressed as the piston moves back up. Reciprocating compressors are commonly used in applications where a high-pressure output is required, such as in natural gas processing, petroleum refining, and chemical processing.

The functions of reciprocating compressors include:

Compression of gas: The primary function of a reciprocating compressor is to compress a gas to a higher pressure, which can then be used for various industrial processes.

Gas transport: Reciprocating compressors can be used to transport gases through pipelines or other systems. The compressed gas can be moved over long distances without losing pressure, making it an efficient method of transport.

Storage: Compressed gas can be stored in tanks or other vessels for later use, and reciprocating compressors can be used to fill these storage containers.

Power generation: Reciprocating compressors can be used to generate power by compressing gas and then using that compressed gas to power a turbine or other type of engine.

Refrigeration: Reciprocating compressors can be used in refrigeration systems to compress refrigerant gases and remove heat from a space or product.

Overall, reciprocating compressors are a versatile type of compressor that can be used for a wide range of industrial applications where high-pressure gas output is required.

• Components of a reciprocating compressors:

A reciprocating compressor is a complex machine made up of several components that work together to compress a gas. The main components of a reciprocating compressor include:

Cylinder: The cylinder is the main body of the compressor where the piston moves back and forth to compress the gas.

Piston: The piston is a cylindrical component that moves back and forth within the cylinder to compress the gas. The piston is typically made of a metal alloy and is attached to a connecting rod.

Connecting rod: The connecting rod connects the piston to the crankshaft and converts the linear motion of the piston into rotational motion of the crankshaft.

Crankshaft: The crankshaft is a shaft that rotates to convert the linear motion of the connecting rod into rotational motion. The crankshaft is typically driven by an electric motor or a combustion engine.

Valves: The compressor has two sets of valves, intake and discharge, that control the flow of gas into and out of the cylinder. The intake valve opens to allow gas to enter the cylinder, and the discharge valve opens to allow compressed gas to exit the cylinder.

Crankcase: The crankcase is a compartment in the compressor that houses the crankshaft and connecting rods. It is typically filled with oil to lubricate the moving parts and reduce wear and tear.

Pressure relief valve: The pressure relief valve is a safety feature that opens when the pressure in the compressor exceeds a certain threshold. This prevents the compressor from being damaged or exploding due to excess pressure.

Overall, each component of a reciprocating compressor plays a critical role in the compressing process and must be designed and maintained to ensure reliable and efficient operation.

• Efficiency of a reciprocating compressor:

The efficiency of a reciprocating compressor is a measure of how effectively it can compress gas while consuming the least amount of energy. The efficiency of a reciprocating compressor can be affected by several factors, including the compressor design, operating conditions, and maintenance practices.

The following are some of the factors that can affect the efficiency of a reciprocating compressor:

Compression ratio: The compression ratio is the ratio of the discharge pressure to the suction pressure. The higher the compression ratio, the lower the compressor efficiency.

Clearance volume: The clearance volume is the volume of gas remaining in the cylinder after the piston has reached the end of its stroke. A larger clearance volume can decrease the efficiency of the compressor.

Gas properties: The physical properties of the gas being compressed, such as its molecular weight, specific heat ratio, and heat capacity, can affect the efficiency of the compressor.

Operating conditions: The operating conditions of the compressor, such as the suction and discharge pressures and temperatures, can also affect its efficiency.

Maintenance: Proper maintenance practices, such as keeping the compressor clean and lubricated, can help maintain its efficiency over time.

To improve the efficiency of a reciprocating compressor, it is important to properly size and design the compressor for the specific application and operating conditions. Proper maintenance practices, such as regular cleaning, lubrication, and inspection, can also help to maintain the efficiency of the compressor over time.

ENGINEERING. MECHANICS:

FORCE AND FORCE SYSTEM

Topic: FORCE SYSTEM

1) What is a FORCE SYSTEM? Classify them with examples and diagrams.

Ans: A force system may be defined as a system where more than one force act on the body. It means that whenever multiple forces act on a body, we term the forces as a force system. We can further classify force system into different sub-categories depending upon the nature of forces and the point of application of the forces.

Different types of force system:


(i) COPLANAR FORCES:

If two or more forces rest on a plane, then they are called coplanar forces. There are many ways in which forces can be manipulated. It is often easier to work with a large, complicated system of forces by reducing it an ever decreasing number of smaller problems. This is called the "resolution" of forces or force systems. This is one way to simplify what may otherwise seem to be an impossible system of forces acting on a body. Certain systems of forces are easier to resolve than others. Coplanar force systems have all the forces acting in in one plane. They may be concurrent, parallel, non-concurrent or non-parallel. All of these systems can be resolved by using graphic statics or algebra.


(ii) CONCURRENT FORCES:

A concurrent coplanar force system is a system of two or more forces whose lines of action ALL intersect at a common point. However, all of the individual vectors might not actually be in contact with the common point. These are the most simple force systems to resolve with any one of many graphical or algebraic options. If the line of actions of two or more forces passes through a certain point simultaneously then they are called concurrent forces. concurrent forces may or may not be coplanar.

(iii) LIKE FORCES:

A parallel coplanar force system consists of two or more forces whose lines of action are ALL parallel. This is commonly the situation when simple beams are analyzed under gravity loads. These can be solved graphically, but are combined most easily using algebraic methods. If the lines of action of two or more forces are parallel to each other, they are called parallel forces and if their directions are same, then they are called LIKE FORCES.

(iv) UNLIKE FORCES: If the parallel forces are such that their directions are opposite to each other, then they are termed as "UNLIKE FORCE".


