Engineering Mechanics - An Introduction | Yoshida Rao | Skillshare

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Engineering Mechanics - An Introduction

teacher avatar Yoshida Rao, GATE Rank 2

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Taught by industry leaders & working professionals
Topics include illustration, design, photography, and more

Lessons in This Class

12 Lessons (1h 9m)
    • 1. Classification of Objects

    • 2. Body Forces and Boundary Forces

    • 3. Deformable and Rigid bodies (Advanced topic - Can be skipped in first viewing without loss of contin

    • 4. Method of Sections

    • 5. Equilibrium Equations

    • 6. Degrees of Freedom

    • 7. Types of Loads

    • 8. Classification of Structures

    • 9. Trusses

    • 10. Beams

    • 11. Cables and Shafts

    • 12. References

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About This Class

This class is for Mechanical Engineering, Applied Mechanics and Aeronautical Engineering under graduate and graduate students. This class starts from the basics of Newton's first law, then builds towards Equilibrium equations and degrees of freedom. It discusses difference between internal force and external force. It shows that the main concern of Engineering Mechanics and subsequent course on Strength of Materials is to determine Internal resistance or force developed in the body in response to external loading. Finally it introduces various structural members like Trusses, Beams, Frames, Cables and Shafts. This class is essential to those who want to make Engineering Mechanics as favorite subject when appearing in examinations and interviews. I have found with my experience that student find this subject difficult and either leave it or spend too much time on it, which takes away time from preparation of other subjects. This course saves time of the student and explains all the concepts in short duration. So best of luck with Engineering Mechanics.

Meet Your Teacher

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Yoshida Rao

GATE Rank 2


Hi, I have done Bachelor's in Mechanical Engineering and Master's in Construction Technology and Management. Both degrees from IITs (Indian Institute of Technology). I have qualified many national level examinations like N.T.S.E. (National Talent Search Examination), GATE (Graduate Aptitude Test in Engineering), where I scored All India Rank 2 in Mechanical Engineering Paper. I also had All India Rank 25 in IES (Engineering Services Exam) in India. My work experience includes working as Planning Engineer in Construction company, and 10 plus years of experience as teaching Mechanical Engineering. I am here to provide first hand experience to students as to what is how to get top ranks in Professional examinations.

And also it is not only about written examination, one ha... See full profile

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1. Classification of Objects: to Let's continue our discussion on engineering mechanics. We will discuss the classification off engineering objects classification Most off the stability that you see are only never day to day. Life can be classified as structures on mechanisms. You know, See what I structure and worked out a mechanism. Structures are built assemblies, which are you? You're a relatively immobile like houses. Bridges supports our They're moving objects within their framework. So on the bridge, cards might be moving. People might be standing so stuck. Just support moving objects. A typical example of structures. Our buildings, bridges or two mobile frame's book shells. Electronic casing. You will see a few examples stop. Just like these are buildings, steel sectors, bridges, cable, stayed bridges. Elektronik is things and the roof trust. These are all example of structures. You see more as we go through the course. No, what is mechanism? It is an assembly off small components which are in contact with each other. There's component side in the state off motion example. So mechanisms are crankshaft rotating shouts years, pulleys, moving cars and bell drives and to see for examples. These are the bed race, the gear transmission, a typewriter is a mechanism, and Land Rover on on surface of a planet is also mechanism. So that's some to dislike. Terrible. Here. Your card in your discussion in the next lecture. Thank you. 2. Body Forces and Boundary Forces: Let's continue our discussion on immunity mechanics. Now we will discuss types of forces, particularly external forces, type of forces acting on a body. There are two types of forces boundary forces and body forces boundary forces. The boundary forces, as the name indicates, act on the boundary off the body. Their forces are usually cause backed contact of body with some other body on task forces, for example, of bridges there and train is going over the bridge and trainees in contacted the body. So this it is causing a burden. Boundary force on the bridge and dismembered, distributed over a particular region off a boundary. For example, a train train is not applying. A concentrated Lord train is applying a distribute reload because the Lord is distributed along the length off the train or after the point concentrated on the boundary of a body. For example, a heavy machine Reese kept on the bridge. At one point that would be called a consent. It'd lord lorded beans. This example you have taken from the key books like the support Really? This is a This is the bridge and this is a train train is applying are distributed load over the bridge for over here. A conservatory lord, for example. Machine is kept over the bridge and hear some rotation Movement Force is applied at the center of the bridge. So these are very example of how a bridge can be loaded. One re forces like this is a bridge and on the bridge were having seen lot off cars which are acting as the Lord on the bridge train going over the bridge, as we discussed, is an example of an external lord Body forces the body forces, on the other hand, act on each particle of the body A gravitational and electromagnetic forces are the example of party forces self IQ, for example this bridges there it is having of it, which is being held by the cable wires. So this is example off a ball off body force self with, like this is a beam, and it's very it is distributed along this total length. So this is a kind office body force 3. Deformable and Rigid bodies (Advanced topic - Can be skipped in first viewing without loss of contin: So let us continue our discussion off engineering mechanics. We will discuss deformation. And what is the Richard party are really classified engineering objects as structure and mechanisms. Now we classify as rigid body and sorted before everybody. You will see. What do we mean by the formation? It is a geometric jeans. It is usually very small Change cause on the particles off the body. You're this technically termed as deformation before mission are inevitable consequence off external interaction off the component. So if you're bridges there and a train is passing over the bridge and extended interaction and external load on the bridge, then that the formation of the bridge will happen. But often the very often in engineering there reversible. For example, when the train passes over the bridge, it goes away, the bridge comes back, streets are in good shape and the object from special in the shape Brenda Lord is removed. The versatility formation it was similar information may be defined as a D for mission. There seizes to exist friend External agents causing before mission are removed So far, a train and a bridge. Example. The bridge is undergoing a reversible deformation caused monster load off, the train is removed, it comes back to the original shape. The ability to sustain the for diversity Bertie formation at a material level is one of the characteristics off solar there. Distinguish it from fluids, for example, of fluid is there if you apply Lord on the fluid than the shape of the fluid will change. And once the Lord is removed, the shape did not come back assaulted before body or kind of really come back. Sit or signal shape off route cannot come back with partnership. What is mechanics off soldiers? The mechanics of solids is more concerned with the internal forces. We'll see what is internal force, which would be the subject of discussion throughout this engineering mechanics associate 13 In geometry off the component involved. The important things in it are the properties of the material used the strength language off. Which will it remind whether the component will trailing break orders in service surface bridges there? What type of material is used? The strength of that material will deter, mined whether their bridge will sustain the Lord's or it will fail during operation. The stiffness by virtually remind acceptable a bunker before mission. So the apart from taking the Lord in materials should not deformed too much. For example, a building is there. If some lower comes on the building, then it will. The shape will slightly change. And when the Lord is removed the shape it will come back to our inner shape, which will not break but still there deformation that is taking place and the brittle materials like tiles on the floors of the building. We'll break if the information is too much. So not is not only about stand, it's also about the before mission and how much information is taking place. So I don't deform. Able Body, the first object of mechanical soil. It's a stranger. Materials is central to the whole activity of engineering design, engineering design. We have to see the shape and whether that shaped was able to take them. Lord and the material which is used to make the substance whether that will be able to sustain the pressure that is stupid is the whole subject of discussion. Usually, the objective analysis will be determination of stress, strength and deflections. Loosen the Lord so this will be object off discussion in a mechanics off solid scores, stand strains and reflections. What is the rigid body now to discuss all of the formal body? Never discussed. What is the rigid body? Right before missions are ignoring the analysis, the component our bodies considered as aged body, we assume that the body nor the formation is taking place. Treatment of components as digit board is is used for touring mechanics, and I'm really using identifying the mechanics load imposed on the individual members in the assembly, for example, we're solving a trust. You will see what is a press. We saw roof dress in the example in the previous a lecture so in we want in each of the members with every information. But when it reminding the Lord on each of the members restated each other members are rigid . You would see in the example did you pour the indigent party? The distance between two points remained same in respect to off the external forces acting on it. There is no change in shape or size of the body. Under the in points off external force, it is important, and it body the distance between two points. Women same, and there is no change in shape or size. Another definition of rigid bodies. That and willow velocity and angle acceleration off all lines on a rigid body is seem. The motion of frigid board is composed of two components. Translation about it, arbitrary point and rotation. About that point, this will continue discussing this course. Uh, thank you. 4. Method of Sections: So let us discuss no decision on engineering mechanics. We will discuss the matter of sections in this lecture. To work is matter of sections, one of the main problems in engineering mechanics or soldiers of the investigation off internal instance off the body. So we want to find what is the internal force in the body, which we are not using. The word in the first you know, we're calling us internal instance that is set up NATO forces at the start of it in a body to balance the effect off externally applied load. For this purpose, a uniformed method of sections is employed, so we use the metal off sections to remind the internal resistance that is there up in the body due to the externally applied forces, a complete tag dramatic sketch of the member to be investigated is prepared on which all the sudden force acting on the body are shown at their respective points off application. So just sketches called a free body diagram. So first step in their method of sections is to draw the free water drag around all forces acting on a body including reactive forces caused by the support and the weight of the body itself do tricks mass are considered external forces. So there are three types of external forces over here, not the forces that are acting on the body forces that are applied at as a reaction. Forces at the superior body supported and third is the weight of the body. Please note that weight of the body is also an external lord in this analysis. Moreover, since a stable body addressed is in equilibrium, the four stepping on it must satisfy the aggressions are starting equilibrium. That's if the forces acting on a body such a short and figure satisfy equations are certainly equilibrium and are as shown acting on it. The sketch is called a free body diagram. So this is a free body diagram. All these forces are acting on the body and they are balancing each other and the body is not moving. Please note that party is not moving in engineering mechanics and structures se metal off sections continue next, since it determination of internal forces caused Baxter no, once is one of the primary concern off the subject. An opportunity section is passed to the body completely, completely, sir, particular into two parts. This process would be referred to as method of sections. So we cut a section through the body. You will see the figure. The figure is coming up. Just wait. Then if the body is whole is in equilibrium any part off it must also be in equilibrium for such part of the body. However, some of the forces necessary to maintain the equilibrium must act at the cart section. These lead to the following come phenomenal conclusions. The externally applied forces on one side often arbitrary act must be balance by internal force. There, look at the card or briefly. External forces are balanced by internal forces. So we will see this figure now We went here we have we have a body volley four forces people be do p three p four are acting These forces are external forces and they are balancing each other meaning to say that the body is not moving You know what we do is record because Nakata section we cut a section through this body and we focus that I channel the top half body and bottom half body through the stop off party. Another first we said that these forces air balancing each other so the body was not moving . Now obviously that only two forces remain p one and p two to build the balancing Fortis Petri and before are gone so the body should move but the body carton but already can't move because the full body is not moving. So how will have party move? We have not cut the body tohave yarrow leaves, focusing our attention on the hard body. So when focusing attention on half party hard party also should not move because the full party was not moving. So now it means there must be some balancing force. This people in p two were earlier being balance where Petri and before now there must be balanced at some force. Ritter acting on this cut section to these forces are the card section are better and seeing the excellent lords pure and redo. And this forces on the card section are Korda's internal forces saying we're in this bottom half of the figure Petri and people are balanced by these Cut from this forces there take art section So the how toe so how to return mine Internal force 1st 8 a total body and sure that total body is not moving at all The forces that balancing each other once you have ensured that the force that balancing each other, then a curtain, arbitrary section in the body and we find that the resultant off these two have been at dissection as the and that recall is the internal force. So we'll continue our discussion in the next lecture. Thank you. 5. Equilibrium Equations: So let us continue our discussion on any mechanics. Now we will discuss. Or do you mean by equilibrium? We would start with Newton's first law. Everybody continues to be in a state of rest or uniform motion. Okay, unless otherwise it too disturbed by an external agency. So the body address continues to be in a state of rest, and the body moving with uniform velocity continues to move with uniform velocity, unless some external as the first act on it. So just unbalanced force or an unbalanced movement. The first law defines the state of the rest off uniform motion off body, your stairs that a state of rest or in for motion of the body is a natural state of the body. If there no at net, external forces acting on it, what it implies settlement force, external forces acting on it. But this, for that implies, is that weapon force external to the body must be zero. It's so what we're trying to say that it is not that there is no force. Acting forces are acting on the body, but the natural, their tent off the forces zero. And that's why the board is in equilibrium. This also implies that external force acting on the board in my balance, each other so that the Net External Force zero to maintain a state of rest or in for motion a body in this 30 said Tobin. Static equilibrium in other words, equilibrium or 30 equilibrium may be treated as a D statement off the state of rest or uniform motion off the body. My body consists often in fright number of particles interconnected through some intermodal clear forces within a boundary or domain. Sat equilibrium off a body implies that every particle of the body is instead off rest, all in for motion up awaiting the Newton's first law equilibrium in Newton's first law, a little body addressed if there is no external force. So this there is a problem off particulate subjected to force. Can bitterness follows. This implies it'll. Particulate addressed or is informally moving in any combinations. So this is a particle and air forces directing on them. But there's desert 20 0 body is addressed so similarly, the equally dominated party can be expressed. The digit body is too. This is a rigid body. Alert was a particle. Now, the force directing on it and submission off the forces is equal to zero. The forces. If I acting on a budget, Borgias either boundary forces or body forces. If the submission off if I is snored as F in the static Librium can be Citrus F equal to zero, it should be noted that a questions if I is a factorial equation, the three directions Forces of Motion of Forces in extraction, equal to zero summation of forces in violation equal to zero and summation of forces in that direction equal to zero. Numerous questions. Unlike a particle religion body has definite shape and size. Because of this, it can undergo rotation due to application of force. In addition to translation, the ball static equilibrium questions off forces does not restrict dissolution. This rotational motion of the rigid body really tripped with sector off mass toe submission of forces at the point for a particle is not sufficient. Three equations, but three questions are not sufficient for your body. Both rigid body can. Apart from moving extradition, why direction is the direction you can repeat about back sex? Is that going to get about My ex is kind of great about their exes. So we need more questions off equilibrium and perform to make the body addressed. It only requires the center of mass of the body be at rest or in motion. He does not receive the other part of the rigid body from accelerated motion rhetoric. Jewish Center off the rigid body about the nexus passing through the center of Mass. Therefore, for the rest of points affiliated body and additionally, question of equilibrium news to be established to a concept off for a moment and about a particular line or excesses introduce it can be realized that the force nearer toe the line or acceleration of the rigid body has less influence on the traditional party, then affords away from the acceleration. So this is a force and the center of mass, and this is the distance from the center of Mass. So if this fourth, if this forces acting more away from the center of mass, it will produce more rotation acceleration, ready solution, the fittest pollutant near center off mass, then it will produce less effect. So that is what is saying that this is a movement. A movement is defined us radius into this force. F this factorial multiplication. Therefore, the definition of women care is with the access and the distance between the accident. A line off the force. It is the least distance to the line affection from the axis that has to be considered in definition. That's the force considered The movement M can be defined as the movement and defined by the question m equal to ardent across F is called the first movement off forced. If F is the night for detecting already dead body, then for body nor to rotate this men should be equal to zero for zero net force condition. M equal to zero is a stronger statement than a mere STI statement off for force off equilibrium. So this is stronger. Statement off equilibrium the disease a woman condition defines new rotation condition since in no movement there is no tendency to rotate the rigid body with the acceleration. Therefore, chemical 20 is an additional statement off equilibrium. He forced a fight clear settlement and my about access considered and their food for equilibrium Portal momento to all forces My speak. We're 20 So this is like this is what we're saying is most emotional moment. Zero moment. About three accents. Moment about tax. Texas Woman wrote Firaxis Moment about their exes. So now we have 60 questions of a group beyond three forced equations. Forces around XX is a core potato. Force along by X is equal to zero force along zero X is equal to zero and momentous three movement to questions about the three exes. We'll continue our discussion in the next lecture. Thank you. 6. Degrees of Freedom: So let's continue Our discussion on any mechanics where people discussed now is degrees of freedom. Degrees of freedom for a system of rigid bodies. A three dimensional idiot body could possibly translating three mutually independent direction and can rotate about three mutually independent access. So of Oregon drums task it in X direction, or it can go in very direction. It can go in their direction or it can rotate around. X axis around via CSIs around their necks is usually independently means like it can go in X axis without going in vire their direction. It can rotate about that. Sex is without rotating. About any of the other dimensions are without going any other directions, so all the six degrees of freedom are independent in the Cartesian coordinate system. These can be identified as translation in X rayed your directions and rotation about X rayed your directions. Therefore, we can say that I read it board in three. Dimension has six mutually independent possibilities off motion. These possibilities are called the degrees of freedom for a set of force acting on a three dimensional body when, as a gendered, six independent equations in six different gas stations and rotational degrees of freedom to solve for the motion. So there. So they're six degrees of freedom. So they every six equilibrium equations, uterus laws only apply to generate this system off six equations 342 questions and three movements. Equations. Now see this. It is a two dimensional body. It will get it going at your direction. Vied, redirection and it candidate about the Lexus examining a tow to damage pain. A two dimensional body. Since the since freedom represent the freedom to move in an independent way, we can earn 53 degrees of freedom for printed rigid body through translation and rotation. First we talked about three dimensional in two dimensional. We had 60 days or freedom include dimensional. We have three degrees of freedom. Do you need to move along? XX is degree to move along via taxes and to rotate about their Texas. When the body rotates about their taxes, it remains in the X Y plane. He doesn't come out of the X Y plane to come out of the excitement and sure about the excesses of I exes. Delia Freedom is said to be independent in a rigid body. If arrest off other degrees of freedom does not affect the motion along the degree of freedom considered. So as we discussed that we can move about echo about that sex is without going in the right direction. Or we can keep on rotating about the axis without translating in the accident direction or going in the right direction. If all the three degrees of freedom are arrested in a plane, everybody, we will find that the digital body has lost all its freedom to move so that it has to be addressed in a diverse. There is no possible woman, a rigid body. If all three degrees of freedom are arrested, there does not consider it system offered your bodies. A story, in part is to be composed of rigid part is connected or not connected to one of each other . Their degrees of freedom or system can be found by understanding the nature of connection between the rigid bodies and their number. For a system consisting of related parties which are disconnected, are not connected with each other, it is easy to find the number of days of freedom. It is equal to the number of rigid bodies and time stand number of release of freedom. Part of your body. If we're having three bodies which are not connected with each other and they're lining a good initial plane, then each off. Then we'll have three degrees of freedom. So their total 90 reserve freedom when bodies are not connected to each other, it is that easy to find. What is the number of degrees of freedom for a system of player? Rigid board is the total number of the future of the three and 43 digit bodies total 3239 along the entire system. There days of freedom are excellent. I want either one x two y two teacher toe exited by three teachers. Three. So these are three bodies which are lying independently in a plane, and I'm not gonna do to each other. So it has nine degrees of freedom in practice. Many times they depended, too. Did Ward is up connected to each other and work in unison to support the external lords. In such cases, it is important to consider constraints that bodies imposed on each other. So reaction produced to do the strange No, consider it your body assuring figure if the point is completely restricted from prostate motion by a hinge. Supposedly we ever we ever change over here. We have a hinge at this point, and this point cannot move this body. This body is gonna trickle this point for the hinge because off that this world, we can't go in the X direction. That body can't go in the right direction. But it can keep on rotating about that things. So this body has lost two degrees of freedom. The four digit body, a arrested from the train station has only one degree of freedom with a set of already forces acting or body forces acting on it. The eastern from the translation motion ity can be achieved. Only the additional forces applied Davis that if either is there total boundary friend body forces acting ideal. So, like we have the bodies air hinge on this board is very conclusive. No, you try to pull this word in the X direction. So there is a force in the X direction Toe body should move in the X direction, but the body can't move about. Body can't move because it is hinged. So it means this hint is applying a reaction force at this point on the body. So if that is a point, you have to understand that this hinges applying a reaction force. This is reaction force, and this is also what type of external force we called sir traditional forces, as as reaction forces or simply reactions which are developed Good Eastern supplied at the point. So when a degree of freedom is stopped, reaction force their loves. Then when? So I stopped with the body with the hints going in the X direction we start with in the Y direction. So because of that, they're the reaction force in the X direction and the reaction force in the Y direction. We will see a lot of examples off this. That's any degree of freedom. Restrained will automatically producer the action at the point, considering there are many ways in Victory, Eastern can be imposed in your body. That Eastern Topher offered from outside the system is called support reaction, depending upon the type of support, different degrees of freedom or Bush and are arrested like if you see the air, this is the ruler. This body can not boom in violation. It cannot go. It's the one degree of freedom is stopped. So this ball stapes system stops one degree of freedom not allowed motion in the Y direction. It allows motion the extradition. It allows the rotation a roller, the roller again this new vie direction Woman This extraction movement is possible and rotation is possible. Rocker. Same reasoning, A smooth surface, same reasoning, no motion in the Y direction. So that s two degree of freedom one. So we are saying that this body No, we apply your force in the right direction when you apply force in the right direction where we should move in the right direction because there is an unbalanced force in the right direction. But this force is not unbalanced. This force is not unbalanced because this is her face is applying a reaction force through balance the degree of freedom that is being stopped. So for free body diagram off these all the frustrations will be this bar and the force in the right direction. Reaction force in the right direction. This will be the free world Now this scene our air having to release off the this a hinge and it cannot move in the x direction. It cannot move in the right direction. It can only rotate so you cannot go in the X direction. So there is the force. This hinges applying in the X direction, which is opposing any off fourth in the extradition which were allowed to move in their way . And this change is applying. So this is the free body diagram effects. If I force in the X direction to stop the motion in X direction of force in the vital Richard to stop the motion in the right direction. Now there's a fixed and support in this effect will discuss this fixed, insupportable, commonly discussion a lot later. We really use the term court cantilever toe. The describe Describe it. Ah, so this affects and support this body cannot move in the X direction. It cannot move in the right direction and clarity. Repeat. Also in the in the in the X y plane. So it is. There are three degrees off 33 questions off reaction three reaction forces the reaction force in the X direction reaction force in the Y direction and the movement in the about a moment of all those a Texas. So these three moon. All the three degrees of freedom are stop. So there are three reaction forces direct do for that. Let's look at the same example Arresting one degrees of freedom like you see over here it can go in this direction. It can rotate, It can move in on collar on smooth roar and it can rotate, but it cannot move perpendicular to the square. Lord, savor this Lord cannot move perpendicular. I took this one day off. The freedom will be there. It's one. So they re one reaction force Free body diagrams offer planners the submitted bodies. Consider the pleasure system as shown below. There are two bars ABC, A, B, C and B A, B, C and B D On a rigid walls on a hinge, the volatility can be taught off as a rigid body whose or degrees of freedom are arrested. So, numbering the regional bodies the devolved to under two bars. The volume centrist three constraint so similarly did due to the strange Cento Putra station motion. So here two degrees of freedom are the stop. This'd voil is all three degrees of freedom stalked and here we are this total we have three bodies want to entry? Totally visa Freedom are nine. No, let us see how many off them are stopped. This is this is freaks toe this stone world this fixed about this with fixed wall has all three degrees of freedom stalked. This changes allowing rotation about this one is not allowing motion. It's a true degrees of freedom. Stop over here. And this hinges Also stopping two degrees of freedom that is not allowing motion in the X direction and via direction. And this angel hair is also stopping to release of freedom total 6 to 2 plus two plus 26 plus three off this fixed body, 9 to 90 degrees of freedom are being stopped. And what we're total Did your freedom available there Three bodies. So three words the 90 days of freedom and all 90 days of freedom are being stopped. So that means this body is not moving. It has no degrees of freedom. So it cannot move, you know, decent. So that is a disgust Over here they're did these three plus two plus two plus 29 constraint on the system on the current religious bodies. So this body, the number of lives of freedom without constant is nine. Since there are nine independent constitutional system, no movement should take place in the system, so the system is Carla stable. 7. Types of Loads: So let's continue this question on any name mechanics. Now we will discuss equilibrium off structural systems. Structure, definition and engineering structure is an assembly of components interconnected with each other and designed to be capable of being immobile when external forces acting on it so external, or is there But they remain immobile and their assembly off components. There are many kind of stuck, just business specific engineering applications. It is important to know that loads that distracters who stand for designing the structure, safety civilly genius need to do analysis to return mind internal forces instructors such as bridges, buildings, flowers, dams, buyers, pavement slabs by planes, tanks and manageable inundating sectors. So we have to find internal forces in all these structural systems, and then we have to see that the material used is able to withstand this Internal force, similarly, in the aircraft sector has to be analyzed would remind force operating at various stages off the aircraft operation she pull. Ship structures such as different panels are part off a ship that attract attention off a neighbor architecture. Chemical engineers deal with pressure vessels, reactors and other similar structures that need to be analyzed and designed to withstand the appropriate roots. The machine parts and the support have to be designed to stand operating and idling. Glued start arising machines designed by mechanical engineers. What is being inverse ized is they're stuck just is used in all types of engineering. Transformer selected electronic circuit boards are spectra structures which are often trust to electrical engineers. Analysis off a structure for important internal forces one of the most important steps in their design procedure through door engineering application Ready widely. The principles of mechanics at Cavanda forces sustained by these structures and their associative movements remain same. Based on the design requirements various types off loads that affect internal forces Instructor can be identified Now we will see what other various types of fluids we have seen what other videos types of structures in different types of engineering. Now we will classify the loads the self it off the structure itself in love with the other immovable footings in the structure that contributed of it is a group together as dead loads to the world. Used over here is dead loads for the weight and the other immovable fittings, the movable items and the moving lords after the structural group together as live loads, for example, of bridges there and the train is moving over the bridge. So that is a live lord about from these lords, such as real lords knows soil pressure hydrostatic case, as they may be. So when Lord soil pressure hydrostatic all. These are also various types off loads that applying on a Steven sector lures such as impact lords and earthquakes loads caused heavy damage to the structure. But since their occasional such tools are many a time not accounted for in their designer structures to impact load something heavy falling on the building earthquake they are. These are very, very events, and these doors do not always apply. And if you designed for these lords, you might be costing too much. So when you have 50 make a judgment on the part off the junior instruct just suggest turbines, jet engines and compassion cylinders. Lures to to increasing temperature are called thermal lords play an important role. So in mechanical equipment, thermal loads are also there 8. Classification of Structures: So there's continual discussion on engineering mechanics. No, we will discuss classification of structures. Typical Lena Rely Spinner structure. If the plane in question is X y plane, then the following questions have meaning. Submission off forces in exploration equal to zero Submission of forces. Environ Election equal to zero A movement about Sarah X is equal to zero. These are the only three questions of equilibrium that apply to a planet structure cool, dimensional in a special structure, forces acting all the three perpendicular directions and three movement questions so total there are 60 questions. Submission or forces in exploration equals zero Summation of force in violation recorded. Zero. So machina forces in their direction. Zero you meant about XX zero women's world via zero moment. About 30 x zero. There are many structures and members for rich. The internal forces are a little insider compressive actual force. The structure in which all internal forces are along the axis of the members is called a trust. You will see it in detail. What is the address? Ah, one dimensional structure consists off travel Slowly read the internal for two. There turns out in the farm off sheer force or a bending moment so the weren't emotional, sexual like This is a beam, and this lent is the important criteria in the beam, the cutter section in the being and over the section we see that the desert and side foods and there is a sheer force. And there's a movement. A sheer force of that bridge erupts along the surface and the actual forces that that acts along the axis off the structure element that is considered. And this is a movement the applied at the point where the section has been card to for example. Over here we cut a section we see Oh, little side Force. This is a single member off trust. Then there is something called beam. In being record a section, we get us year forced movement and actual force itself and what head like forces are filled of. Lord is acting at the angle Is the part off a frame over here. When we cut a section, we will get a at Steerforth and Style Force and the movement all these. We will go into detail cables. They cannot sustain compression. Also, cables cannot have bending moments. They are the only they can militate and side force. They are quite flexible and can take different on, like trust members, which are rigid unlike cables. So the cables We can see a figure in a next video, so find her summarize plus actual force tension or compression only beam sheer force and bending woman frame. Actual first year force and Brendan Woman cable, then style action for solely shaft, sheer fourth national movement and a bending Moment and VIPs, sheer force actual personal and bending movements. In all, these stuck tested members are mostly prismatic, which with one dimension considered really large as compared to other two dimensions. So we could like it in a trust. Me take a member as a line was that line is important. The other dimension, Brevard told the line. That is not important. Who'd such price of members are called as prismatic members? Lourdes that after members having single prominent dimension can cause sheer force and bending movements, Inclined forces cause internal forces that that actually along the axis of the members there, the court action forces there are members in which the actual force can also out on the bream structures, causing internal actual forces in the beams. If if there is a beam Mr is the line and there's a force acting on industry perpendicular direction, it will not cause that shell force. But if a forced acting at that angle on the beam, then it will cause an actual force. Then we will also become actual force member, a typical example of factual forces. A column are a pillar, the main actually national forces, actual direction. So if we see there is a column calling me, you understand when we bake a building, we make us vertical structures called columns. And on the columns we make the roof. Some such types of on the column. The Lord is coming only along the axis off the column, their dresses there. Many other members Dr Center I realize to be actual members are designed for present for calculations literature. One sector of design force dresses play a major role in the internal forces. At their example of factual force numbers are base entry walls, monolithic towers, chimneys, spools off legs off our meter and and like mainly two types of Lords X on actual force members. One type of lord's body force with excellent every particle of the body to be talked off that there's a column in the building on which the roof is turning. So this column will take the load off the roof. But this column will have its own weight out so it will take its own weight to self. Ritual is also consideration in actual four members. The other types of there are distributed or concentrated, lose only equilibrium along the length of the members needs to be solved for the internal force in the actual member. So only one equal one equation off equilibrium will be there in actual force members that is, in the X direction along the direction off the member. So only one equilibrium in question. So let us see an example. We're here. Over here, Lord P. Exactly one is acting You do is acting on it be trees acting over there. No view Greek art a section record a section and then write an equilibrium equation Along this axis off the member internal forest, alerted along the length of the member can be found by simply sectioning normal to the exit off the required point and applying equilibrium equations for the free body off any one portion of the member that's obtained. So we cut the member and we really need to write free boarded the equilibrium A questions off the diagram off either this left side of the right side. So when we consider the left side the forces, we are having our people and we do. If we would have cost the right side, we would have to have the four speed three, but didn't let well. Let us have a leap p one and P two over here. And they say that this is unknown force at this point where the section has been cut, for example, in the member like forces in the members insp even plus B two plus FBC equal to zero this be one plus B two plus fbc is other plus all Ali all electing the plus direction. So they're all added and the summation that desert consummation is equal to zero. Because this board is not moving, the board is addressed, so the submission of forces acting on the body should be equal to zero. So the falls a P one plus P two plus forced BC equal to zero. Therefore forced B C is equal to minus P one plus p two. Since the external forces actual forces acting on that ship member may also change continuously with the length The normal practice is to evaluate expression for the intern force as a function off lengthwise Coordinate. So we have to that they from their representative variation off actual force, is called as the actual force diagram. So what it is being said over here is that this member force they if we cut section over here forces different If we cut section over here forces different a free card section over here forces different internal force will keep on changing throughout the being because at different point, different lords are coming into play. So along the lead, the actual forces Very so what is suggested is you. We started this point and call it zero and we'd cut a section after distance X and first the X lies between these people and we do began we then the x lies between BNC and then their slice between cnd. So we need because some after this at this point, the new Lord has come into play. So the situation will be different from what it is from cutting section over here. And where this cutting section we're here. So if the ones wherever there is road change, they need toe, apply a new card section Visual call at Registers X and then Florida actually forced diagram as the function off X. This diagram is Carl is the actual force. 9. Trusses: so we'll continue our discussion on engineering mechanics. Now we will discuss what this card as trusses precedence. Structural assembly off. Remember that supports the Lord's prime relief by taking internal actual forces. So in plus we have only a shell force. Usually the way it is assembled is responsible for the nature off Internal forces in the member mean actual forces, even though the member are capable of taking other types of force. Numbers can take other types of force, but the assemblies in such a way that it takes merely actuals. In practice, the trust members are connected to each other with gazette, grades and boards. Nuts. Our vents. These connections are north, sir. Idealized aspirin joints, interest analysis so desired. A truss. These are supported at two ends, and these are the individual members. You might have seen a dressing weird roofs or in the bridges or in the walk part ways. So these are very various types off trusses practice. How trust were intra skaters and Bharti motorists. These are more types of dresses practice how trust being think. Plus, these are for the roof dresses. Buses are used in many applications in engineering. They can be seen in still greedy roofing system transmission towers, display boards, screens that sector. They are simplest and are declaring in a system the Internet forcing trust member, which are actually maybe either inside or compressive. I remember his intention. All the particles of the members have been pulled apart, so this is a member, and it is in the compression or it is intention. Therefore, when the free board diagram off, the member is drawn, the actual four said the answer. The members will point away from each other, so they were pointing away from each other. Or they're pointing up opposite direction the national forces at the mentally members who works each other acting compression. Hence the member is in compression assembly of conventional dress. A trust consist of straight members being that there ends to each other who are to the support. The pain is an essential element. Interest system there transfers force from one member to the other. One number connected to the other. Bipin joint, or hinges are free to rotate about the pain through which they are connected. There are many situations in which more than two members are connected to each other to a single pin since being is a very small body. All forces on the peanuts you to become current at the center of the Quran and there is no movement existing about the center of the print. The following is a chance and get two sticks of trust system. Maybe Notre forces entrustment would always be along. The X is off the member external or supplied earlier insurance In a trust system, lording is only are the joints there is. That is what we assume. And if the laurel is at the center off, remember we dick, you're respected to bring it to the pain. In joints, only members offer trust are joined with each other trooping joints. Trust members are resumed with it less. There is no self. It only lowered its external learning institutions were loading is distributed. Another cast member e que and concentric ring roads are always applied at the ends off the member. Like we see that this is a This is important for us. These are members of the tests, and the Lord is applied at the pin joint. Yeah, consider it would imagine stress typically didn't figure that dress has five joints members three intact resources Family isn't extracted equilibrium in stationary. So there are 12345 and 12345 joints. These each of the joint sustains two degrees of freedom. Joint only allows the patient it doesn't allow translation motion, so it will be strange. The translation motions in X direction via direction. This means that we can have 5 to 2 equations of equilibrium available from five joints, so tiny questions are equilibrium are available. Removing the external constraints supports of the class system. We have a free body trust with three are known components off duty acting. Since each everybody off, the members will have one unknown. They're seven and no. One corresponding to seven and members that have to be sold for just there. Seven. Interest plus 3 10 and loans to be sold. So there are leg. They're too reaction food. One reaction force over here and there to reaction force overhead at the speed is support. And there is one reaction force in the Y direction at this support because this support stops two degrees of freedom, he doesn't allow motion. I selection. It doesn't allow motion very direction. The food it has to reaction forces in X direction and very direction, and this allows motion in the X direction it allow. The rotation, also holy, doesn't allow motion in the Y direction. So it is stopping one degrees of freedom. So it has one reaction. So there are three reaction forces and now there are 1234567 members. So each member has one internal force live either tension or compression. So there are seven and nose from the internal forces and there are three year knows from the reaction. So there are 10. Unknown is to direct n unknowns that have to be sold since the any questions are available , it is possible for to solve for any many unknown that arise from the structure you trust the unknowns are the reaction force is corresponding to the the strange, the magnitude of forces he needs. Member. Thus, in general, for a plane, a trustee number of questions there can be generated forest rating equilibrium off trust is equal to price the number off being joints because being joints stop stories of freedom, so there to equilibrium questions this number two into patient master number off unknowns that arise from their diet dress as the body with support reactions being are and let the number for unknowns, the rise from the member forces be equal to em. That's the crisis all said to be completely interminable. A soul label using questions over equilibrium alone if I m plus R Equal toe groupie Booby GOP is the number off being joined. So number of joints and has every pin joint has two questions off equilibrium to be questions of equilibrium and is the number off members. And our is the number off the reaction forces. If these two are equal, then equilibrium questions are sufficient to solve for the unknowns. Such trusts our core determinate dress or just read it Planet Russ for a joint. The Dude that three dimensional space turns in the Murphy Questions becomes three Purple Butt joint and the Ford's condition off for full term in issues, protesters becomes M plus three for +23 p. This is for three dimensional stress, if in the equations on the left side, and the more often known is less than the right side in a more off questions possible. The end. In order to solve this store knows we have more questions that needed. This will lead to more than one possible solution. In other words, there is no uniqueness in the solution. If there are more number of questions than the unknowns, then the solution will not be unique. This we know from the linear algebra there are more confusion system possible, and this gun off. I don't leave. The system ceases to be starting Libya and that there is a possibility off motion, so it is no longer a structure. So to test system is called unstable trust or under do tress. On the other hand, when the left hand side they question more for noticed better than I can cite in the perfectly questions, then in order to sizzle, to stumble briefly when you small number for questions. So it's number for questions is less and number of unknown since more then you cannot solve the system from the equilibrium equations. We need war number for questions such a trusted scored indeterminate system or over radio tress. For such a system, we must look up close Leander deformations in each member must because this turn with respect to each other, so that total displacement of the joy is unique in a dress system. Two. From the deformations, we get another. The questions which we can solve along with the equilibrium equation to solve for the rest system, a system of consistency off deformations in various members is compatibility in conditions , so these deformation equations are called from practically questions. So we're cool Taizo questions, equilibrium questions and compatibility questions. When equilibrium equations are not sufficient to solve for the system. This is the executions are less and the unknowns are more than we require more Rick Lucien's and here comes in the rule of the compatibility conditions by the force in the two Terminators are blind, so the properties off members, the force in the indeterminate trust will be function off section properties that has lent of the member prosection lady a more bless off elasticity 10. Beams: so notice. Continue our discussion. Engineering mechanics. Now we will discuss beams. Dreams are members that undergo prime really bending. Why taking a little? They don't foresee that appearing beams are by any moments, and sheer force will see their terrible this pregnant moment. And where do the sheer force? The geometry of the beam is usually prismatic and straight. What do you mean by prismatic? We discussed earlier that if one dimension is prominent compared to other directions, then it is called the prismatic, so it will be let off. The beam is important to their displacement. E teams are often parts of frame structures being an important part in many applications. The good understanding off the characteristics and analysis of beeps is essential in design . It is important to know if the beam considered has the capacity to withstand the internal forces that appear in the beam. So these are various types of beams, a simply supported beam on it being joined at one and ruler 200. Other than a cantilever beam, it is fixed at one end. A propped cantilever cantilever at Vernon and supported at other than fixed, be fixed at both the ends continuous being the span over various types, off hinges and sub ruler supports. According to us being, this is a continuous beam, and if you cut a section over here, we can see the sheer force and the bending moment acting on this section from the equations equilibrium conditions, it is possible to arrive with the internal forces acting out on the beam next from like we have enough. We haven't internal force this year. 47 Burning moment. Now we write Equitable Immigration System, Mission of Forces in Violation equal to zero and submission of forces in X direction equal to zero, and movement about the X is equal to zero. If Writethr equilibrium conditions, we can arrive at the internal force off the numbers. Acting at the dream, the knowledge off helps in defining out Jesse's. Once you find internal force, you can find stresses, strains and displacements, which are vital for us. They re signal existing capacity for the external loan. A beam is usually Laurie Trance Worsley. We're doing the looting transfer Sleep. Is that your hair? The beam this'll oor beam is prismatic. It is in this direction, and trance worse is put in a particular direction. Lord is generally coming on the beam. Sometimes the conservative movement could be getting us or to a bream structural component . Very really. One man contact form of distributed movements they still transfers. Rules are often concentrated force or distributed lords to be a writer. Concentric loads are distributed. Force beams can be. I realized his lying structure, since only one them in China. Along the length is necessary for the evaluation off internal forces off the beam, The bending moment and this year force at any given section can be well, Richard, we're considering the static equilibrium off any two sections. There. Dallas I. Senator Divide Growing the free body diagram off the section to redraw free world. It is very clear that the bending moment and shear force memory along the length of the beam. The relation of these many momentum shear forces and of the letter of the beam can be represented by diagrams called by any woman diagrams and sheer force diagrams. Dreams frames are structures with components, having internal force you to actually transfers except external lords. Typically they Denel four SAARC, actually and sheer force resultant along the any moments off the resultant So he's got desire. The various types off frames. Lord is acting like this is actual or on this member. And this is a transfer US Lord. So this is this is a conservatory lure we can trust. We cut a section over here so we can test when we cut a section, we get three floors, the sheer force, the burning woman and the actual forced to VeriSign beams we had made this year for some burning movement into frames. We have the actual force also, that these are the various examples or frames for all the members of a frame. It is possible to pro action for sheer force of bending my diagram seen all since all their dinner forces approximating this tape off. 11. Cables and Shafts: So So let's continue our discussion on engineering mechanics. Now we will discuss cables and shops. So what are cables? Cables are flexible, lower caring members that carry transfers. Lord, by the extra attention, they're similar toe beams in there. They carried Lord applied transfers to them. They are similar to trust members, since they resist lords only by actual tension. Cables are normally used to carry distributed cable systems in cable stayed bridges. So over here we see better. This this is a This is a cable and this bridge is hanging with the cable. And this Various lords, concentrated lords are acting on the cable. And this is this thesis. Lords are perpendicular to the cable. Should they're called transports Lord. But the Lord that is developed internal force, that is their been their cable. It is there tension force This forced retain the tension forces ever been the cable. So this is similar to trust because they like attention force. And they're similar toe beams because they carry the transfer slower. If you were example off cable stayed. Bridges are here. This cable is there and this is the bridge. And this concept point lords are acting on the cable supporting the weight off the bridge. And now this is another example off the Brooklyn Bridge in New York. It is a cable stayed bridge. The cables are held to the bridge, and this overall, the bigger cable is taking all the Lord. Another example of cable stayed bridges is This is the cable, and these are the lords, which are acting on the gable, so cables are used to carry the deck loads in the cable stayed bridges. Some of the prominent devastated, but isn't NVR knew how Rusbridger Calcutta and the footbridge off Tom Dula and luxury jeweler at Rishikesh. From an engineering perspective, the constraints available in the design off a cable system are the coordinate off the supports between which there cable is to spend, as well as the lords that need to be supported by the cable system. The design parameters that need to decided are the profile on lent off the table and the maximum load our attention in the cable. Since the cable is a flexible member, it will SAG and Azuma provide that is best suited to carry the Lord's intention. The extent to which the gable sex is not a function off only off lords but also the intentions that are applied to the cable. This phenomenon is evident in our billions billions of fastening groups to hand groups. So when you put a rope to hang the clothes, then you put clothes. The cable will sag, it will come down. But if it is Harry Reid, I cleared the ends. It is being pulled that I cleared the ends. Then it will not sag. That is what it is saying that cables for the cable sang is a function not only off the Lord applied, but also on the intention there supplied to the cable. The span of the cable is the horizontal end off the cable between the supports. So here we see the these are the cable like we saw in the bridges. And this is the bridge and this other rope teach our time. And these are applying point loads after the cable. Ideally, this caper should be Lord should be so close to each other that it becomes a uniformly little distribution. And when it will be uniformly loaded, the shape it will assume will be a parabola. But when it is not involved Loaded point loads are there. It will assume this kind of shape shafts a typical example off number that primary care is national movements. Is that off the shelf? The chest x l components attached to motors to transmit Talk to our lord system so more that is connected to a purely through a shaft. Other applications the range from springs to corner of the beams off building frame springs are also example where Dorschner loads are coming. So we see this is a motor and a shaft will be connected to do this motor. Good Apuuli. So this is the rotor and the rotor is rotating on a shaft. So the way this is buried try system this girls and girls are connected through shaft to other police or other gear make and very time mechanisms. Such structural components are usually prismatic and are subject dark producing force at the different locations. So the prismatic means we discussed previously Also, that one dimension is from Internet. There are two ways to represent Arc one back of radio, anti clockwise and clockwise Negative. Well, I other by a double headed arrow. So we can so we'll see soon enough figure. So we're here. The torch in this talk is applied. The stork is applying for these areas. Gears and this are the shaft. And are these every gears on this matter? Bad, poorly Arraignment This it is applying a talk. So we got the section over here and we focused our attention on this section. This ISTEA one and the Sistine too. One is there thinking our direction to do their thing other direction and resume their TX is acting in this direction. Then we take submission of movements about this X X is equal to zero interest even minus t two plus t X equals zero. So T X is equal to t one t two minus t one. The Lord's in the stock just can visit the soul before internal talk by applying to Arsenal Moment equilibrium equation on the free body octane Best action at a given point at a distance. X from one end of the shaft, as depicted in the figure. So like three is a free body diagram and we caught a section at a distance X and then we flying the internal torch in the distance develop in the body 12. 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