So we have a negative or right. Ah, that is times 100 millimeters squared. So, in fact, forced. We cannot look at, uh, this section here We have members D C, D B and C J. All right. So as you can see, zero is on the right of the decimal point because it decimal point is there and zeros afterwards, and it's to the right off all non zero significant digits. It is acting clockwise, which is into the page So by Victor analysis, I mean, you have i, j and K components off the forces. It's off each of the shapes, plus the areas off each of the shapes times the part of the perpendicular distance between the access off I and the access off I hat. We will have to calculate the result in moments. Both then And it'll look like this. All right, we can then calculate third area. Why, all right, And just another little hints for pretty systems watching. Alrighty. So to calculate the moment m o about 00.0 If the position Vector z could do this and the force is equal to this, you would do it like this. All right. The magnitude of the force if is given as 300 Newtons, so he could simply then do this. If why multiplied by J? As you can see here, X is equal to negative B X. So what if somebody did? I So that's just a way to figure it out. All right, so this means we have to section point B, and then you can choose whether you want to work with the left hand side or the right inside. And if we have the Cartesian plane about 0.0 and going towards the right. So the moments some of the moment about point a must equal zero. So therefore em is equal to mine. We're right. All right, then, if b cause 40 multiplied by 888. Vector Operations Example 2: Hey, guys. Three. Town becomes 10 to the power of minus one. So I'm just going to write that out. So something you'll notice in this module. That six meters minus 10 at six meters. For example, here you haven't unknown A Y and B why, If you do the some of the moments that point A. All right, so that's one of the 86 at times 1 40 All right, because the height is once again 1 40 This height here on the base length is 200. HB is a zero force member. So if you have a Cartesian plane, x and Y axes on, you have a force, all right. So you know that's negative. All right. So you'd be left with five Killer Newtons multiplied by cause 21.8 in the J direction plus five killing U turns multiplied by sine 21.8 could not be working with 2/7 Sign the opposite of the hard part in use in the que direction all rights And then that is basically the exact same thing that will both give you the same value. All right, and then see X. But you can just flip through your textbook and you will find a summary off these drawings with the definitions Andi, the forces and moments that acts on those certain situations. C, we use the formula. We will do it about the origin about points have been. Positives it direction, which is plus 300 sign 50. So here we have the eyes. It's negative. SI Units and Prefixes: in this video, I'll be discussing s i units on its prefixes. Then both the members are zero force members. In our case, it's the Y axis on the access off I had, which is the access through the central right off the shape as defined over here. So basically, if you you get a negative answer, the force chosen acts in the opposite direction to the direction chosen in the free body diagram. So you have the 300 new tunes. That is not Colin. And you could also draw a free body diagram at B, which is on the actual weight. And the notice that X is equal to 1.667 meters. All right, so if we start in the why direction we know this angle here is equal to 30 degrees, all right, because we quite alternating angles. Force a d multiplied by visit components length five divided by the high part in use, which is 7.874 All right, so he said five divided by this length. Centroids and Inertia. Positive 1.5 x minus three multiplied. So if gg multiplied by sine off duty All right, um, minus four. There's a free body diagram. 25. All right, so that's from zero two meters. If now we could, either. In this case, it's meters because the length of the rope is five meters. And some markers might not even give you, um, the mark for the final answer if you didn't show waking out. All right, then, The third member that is not Colin. But this is actually a three. All right. If that angle vase offer and that angle days beater, it's equal. So you're basically just add all these valued minus three I plus four j plus four I plus two j plus three I minus five j So are highlighted all the eyes and all the jays of in you . Just know that those two things mean exactly the same thing. Um, so here we have 300 cost 60 minus 300. That's equal to sine theta minus 110 plus 10. All right, so now we can do that. So then the force A D is equal to see the following You can just like the Intrakota Later, for 100 times. If you ever see a letter, for example, if on its own, then that means it's the magnitude off if. In the next video, we will be doing a recap off geometry because geometry is also highly used in this marginal . So the central oId off the rectangle is in the middle and the century off this rectangle is in its middle. Length can be different, but basically you use these formulas over here to find unknowns. All right, so we have the beam section. Which is equal to cause Peter if one plus 400 all right, that actually wouldn't solve anything. So this distance here all right, is three points, 308 So if we redraw that, yeah, 3.38 meters at an unknown height. Is this length over here? But I always do this. All right, so the question asked us to determine the result in force and specify were on the beam. 11. So therefore, force A's and compression force be alright. We have a force acting along the Does it explain? He three minus eight times seven. Negative force a D multiplied by its components, which is the y Direction six divided by the high party. So you basically need to know how to calculate the area off a rectangle and a triangle, which is length times, breadth. Why, that is because the market may refuse to mark a question, um, without and accompanied free body diagram. But if you want to rot it as a Cartesian victor, you put a line on top of it. So this may be here is zero force member cancer gave me applying scenario to all right this year, so this may be here. That is 6.8 three meters. You could have done this with just knew temper meters, and then get Carter answer in mutants. Um, and now we can some them. All right, So if I withdrew this force to look like this, this is at a distance off 0.5 meters above his it access. All right. All right, then. So that means we have a negative J that is negative 0.6 j. He's two answers all the same, which means these two couples, our equivalence couples. Once again, it's clockwise direction. All right. Yeah, we have a 500 meter rates. We have the force a D as a component, acting in a negative Y direction All right, so right. If you have two zeros. Position Vectors and Vectors Directed Along A Line Example: a rope causes a force off. So when you rounding off, if the values above five year round up, if it's below five, you don't round off. We also have our seven killer Newton force, creating a negative moments about point D. So that's minus 7000 multiplied by the distance between them. So four multiplied by 1.5 is six, six kill. See search results for this author. So that length is one. 1.2 I All right? So first step to these equilibrium problems is drawing the free body diagram. So this is now our position. All right. The Fundamentals of Engineering (FE) exam is generally your first step in the process to becoming a professional licensed engineer (P.E.). Diagram on that is your final answer All right, So how do you do this? How the signs come into play when calculating the same droid. This forms of square. All right, so that does not mean it is equal to 400. Um, always use your equilibrium equations to answer these questions. Fundamentals of Engineering Exam Review Other Disciplines FE Specifications Topic: Fluid Mechanics and Dynamics of Liquids 8-12 FE exam problems Exam Problem Numbers A. Fluid properties (e.g., Newtonian, non-Newtonian) 73, 77 B. Oh, is this point here, which is the center off this bar? E i and I j or Kaleena. The answer is 180. All right, if you look here. Right. But the Cartesian victor off if two is not given to us. All right? There you have. And then, if you do some of my moments that be, you are would cancel our because there's no perpendicular distance between B y and the point B, and then you'd be able to calculate a what. Um, this Because zero force members are used to increased ability off the trust during construction. That would then mean that you would have to use the central off a common shape. And here we have the which represents the sheer force in Killer Newtons. So now we have when equation One unknown. Jay, I crossed K is negative j So I noticed. Rigid Body Equilibrium in Two Dimensions Example, 43. Loading is 1.5 killer Newtons per meter multiplied by X minus two. I hat here, we have positive Jay hat on Dhere. All right, so in this video, we will be drawing the bending moment off being so we can do that by storm. So then force deejay the not equal to Zahra and Force D. C is not equal to Zahra. How to do the Cross Product on your Calculator, 29. Andi, there you have. Andi, half length times breath, respectively. All right, if you want to calculate, calculate the force Victor directed along the line, you then multiply this unit, Victor by the magnitude off the force. It's a shame that acts in this direction de eggs. All right, so now this makes an angle with the horizontal. On this distance. On. Um, plus 1.2 I times. All right, so, looking at this again, we want to calculate this angle over here offer, All right, because if we have offer, offer is equal to deter plus 20 so we can equate offer to theater plus 20 on we can, then soul four feet. Density 5. So we know 2.4 meters. This one's a little bit more complicated, but it's not too complicated. Divide that by two, you're going to have four times to which is eight and then you are going to be left with four killer Newtons. So that is what you're actually looking for. A. All right, so now, to calculate the unit victor off B. So now, um, if you want to convert these s i units to, um to like exponential or scientific notation, you then use the following. All right, All right. Are you an author? All right, so, um, if you're negative answer, obviously art means compression and in means tension. So now we can go along and do our equilibrium equations. So step one is the side Great yukata section the members so that we know. And we get a value of 18,000 mutants. So the first step you need to do is define your X and y axis. So we'll do the cross product. Position Vectors and Vectors Directed Along A Line, 14. Calculate the X and Y locations off. I'm just going to say equals 60 mutants. And wherever there isn't the metal work piece that would represent the negative space, Alright. So, using our calculator, we can just plug in all these values minus six times three plus four times three plus five times zero, which is just there. So basically, that just means you can substitute minus 1.5 when X is too minus one. For trigonometry, this is going to be used everywhere in this module, especially these things are very, very common. And the third is that the tension in the same rope is always equal. Ethics and Business - Engineering economics, Contracts. All right, so here we have seven mutants. You can use the brie abbreviation F B D in tests if BD stands for free body diagram, there's a video on free body diagrams. Computational Tools. So it's three divided by three. So that would be left with 1.2 as well, J All right. So it's an I, but in the negative direction, because this is hitting in the negative high direction. Particle Equilibrium in Two Dimensions, 22. If use the following formulas All right, the angle between the Cartesian for Victor force on the X axis is offer. So that is equal to the sum off the moments. Well, verse cross product equal. We will then have the following. A journal bearing will have, ah, if X and if said, as well as a moment X and a moment, said notice. But in the next video, we will be doing an example off identifying the zero force members from a trust. A couple moments is formed when to Colin ear forces. All right, and then the same with the heights. So then he could not arrive force if e is not equal cheese era force e I is not equal to zero, and force e d is not equal to sever. So, like I mentioned to you earlier, how do you know to use the mythical sections? Searched 2.4145? Then that point, they would represent the central or your shape. So then you define this inertia as negative, all right, because it triangle is positive space. All right, because I would rotate point G in this direction, which is clockwise or I g to force. If you have a roller, the forceful act perpendicular to, um, the surface once again that it is really not. So where we can do now is define our A and R O C. And then do the cross product. That is how you had to draw your final answer. So the area is equal to the magnitude off the force. So if we are doing some of the forces in the X direction, All right. So if we assume it's an equilateral triangle and that means the high part in use length here, his six meters. Right. Oh, about 00.0 equals zero. And then we have the third external force beat J on. And then secondly, the bending moment within the section off the distributed learning So you can start by drawing the free body diagram. So if we look at this diagram here, um, we have the situation of here where we have forced Member F G and member G E that are connected at a point. So that is, is there a 0.6 meters in the J direction just right? So if the moment m is acting anti clockwise, you know, aim is positive, all right? There are 26 whole. So if we taking the left hand side off section beam, then the sign convention means the moment acts in the anti clockwise direction. A 1350.8. All right. So in the next video, we will be doing an example off, hard to calculate the same toyed off a worth piece or a compass. He's all have little hats on top of them. So we know Force E. D. Is an article 20 Andi, we then follow the same rules as the scenario to over here. Onda six meters, where this formula is the moment between zero meters and two meters. You could have just used this length, which is 3.6 meters. So here we have, um, external force acting at the trust joint. Calculate the the nausea or the moment of inertia about the Y axis. So there are three things you need to know. So then, plus minus five, I cross minus 28 j plus minus five. So could be centimeters. Four comma 642 j. I divided by that which will give you 0.685 to I Farraj, then eight divided by the magnitude of the force, which is equal to 0.5482 J, right, and then minus seven, divided by the magnitude of the force is equal to minus 0.47 96 K And then once again, no units or right. So, therefore be X is equal to negative eggs. Fundamentals of Mechanical Engineering. by S S Bhavikatti | Read Reviews. • Knowledge of Engineering Mechanics is very essential for an engineer in planning, designing and construction of various types of structures & machines. Moment of a Force About a Point: determine the moment off the force at a about point B, give the answer as a Cartesian victor. So then I d equal to the square it off. I notice how we get a positive value for B Y, which means we assume the correct direction off B Y. Be sure not to forget that minus 600 equals plus 5 92.6 K. And that is equal well, in the units mutiny meters. Clockwise is always positive. How do you do that? All right, so this means we have to first define the force as a Cartesian victor as well as defined the unit victor off B. C. So I'll start off by doing the Cartesian victor off this force if all right, So obviously you have to use these angles to find the i j and K components of this force. 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