(v) NON COPLANAR FORCES:
The last illustration is of a "non-concurrent and non-parallel system". This consists of a number of vectors that do not meet at a single point and none of them are parallel. These systems are essentially a jumble of forces and take considerable care to resolve.

_________________________________________________________________________________
N.B. Almost any system of known forces can be resolved into a single force called a resultant force or simply a Resultant. The resultant is a representative force which has the same effect on the body as the group of forces it replaces. (A couple is an exception to this) It, as one single force, can represent any number of forces and is very useful when resolving multiple groups of forces. One can progressively resolve pairs or small groups of forces into resultants. Then another resultant of the resultants can be found and so on until all of the forces have been combined into one force. This is one way to save time with the tedious "bookkeeping" involved with a large number of individual forces. Resultants can be determined both graphically and algebraically.The Parallelogram Method and the Triangle Method. It is important to note that for any given system of forces, there is only one resultant.


It is often convenient to decompose a single force into two distinct forces. These forces, when acting together, have the same external effect on a body as the original force. They are known as components. Finding the components of a force can be viewed as the converse of finding a resultant. There are an infinite number of components to any single force. And, the correct choice of the pair to represent a force depends upon the most convenient geometry. For simplicity, the most convenient is often the coordinate axis of a structure.


A force can be represented as a pair of components that correspond with the X and Y axis. These are known as the rectangular components of a force. Rectangular components can be thought of as the two sides of a right angle which are at ninety degrees to each other. The resultant of these components ...


is the hypotenuse of the triangle. The rectangular components for any force can be found with trigonometrical relationships: F_x = Fcosθ, Fy = Fsinθ. There are a few geometric relationships that seem to common in general building practice in North America. These relationships relate to roof pitches, stair pitches, and common slopes or relationships between truss members. Some of these are triangles with sides of ratios of 3-4-5, 1-2-sqrt3, 1-1-sqrt2, 5-12-13 or 8-15-17. Committing the first three to memory will simplify the determination of vector magnitudes when resolving more difficult problems.


When forces are being represented as vectors, it is important to should show a clear distinction between a resultant and its components. The resultant could be shown with color or as a dashed line and the components as solid lines, or vice versa. NEVER represent the resultant in the same graphic way as its components.


Any concurrent set of forces, not in equilibrium, can be put into a state of equilibrium by a single force. This force is called the Equilibrant. It is equal in magnitude, opposite in sense and co-linear with the resultant. When this force is added to the force system, the sum of all of the forces is equal to zero. A non-concurrent or a parallel force system can actually be in equilibrium with respect to all of the forces, but not be in equilibrium with respect to moments.
__________________________________________________________________________________


2) What is STATIC EQUILIBRIUM? 
    What are the conditions of static equilibrium for
            (i) concurrent force system
            (ii) coplanar non concurrent force system.

Ans: A body is said to be in equilibrium when there is no change in position as well as no rotation exist on the body. So to be in equilibrium process, there must not be any kind of motions ie there must not be any kind of translational motion as well as rotational motion.

We also know that to have a linear translational motion we need a net force acting on the object towards the direction of motion, again to induce an any kind of rotational motion, a net moment must exists acting on the body. Further it can be said that any kind of complex motion can be resolved into a translational motion coupled with a rotating motion.

Therefore a body subjected to a force system would be at rest if and only if the net force as well as the net moment on the body be zero. Therefore the general condition of any system to be in static equilibrium we have to satisfy two conditions

(i) Net force on the body must be zero ie, ΣF_i = 0;
(ii) Net moment on the body must be zero ie, ΣM_i = 0.

Now we can apply these general conditions to different types of Force System.

For concurrent force system total moment about the concurrent point is always zero as all the forces pass through the point, and we know the moment of a force passing through the point about which we shall take moment is always zero. Hence, the conditions of equilibrium for concurrent forces will be  

Net force on the body must be zero ie, ΣF_i = 0; and we can resolve it along X axis and along Y axis, ie.  (i) ΣF_x = 0; and  (ii) ΣF_y = 0.

for coplanar non concurrent force system, the equilibrium conditions are

(i) ΣF_x = 0; and  (ii) ΣF_y = 0.  (iii)  ΣM_i = 0.

 Moment on a plane:

For a force system the total resultant moment about any arbitrary point due to the individual forces are equal to the moment produced by the resultant about the same point. Now if the system is at equilibrium condition, then the resultant force would be zero. Hence, the moment produced by the resultant about any arbitrary point is zero. In case of coplanar & concurrent force system, as the forces are concurrent ie. each of the force passes through a common point. Hence, about that common point total moment of all the forces will be zero.

3) What are different types of joint? discuss them in details.

Answer: The Concepts of Joints. In Engineering terminology any force carrying linear member is called as links. Links can be attached to each other by the fasteners or joints. Hence, we can say to prevent the relative motion between two links completely or partially we use fasteners or joints.



Basically there are three types of joints which we shall discuss and they are named as,
(i) pin/ hinged joints, 
(ii) roller joints and 
(iii) fixed joints.


PIN JOINTS:

They are classified according to the degrees of freedom of the links they would allow. Like a pin or hinge joint is consisted of two links joined by the insertion of a pin at the pivot hole. A pin joint doesn't allow a vertical or horizontal relative velocities between the two links.

For better understanding of the mechanism of pin joint we would like to make a simplest type of pin joints. Suppose we would take two links and make holes at one of the ends of each link. Now if we insert a bolt through the holes of both the links, then what we get is an example of pin/hinge joints.

A pin joint although restricts any kind of horizontal or vertical displacement but they can not restrict rotation about an axis passing through the hole, in clockwise or anti clockwise direction. Hence it provides two reactions one vertical and one horizontal to restrict any kind of movement along that direction.

ROLLER JOINTS: