STRATIFIED CHARGE INTERNAL COMBUSTION ENGINE

Internal combustion engines or popularly known as IC Engines are life line of human society which mostly served as a mobile, portable energy generator and extensively used in the transportation around the world. 

There are many types of IC Engines, but among them two types known as petrol or SI engines and diesel or CI engines are well established. Most of the automotive vehicles run on either of the engines. Despite their wide popularity and extensive uses, they are not fault free. 

Both SI Engines and CI Engines have their own demerits and limitations. 


Limitations of SI Engines (Petrol Engines) 

Although petrol engines have very good full load power characteristics, but they show very poor performances when run on part load. 

Petrol engines have high degree of air utilisation and high speed and flexibility but they can not be used for high compression ratio due to knocking and detonation. 

Limitations of CI or Diesel Engines: 

On the other hand, Diesel engines show very good part load characteristics but very poor air utilisation, and produces unburnt particulate matters in their exhaust. They also show low smoke limited power and higher weight to power ratio. 

The use of very high compression ratio for better starting and good combustion a wide range of engine operation is one of the most important compulsion in diesel engines. High compression ratio creates additional problems of high maintenance cost and high losses in diesel engine operation. 

For an automotive engine both part load efficiency and power at full load are very important issues as 90% of their operating cycle, the engines work under part load conditions and maximum power output at full load controls the speed, acceleration and other vital characteristics of the vehicle performance. 

Both the Petrol and Diesel engines fail to meet the both of the requirements as petrol engines show good efficiency at full load but very poor at part load conditions, where as diesel engines show remarkable performance at part load but fail to achieve good efficiency at full load conditions. 

Therefore, there is a need to develop an engine which can combines the advantages of both petrol and diesel engines and at the same time avoids their disadvantages as far as possible. 

Working Procedures: 

Stratified charged engine is an attempt in this direction. It is an engine which is at mid way between the homogeneous charge SI engines and heterogeneous charge CI engines. 

Charge Stratification means providing different fuel-air mixture strengths at various places inside the combustion chamber. 

It provides a relatively rich mixture at and in the vicinity of spark plug, where as a leaner mixture in the rest of the combustion chamber. 

Hence, we can say that fuel-air mixture in a stratified charge engine is distributed in layers or stratas of different mixture strengths across the combustion chamber and burns overall a leaner fuel-air mixture although it provides a rich fuel-air mixture at and around spark plug. 

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.

CONCEPTS OF BASIC THERMODYNAMICS

¤ Introduction:

The most of general sense of thermodynamics is the study of energy and its relationship to the properties of matter. All activities in nature involve some interaction between energy and matter. Thermodynamics is a science that governs the following:

• (i) Energy and its transformation
• (ii) Feasibility of a process involving transformation of energy
• (iii) Feasibility of a process involving transfer of energy
• (iv) Equilibrium processes

More specifically, thermodynamics deals with energy conversion, energy exchange and the direction of exchange.

¤ Areas of Application of Thermodynamics:

All natural processes are governed by the principles of thermodynamics. However, the following engineering devices are typically designed based on the principles of thermodynamics.

Automotive engines, Turbines, Compressors, Pumps, Fossil and Nuclear Power Plants, Propulsion systems for the Aircrafts, Separation and Liquefaction Plant, Refrigeration, Air-conditioning and Heating Devices.

The principles of thermodynamics are summarized in the form of a set of axioms. These axioms are known as four thermodynamic laws:

• Zeroth law of thermodynamics,
• First law of thermodynamics,
• Second law of thermodynamics, and
• Third law of thermodynamics.

The Zeroth Law deals with thermal equilibrium and provides a means for measuring temperatures.

The First Law deals with the conservation of energy and introduces the concept of internal energy.

The Second Law of thermodynamics provides with the guidelines on the conversion of internal energy of matter into work. It also introduces the concept of entropy.

The Third Law of thermodynamics defines the absolute zero of entropy. The entropy of a pure crystalline substance at absolute zero temperature is zero.


¤ Different Approaches in the Study of Thermodynamics:

There are two ways through which the subject of thermodynamics can be studied

• Macroscopic Approach
• Microscopic Approach

¤ Macroscopic Approach:

Consider a certain amount of gas in a cylindrical container. The volume (V) can be measured by measuring the diameter and the height of the cylinder. The pressure (P) of the gas can be measured by a pressure gauge. The temperature (T) of the gas can be measured using a thermometer. The state of the gas can be specified by the measured P, V and T . The values of these variables are space averaged characteristics of the properties of the gas under consideration. In classical thermodynamics, we often use this macroscopic approach. The macroscopic approach has the following features.

• The structure of the matter is not considered.
• A few variables are used to describe the state of the matter under consideration. The values of these variables are measurable following the available techniques of experimental physics.

¤ Microscopic Approach:

On the other hand, the gas can be considered as assemblage of a large number of particles each of which moves randomly with independent velocity. The state of each particle can be specified in terms of position coordinates ( x_i , y_i , z_i ) and the momentum components ( p_xi , p_yi , p_zi ). If we consider a gas occupying a volume of 1 cm³ at ambient temperature and pressure, the number of particles present in it is of the order of 10²⁰. The same number of position coordinates and momentum components are needed to specify the state of the gas. The microscopic approach can be summarized as:

• A knowledge of the molecular structure of matter under consideration is essential.
• A large number of variables are needed for a complete specification of the state of the matter.

¤ Zeroth Law of Thermodynamics: 

This is one of the most fundamental laws of thermodynamics. It is the basis of temperature and heat transfer between two systems. Suppose we take three thermodynamic system named System A, System B and System C. Now let that system A is in thermal equilibrium with system B. By thermal equilibrium we mean that there is no heat transfer between system A and system B when they are brought in contact with each other. Now, suppose system A is in thermal equilibrium with system C too and there is no contact between system B and system C. It implies that although system B and C are isolated from each other, they will remain at thermal equilibrium to each other. It means that there will be no heat transfer between system B and C, when they are brought in contact with each other. This is called the Zeroth Law of thermodynamics.


¤ Basis of Temperature: 

When two bodies are kept at contact with each other and if there is no heat transfer between them we say that their body temperatures are same. It means that temperature is the property of a system which decides whether there will be any heat transfer between two different bodies. Heat transfer always occur from a higher temperature body to a lower temperature body. Further whenever there is any heat inflow to a body, it raises its temperature and conversely, if heat outflow occurs from a system it lowers its temperature.

Suppose we take two bodies one of which is at higher temperature than the other. Now when we bring the bodies at contact, heat will be transformed from a higher temperature body to that of lower temperature. Then what will be its effect, we may ask as a result of this heat transfer? Is this heat transfer a perpetual process? Our common life experiences tell us that it will not be the case. Although, at first heat transfer will take place, but its amount will be gradually decreased and after some time, a situation will come when there will be no heat transfer between the bodies or the bodies will come to a state of thermal equilibrium with each other. So, what is the reason for that? Can we justify the situation?

Yes, we can justify it as the hotter body releases heat to the colder body, the temperature of the hotter body decreases where as the temperature of the colder body increases and after sufficient time both the bodies will have equal temperature and a state of thermal equilibrium will be achieved.


¤ Temperature Measurement: 

We know the temperature of a body can be measured with a thermometer. How can we actually calculate the temperature of a body with the help of thermodynamics?


¤ Thermometer:

A thermometer is a temperature measuring instrument. It is made of a thin capillary glass tube, one end is closed and the other end is fitted with metallic bulb full of mercury. The mercury is in thermal equilibrium with the metallic bulb. Therefore, the temperature of the mercury is equal to the temperature of the metallic bulb. 
Mercury has a good coefficient of volume expansion and it means that as the temperature of the mercury increases, its volume increases too and as a result mercury column inside the capillary rises up. 

The capillary tube has been graduated with the help of calibrating with standard temperature sources. Therefore, the temperature of the mercury can be measured from the height of mercury column as the tube is finely graduated. 

Whenever we want to measure the temperature of a body, we kept the body in contact with the metallic bulb of the thermometer. When thermal equilibrium is established between the body and the metallic bulb of the thermoneter, the temperature of both the body will be equal again the metallic bulb is in thermal equilibrium with mercury then the temperature of the mercury will be equal to the temperature of the metallic bulb and the temperature of the object.


As we can measure the temperature of the mercury from the column height, hence we can also determine the temperature of the object as they are equal to each other.

DISCUSSION:
Microscopic basis of temperature and pressure:
Here we shall try to discuss the basis of temperature and pressure only qualitatively, without any mathematical expression. 






.....................contact me at email: subhankarkarma@gmail.com for more notes

CENTROID OF AN AREA

 

CENTROID OF AN AREA

Engineering Mechanics EME-102

Geometrical Center of an area (A) is often termed as Centroid or Center of an Area.

Suppose we have an area A in a certain X-Y coordinate system, we divide the area into n parts and named them as A₁, A₂, A₃, .... A_n,. Let the coordinates of those tiny elemental areas are as (X₁,Y₁), (X₂,Y₂), (X₃,Y₃) ..... (X_n,Y_n).

As area can be represented by a vector, hence, Area A can be treated as the resultant of the tiny elemental vectors A₁, A₂, A₃, .... A_n... Let the direction of the resultant vector passes through the point G(X_g,Y_g) on the plane of the area. The point G(X_g,Y_g) is called the CENTROID of the area A. (The direction of any area is along the perpendicular to the area drawn at the centroid of the area).

Like other vectors, an area has a moment about an axis and be represented by the product of the radial distance between the area and the axis and the area itself. So if an elementary area A₁ has a coordinate (X₁,Y₁) it means the area is at a distance X₁ from the Y axis and Y₁ from the X axis. Therefore the moment produced by A1 about Y axis is X₁A₁ and about X axis is Y₁A₁.

 Therefore the summation of all the moments produced by each and every elemental area about Y axis will be ∑A_iX_i and about X axis will be ∑A_iY_i.

Again, the resultant area A passes through the point G(X_g,Y_g). Therefore the moment produced by the area A about Y axis will be AX_g and about X axis will be AY_g.

Like other vectors, it will obey the Moment Theorem which states the total moment produced by individual vectors will be exactly equal to the moment produced by the resultant vector about a certain axis.

Therefore,
AX_g = A₁X₁ + A₂X₂ + A₃X₃ + ...... + A_nX_n

and
AY_g = A₁Y₁ + A₂Y₂ + A₃Y₃ + ...... + A_nY_n

           

                 For an area, a centroid G(X_g,Y_g) can be defined using calculus by the equations,

X_g = (1/A)∫x.dA   ------ (i)

Where dA = elemental area and A= total area.

Y_g = (1/A)∫y.dA   ------ (ii)

HOW TO DERIVE THE VALUES OF X_g and Y_g FOR BASIC GEOMETRIC FIGURE:

STEPS TO FIND X_g


i) Draw the figure in a Coordinate System.

ii) Draw a thin strip of area of thickness (dx) parallel to Y axis and at a distance (x) from Y axis.

iii) Find the height of the strip. Either the height will be constant or the height is a function of (x), that can be calculated from the equation of the figure.

iv) Calculate the elemental area of the strip, and named as dA. Hence, dA = hdx

v) integrate the expression ∫xdA, but dA = hdx. Therefore, we shall integrate  ∫hxdx over the total area.

vi) X_g = (∫ xdA)/A = (∫ hxdx)/A ; where A = total area = ∫dA = ∫hdx


STEPS TO FIND Yg

i) Draw the figure in a Coordinate System.

ii) Draw a thin strip of area of thickness (dy) parallel to X axis and at a distance (y) from X axis.

iii) Find the length (b) of the strip. Either the length will be constant or the length is a function of (y), that can be calculated from the equation of the figure.

iv) Calculate the elemental area of the strip, and named as dA. Hence, dA = bdy

v) integrate the expression ∫ydA, but dA = bdy. Therefore, we shall integrate ∫bydy over the total area.

vi) Y_g = (∫ ydA)/A = (∫bydy)/A





CENTROID OF A COMPOSITE AREA:




HOW TO FIND THE CENTROID OF A COMPOSITE AREA

(a composite area consists of several straight or curved lines.)

(i) Draw the figure in a coordinate system. Draw the dimensions too. Every dimensions will be measured with respect to origin of the coordinate system

(ii) Divide the composite area into several parts of basic geometric areas. Lebel them as part-1, part-2, part-3, .......part-n. Let the corresponding areas are A₁, A₂, A₃, .... A_n. Let the centroids are G₁(X₁,Y₁), G₂(X₂,Y₂), G₃(X₃,Y₃), ...... G_n(X_n,Y_n).

(iii) Let the centroid of the composite area be G(Xg,Yg). Hence,
Xg = (A₁X₁ + A₂X₂ +A₃X₃)/(A₁ + A₂ + A₃)

Yg = (A₁Y₁ + A₂Y₂ +A₃Y₃)/(A₁ + A₂ + A₃)

(a) Suppose we have certain area of magnitude (A) in a coordinate system. The centroid of the area will be at its mid-point. A centroid is denoted by G.
 
                       In the figure we have a complex geometrical area composed of three basic geometrical areas. A rectangle, a semi circle and a isosceles triangle. Let us denote the centroids as G₁, G₂, G₃ for the given areas in the figure.

We shall have to find the Centroid of the entire area composed of  A₁, A₂, A₃. 

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

Part -1 : The semi-circle : Let the centroid of the area A₁ be G₁(X₁,Y₁)

Area, A₁ = (π/2)x(25)² mm² = 981.74 mm²                  
          X₁ = { 25 -  (4x25)/(3xπ)} mm = 14.39 mm
          Y₁ = 25 mm

Part -2 : The Rectangle : Let the centroid of the A₂ be G₂(X₂,Y₂)

Area, A₂ = 100 x 50  mm² = 5000 mm²                 
          X₂ = 25 + (100/2) = 75 mm
          Y₂ = 25 mm
Part -3 : The Triangle : Let the centroid of the area Area, A₃ be G₃(X₃,Y₃)

Area, A₃ = (1/2) x 50 x 50 mm² = 1250 mm²                 
          X₃ = 25 + 50 + 25 = 100 mm
          Y₃ = 50 + (50/3) =  66.67 mm



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

X_g = (∑A_iX_i)/(∑A_i) 

    = (A₁X₁ + A₂X₂ +A₃X₃)/(A₁ + A₂ + A₃)
    = (981.74 x 14.39 + 5000 x 75 + 1250 x 100)/( 981.74 + 5000 + 1250)
    = 71.09
     

Y_g = (∑A_iY_i)/(∑A_i) 

    = (A₁Y₁ + A₂Y₂ +A₃Y₃)/(A₁ + A₂ + A₃)
    = (981.74 x 25 + 5000 x 25 + 1250 x 66.67)/ ( 981.74 + 5000 + 1250)
    = 32.20

NEED OF QUALITY ASSURANCE

NEED OF QUALITY ASSURANCE

Quality assurance can be a confusing realm for those who don't have any prior experience in this field. Many commonly asked questions by first timers include wanting to know exactly what quality assurance is and why they require such a service. Read on to find out the answers.

How Can We Define Quality Assurance?

Quality assurance is the process of ascertaining, through a systematic set of procedures, whether or not a product or service satisfies the customers' requirements. This is the simplest and most basic definition for quality assurance.

Why Do We Need Quality Assurance?

If your company has manufactured a certain product, it is necessary to get that product checked to verify that it conforms to the expectations and requirements of the customer. This process of checking and verifying a product's quality is known as quality assurance.

On the other hand, if you are the customer, you would definitely want to ascertain that the product that you are purchasing satisfies your requirements. If the product fails in some way to meet your expectations, you can provide feedback to the company who will then try to improve their quality standards for that particular product in order to improve their product performance.

Thus quality assurance works both ways, ensuring satisfied manufacturers as well as customers.

The mass industrialization period saw the widespread introduction of mass production and piecework, which created problems as workmen could now earn more money by the production of extra products, which in turn led to bad workmanship being passed on to the assembly lines. To counter bad workmanship, full time inspectors were introduced into the factory to identify, quarantine and ideally correct product quality failures. Quality control by inspection in the 1920s and 1930s led to the growth of quality inspection functions, separately organised from production and big enough to be headed by superintendents.

The systematic approach to quality started in industrial manufacture during the 1930s, mostly in the USA, when some attention was given to the cost of scrap and rework. With the impact of mass production, which was required during the Second World War, it became necessary to introduce a more appropriate form of quality control which can be identified as Statistical Quality Control, or SQC. Some of the initial work for SQC is credited to Walter A. Shewhart of Bell Labs, starting with his famous one-page memorandum of 1924.

SQC came about with the realization that quality cannot be fully inspected into an important batch of items. By extending the inspection phase and making inspection organizations more efficient, it provides inspectors with control tools such as sampling and control charts, even where 100 per cent inspection is not practicable. Standard statistical techniques allow the producer to sample and test a certain proportion of the products for quality to achieve the desired level of confidence in the quality of the entire batch or production run.


At Total Quality Assurance, all your quality needs are taken care of.
Visit click for more to find out more.

short url for this entry: http://goo.gl/SF07

WHAT IS QUALITY?

QUALITY SYSTEM & MANAGEMENT:

 

Definitions: QUALITY, QUALITY ASSURANCE, QUALITY CONTROL

 

INTRODUCTION:

Quality of product signifies the "degree of its excellence and fitness for the purpose. Although some of the quality characteristics can be specified in quantitative terms, but no single characteristics can be used to measure quality of a product on an "absolute scale".

So, quality of a product means all those activities which are directed to maintaining and improving such as

(i) Setting of Quality Targets,
(ii) Appraisal of Conformance,
(iii) Adopting Corrective Action

where any deviation is noticed, analysed and planning for improvements in Quality.



DEFINITIONS OF QUALITY

1. General: Measure of excellence or state of being free from defects, deficiencies, and significant variations. ISO 8402-1986 standard defines quality as "the totality of features and characteristics of a product or service that bears its ability to satisfy stated or implied needs."

2. Manufacturing: Strict and consistent adherence to measurable and verifiable standards to achieve uniformity of output that satisfies specific customer or user requirements.

3. Objective: Measurable and verifiable aspect of a thing or phenomenon, expressed in numbers or quantities, such as lightness or heaviness, thickness or thinness, softness or hardness.

4. Subjective: Attribute, characteristic, or property of a thing or phenomenon that can be observed and interpreted, and may be approximated (quantified) but cannot be measured, such as beauty, feel, flavor, taste.



CHARACTERISTICS OF QUALITY:

(i) Quality in business, engineering and manufacturing has a pragmatic interpretation as the non-inferiority or superiority of something.

(ii) Quality is a perceptual, conditional and somewhat subjective attribute and may be understood differently by different people.

(iii) Consumers may focus on the specification quality of a product/service, or how it compares to competitors in the marketplace.

(iv) Producers might measure the conformance quality, or degree to which the product/service was produced correctly.

Numerous definitions and methodologies have been created to assist in managing the quality-affecting aspects of business operations.

Many different techniques and concepts have evolved to improve product or service quality.



QUALITY RELATED FUNCTIONS:

There are two common quality-related functions within a business.

(a) One is quality assurance which is the prevention of defects, such as by the deployment of a quality management system and preventative activities like FMEA.

(b) The other is quality control which is the detection of defects, most commonly associated with testing which takes place within a quality management system typically referred to as verification and validation.




BUSINESS DEFINITION OF QUALITY:

(a) The common element of the business definitions is that the quality of a product or service refers to the perception of the degree to which the product or service meets the customer's expectations.

(b) Quality has no specific meaning unless related to a specific function and/or object. Quality is a perceptual, conditional and somewhat subjective attribute.



QUALITY & PRODUCTIVITY:

In the manufacturing industry it is commonly stated that “Quality drives productivity.” Improved productivity is a source of greater revenues, employment opportunities and technological advances.






CHARACTERISTICS OF MODERN QUALITY MANAGEMENT SYSTEM

However, there is one characteristic of modern quality that is universal. In the past, when we tried to improve quality, typically defined as producing fewer defective parts, we did so at the expense of increased cost, increased task time, longer cycle time, etc. We could not get fewer defective parts and lower cost and shorter cycle times, and so on.

However, when modern quality techniques are applied correctly to business, engineering, manufacturing or assembly processes, all aspects of quality - customer satisfaction and fewer defects/errors and cycle time and task time/productivity and total cost, etc.- must all improve or, if one of these aspects does not improve, it must at least stay stable and not decline. So modern quality has the characteristic that it creates AND-based benefits, not OR-based benefits.

The most progressive view of quality is that it is defined entirely by the customer or end user and is based upon that person's evaluation of his or her entire customer experience. The customer experience is the aggregate of all the touch points that customers have with the company's product and services, and is by definition a combination of these. For example, any time one buys a product one forms an impression based on how it was sold, how it was delivered, how it performed, how well it was supported etc.

Quality Management Techniques:
_____________________________________
* Quality Management Systems
* Total Quality Management (TQM)
* Design of experiments
* Continuous improvement
* Six Sigma
* Statistical Process Control (SPC)
* Quality circles
* Requirements analysis
* Verification and Validation
* Zero Defects
* Theory of Constraints (TOC)
* Business Process Management (BPM)
* Business process re-engineering
* Capability Maturity Models

Quality Awards:

* Malcolm Baldrige National Quality Award
* EFQM
* Deming Prize

SECOND SESSIONAL TEST (odd SEMESTER 2009-10) B.Tech…first Semester Sub Name: Engineering Mechanics

SECOND SESSIONAL TEST (odd SEMESTER 2009-10)

B.Tech…first Semester

Sub Name: Engineering Mechanics                                         Max. Marks: 30

Sub Code: EME-201                                                          Max. Time: 2: 00 Hr

Group A

Q.1 Choose the correct answer of the following questions 1x6=6

(i) If two forces of equal magnitudes have a resultant force of the same magnitude then the angle between them is

(a) 0⁰          (b) 90⁰         (c) 120⁰          (d) 135⁰

Ans: ( c)

Explanation: P² = P² + P² +2P.P.cos θ

ð      P²= P² (1+2cos θ)

ð      cos θ = -½

ð      θ = 120°

(ii) If a ladder is kept at rest on a vertical wall making an angle θ with horizontal. If co-efficient of the friction in all the surfaces be µ, then the tangent of the angle θ will be equal to

(a) (1-µ²)/2µ                                  (b) (1-µ)² /2µ

(c) (1-µ)/2µ                                   (d) none of the above

Explanation: (a) (1-µ²)/2µ

(iv) Varignon’s theorem is related with _____________ .

Answer: moment

(v) If two forces of equal magnitudes P having an angle (90°- θ) between them, then their resultant force will be equal to ________.

Answer: √2P (1+sin θ)

(vi) A fixed joint produces

(a) 1             (b) 2             (c) 3               (d) 4         reactions

Answer: (c ) 3

(vii) The equilibrium conditions of concurrent force system is_________.

Answer: ∑Fx =0; ∑Fy=0.

Group B                                                                                                                  8x3=24

Attempt any three questions

Q.2. State and explain Varignon’s theorem of moment. Three forces of magnitudes 3 KN, 4 KN and 2KN act along the three side of an equilateral triangle ∆ABC in order. Find the position, direction and magnitude of the resultant force.         4+4

Answer: resultant force: √3 KN

Q.3  (a) Two cylindrical rollers are kept at equilibrium inside a jar or channel as shown in the figure. The channel width is 1000 mm, where as the rollers have diameters 600 mm and 800 mm respectively. The weights are 2 kN and 5 kN respectively. Find all the reactions at contacts.

                                                                                            4+4

(b) What is pure bending? If a stone is thrown with a velocity 400 m/s then find the maximum height that the stone can reach.

Q:4)  a) Classify different types of joints in beam with proper explanations.

(b) Find the reactions at the support for the beam as shown in the figure.                                           4+4

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: