We were looking at the dispersion relation for capillary gravity waves in deep water. We had found that the dispersion relation was given by this relation G k plus T k cube by rho the whole thing to the power half. We had plotted the phase speed as a function of k and we had found that there is a qualitative difference due to the inclusion of surface tension. In particular, the phase speed for a pure gravity wave is a monotonic curve whereas the phase speed for a capillary gravity dispersion relation has decreases at small k but then again starts increasing at large k. So, there is a minimum. So, this is the minimum. We had also found that for sufficiently small k, the dispersion relation can be well approximated as if it is a pure gravity wave. For sufficiently large k, it can be again approximated as a pure capillary wave. In an intermediate regime which is in this regime, neither the green curve nor the orange curve represents the full dispersion relation accurately. In that region, one has to take into account the effect of both gravity and capillarity. Let us make a quick estimate of what is the wavelength when we should be taking full both gravity and capillarity into account and what are the wavelengths where we do not need to worry about one of them. So, as you can see the phase speed expression has two parts to it g by k plus tk by rho to the power half. For k going to 0, Cp is well approximated as g by k to the power half. For k going to infinity, Cp is once again well approximated by tk by rho to the power half. At intermediate values, we expect both terms to be of the same size and that is the regime when both capillarity and gravity effects are of the same size and neither of them can be neglected in favor of the other. So, we can make a very quick estimate. We are saying that we are looking for that range of k where g by k is the same size as tk by rho. g, t and rho are fixed. For a given set of fluid parameters, surface tension, the density of the fluid and acceleration due to gravity is fixed. This tells us the range of wave numbers or a particular cutoff wave number around which capillary gravity waves are important or rather capillary gravity effects are important and far away one of these two limits is valid. So, you can immediately see that that k is given by rho g by t to the power half. If we compute the lambda corresponding to that k, so k is given by rho g by t to the power half, k is 2 pi by lambda. So, this is 2 pi by lambda which is equal to rho g by t to the power half. So, one can compute lambda is 2 pi t by rho g to the power half. If you plug in air water values of surface tension t that is around 72 in CGS units, rho is 1 for water and g is 980 in CGS units. If you plug in this and calculate, you will find that lambda is approximately 17 millimeter. So, this is telling you that for wavelengths lambda much, much greater than 17 millimeter, the wave is nearly a pure gravity wave. So, lambda becoming very large, this implies k going to 0. Lambda much, much less than 17 millimeter, this is nearly a pure capillary wave. Lambda in the window of 17 millimeter, 17 plus minus some delta, capillary and gravity effects are both important and this becomes a capillary gravity waves. One cannot drop either gravity from the dispersion relation or capillary from the dispersion relation. Again, these estimates are valid only for air and water. If we change the fluid, then the surface tension value will change and so these estimates will change. In this region, when neither the green curve nor the orange curve are good approximations to the blue curve, we have to be careful and we have to include both capillary t effects and gravity into the dispersion relation and the resultant waves will behave as capillary gravity waves. Note that the phase speed has a minimum. The phase speed is not a monotonic function. In particular, I encourage you to think about the groups velocity of a capillary gravity wave. You will see that the group velocity, so if you take the full dispersion relation, omega is equal to g by k plus t k by rho to the power half and if you compute d omega by d k, the group velocity for capillary gravity waves, you will find that even that has a minimum. This has a lot of physical consequences. For example, the existence of this minimum and below which there is no, so the phase speed looks like this as we have seen. A similar curve will also be there for group velocity. This has physical consequences. I encourage you to think about this, particularly in relation to the Cauchy Poisson problem. In the Cauchy Poisson problem, we had found that omega by k, so for t going to infinity and for an observer whose x by t is constant, we had found that omega by k or rather d omega by d k is the dominant contribution is given by this equation. Now, when your group velocity curve has a minimum, then below a certain speed, this equation does not have any solutions. So, when x by t is below a certain speed, there is no solutions to this equation. Above a certain speed, there are two solutions. There is one k here and there is another k there. One k coming from the capillary branch of the dispersion relation, another coming from the gravity branch of the dispersion relation. The wavelengths will be very different. This has physical consequences for what the observer sees locally. I encourage you to think about it. Now, let us look at this limit of lambda becoming much, much greater than 17 millimeter. So, in the case of air water, you can immediately see that if we deal with let us say a 1 meter wave, which would be the case when we are in an oceanic context, then you can immediately see then in oceans, waves are almost exclusively gravity waves. So, a wave of this wavelength or above is typically a gravity wave. Tsunamis are entirely gravity waves. In fact, they do not even behave like deep water waves as we will see shortly. Now, as we take this limit lambda going to infinity, it is also clear that the deep water approximation itself is going to break down. Remember that we had said that we are going to assume that the depth of the fluid is infinite. Now, in practice, in a given situation, the depth is never infinite. And so, that approximation is valid only when the waves that we are looking at are sufficiently the wavelength of the waves is sufficiently small compared to the depth of the fluid. So, if I have a situation where the wavelength of the fluid of the wave is much, much smaller than the depth, the undisturbed depth h. So, this is the wavelength. Then I expect this to be a situation. So, lambda is much, much less than h. So, I expect this to be a situation where the deep water approximation should hold good. However, as I make lambda bigger and bigger, you can see that the deep water approximation is going to fail because as lambda becomes of the same size of h, the wave will start feeling the presence of a bottom wall. In particular, when lambda becomes much, much greater than h, then we have the reverse limit which is called the shallow water approximation. We will look at the shallow water approximation in some detail later in the course. Let us first work out what is the correction to the dispersion relation when we have a pool of finite depth. So, waves on a pool of finite depth. Until now, we have only done deep water. We have looked at capillary waves, we have looked at gravity waves, we have looked at capillary gravity waves.  Our coordinate system remains exactly the same as before. So, this is my interface, this is my undisturbed surface at z is equal to 0. Earlier, z was going all the way to minus infinity. Now, it will go to some lower level capital H. So, put a bottom wall and the depth is a constant h. So, this is a wall and so we will have to repeat our analysis. You can see that this is just a small modification to the boundary condition. However, the expressions will become slightly different now because earlier we had boundedness constraints at z is equal to minus infinity. We use that to eliminate one of the exponentials in z. Now, both the exponentials will survive. That is the essential difference which will be there as far as the mathematical calculation is concerned. So, let us do it. So, we have the Laplace equation del square phi by del x square plus del square phi by del z square is equal to 0. This is like before. Then we have, so I am going to do it only for gravity waves. And the homework for you will be to try this by putting in surface tension also. It is just a modification to the pressure boundary condition. One has to just replace pressure with t by rho times divergence of N as I did in the last example. I will right now assume pressure to be 0 as we have done so far. So, I will do it for gravity waves on finite depth. So, let us write down the relations. So, the Bernoulli equation pressure is 0. So, there is no pressure term in the Bernoulli equation. This is Bernoulli equation applied at the surface like before plus g eta is equal to 0. Then we have the kinematic boundary condition linearized minus del phi by del z. Again at z is equal to 0 is 0. And then we also have a no penetration condition. So, no fluid goes through the wall. So, no penetration. We have to remember that we cannot impose no slip. This is an inviscid analysis. We cannot impose two boundary conditions at the wall. We can only impose one. Where if you do a viscous analysis, then you will be able to impose a no slip condition in order to in addition to the no penetration condition. So, we will have a no penetration condition which is del phi by del z which tells me the vertical velocity at the wall is 0. So, del phi by del z at z is equal to minus h. We call that the positive z direction is upwards. So, the negative z direction is downwards and this h is a capital is a positive quantity. So, h is greater than 0 is 0. So, this is the only difference. Rest of the equations remain the same like before and we have to ask ourselves how does this modify the analysis. So, let us look at it. So, by variable separation arguments once again, it is a linear combination of cos kx and sin kx. I will put a prime here because these constants will get multiplied by something and then I will eliminate the prime. So, cos kx plus b prime sin kx. In the vertical direction earlier we were only putting exponential kz into a constant. Now, we will have to put both the exponentials because the domain is finite in the vertical direction. So, in general in this direction in the z direction it is C e to the power kz plus d e to the power minus kz. This second term was not there earlier now it is going to be there e to the power i omega t eta is equal to like before some e cos kx plus f sin kx into e to the power i omega t. This is let us call it 1 and 2. We can go and plug it into the boundary conditions. Now, if let us first eliminate the no penetration condition or let us first satisfy the no penetration condition. The no penetration condition says del phi by del z at z is equal to minus h is 0. This is the only part which depends on z the rest is z independent. So, I can differentiate this with respect to z at z is equal to minus h and set the resultant expression to 0. That gives me one equation which says k times C e to the power kh or k minus h minus d because there is a derivative with respect to z. So, minus k will come here e to the power plus kh is equal to 0. This is the equation that we obtain. This allows me to determine C in terms of D or rather D in terms of C. So, you can see that C is equal to D e to the power twice kh or let me express D in terms of C. So, D is C e to the power minus 2 kh. I am going to use this to get rid of D in all my expressions. So, this tells me that phi is a prime cos kx plus b prime sin kx into you can see that I am going to get rid of D and express it in terms of C. So, C e to the power kz plus C e to the power minus kz minus twice kh into e to the power i omega t. I am going to pull out this C and multiply it with a prime and b prime. These are in general complex constants and a prime into C is going to be a and b prime into C is going to be b. This is why I had put a prime so that I could use the symbols a and b later.  So, this is our normal mode form and now we have already taken into account the no penetration boundary condition. Now, all we need to do is just like what we have done until now take these two expressions substitute them into the two boundary conditions that we have and obtain the dispersion relation. Once again the algebra is straightforward you can do it yourself. I am just going to write down the final answers. So, once again we are going to get four algebraic equations in four unknowns. They are coming from the coefficients of cos kx and sin kx and of course, there is a complex conjugate part like before. So, our equations are going to be. So, I am going to skip the algebra I encourage you to try it for yourself. You just have to take these expressions that I have written the expression for phi. So, these two expressions take this and plug it into the two boundary conditions these two. Note that we are not putting surface tension. So, we do not have to worry about calculation of divergence of unit normal and so on and so forth. Once you have done this calculation, then you can restore surface tension back into the Bernoulli equation, add that term and calculate what is the modified dispersion relation for capillary gravity waves on a pool of finite depth. Right now we are just doing surface gravity waves on a pool of finite depth. There is no contribution from surface tension. So, we have to take the expressions that I have put in this rectangular box here and we have to substitute it into these two boundary conditions. And then we have to eliminate we have to set the coefficients of cos kx and sin kx in both the equations to 0 that will give us four equations in four unknowns. Our unknowns are going to be a, b, e and f. So, a, b, e and f in general these are complex constants as usual. So, I am going to straight away write down the equations that one would obtain. You can substitute and cross check that these equations are correct. So, one equation is i omega 1 plus e to the power minus twice k h a plus g e is equal to 0. The next equation is this is all coefficients of cos x and sin x cos kx and sin kx. Then one, two more. So, two of them will come from the Bernoulli equation, the other two will come from the enigmatic boundary condition. So, i omega e minus k a into 1 minus e minus 2 k h is equal to 0.  So, like before we have four equations in four unknowns. How do you check the validity of these equations? You can take the limit h going to infinity. All the exponential terms will drop because they will go to 0. And in that limit you should recover exactly the same equation that we had earlier found for surface gravity waves in deep water. I encourage you to try this on your own and compare with the results that we had earlier and make sure that the equation that you recover in this limit of h going to infinity, deep water limit is gives you the same equations as before. Let us continue. So, the matrix. So, this is like usual. This is a matrix for a, b, e and f is equal to homogeneous set of equations 0, 0, 0, 0. And we are looking for a non-trivial solution. So, the elements are i omega 1 plus exponential minus 2 k h. That is the coefficient of a, then 0 is the coefficient of b, the coefficient of e is g and then 0. Similarly, 0, the second element coefficient of b is i omega plus e to the power minus 2 is k h. The third element is 0 and the fourth element is g. Then the coefficient of a is minus k, 1 minus e to the power minus 2 is k h. Second element is 0, the coefficient of e is i omega and then 0. And then this is 0 minus k, the coefficient of b, 0 i omega. If you take the determinant of that matrix to 0, this gives you the dispersion relation. Once again you will get a quartic. The quartic is factorizable as a quadratic. So, you will get the quartic omega square into 1 plus e to the power minus 2 k h minus g k into 1 minus exponential of minus 2 k h whole square is equal to 0. I have written it in such a form that if you said this term, if you take this limit h going to infinity, then this term and this term will go to 0 and you will recover your old quartic which was omega square minus g k whole square is equal to 0. We had done this earlier when we did surface gravity waves in deep water. So, this just generalizes that bringing in the effect of finite depth. So, those factors that we are getting represent the effect of finite depth. So, let us work on this. So, we obtain omega square is equal to g k into 1 minus exponential of minus 2 k h divided by 1 plus exponential of minus 2 k h. I can simplify this a little bit by multiplying numerator and denominator by exponential k h. If I do that then this becomes omega square is equal to g k exponential of k h minus exponential of minus k h divided by exponential of k h plus exponential of minus k h. Recall that this is related to hyperbolic functions. Hyperbolic functions are defined as by taking exponential and splitting it into odd and even parts. So, the even part is e to the power x plus e to the power minus x by 2 and the odd part is e to the power minus x by 2. This is cos hyperbolic of x and this is sine hyperbolic of x. Sine hyperbolic by cos hyperbolic is tan hyperbolic of x and tan hyperbolic of x looks like this. So, this is exactly of the tan hyperbolic form. So, I can write this as g k tan hyperbolic k h and so comes out our dispersion relation for surface gravity waves on finite depth. Dispersion relation for surface gravity waves on a pool of finite depth. What is this telling us physically? Recall that we had said that as lambda becomes bigger and bigger. So, lambda goes to infinity or k goes to 0, we get gravity waves. Now earlier we had found that the phase speed of gravity waves actually increases without bound in deep water. So, if you recall our earlier dispersion relation for the capital gravity waves in deep water, you can see that as k goes to 0, the blue curve increases without bound. So, the phase speed is becoming bigger and bigger and bigger as the wavelength is becoming longer and longer. In the Cauchy Poisson problem, we have seen this behavior for gravity waves. The further we go outward, the longer is the wave and the faster it travels. So, this behavior gets rectified once we put in finite depth. As I said earlier, the effect of finite depth starts to be felt when the wavelength of the wave starts getting comparable to the depth of the pool on which the wave is propagating. So, if we start with a pool of finite depth and if we have waves whose wavelengths are very short compared to the depth, then these waves behave as if they are propagating on deep water. However, if we take waves which are much, which are whose wavelength is comparable to the depth, then they start feeling the bottom and then the correction to the dispersion relation is becomes necessary. In particular, if we take the limit of lambda going to infinity. So, lambda going to infinity. So, holding h fixed, I hold the depth of the pool fixed and I take lambda going to infinity. This is equivalent to the limit k h going to 0, because when lambda goes to infinity, h is anyway fixed. So, k goes to 0. So, k h goes to 0. What happens to this dispersion relation? This dispersion relation suffers a qualitative change. So, you can see what is the behavior of tan hyperbolic x for very small x. That is because our tan hyperbolic has argument k h and I want this limit k h going to 0. So, tan hyperbolic x for very small x. You can see the tan hyperbolic x for very small x is just x. You can do a Taylor series expansion on this and convince yourself the tan hyperbolic x for very small x is just x. The first term is x and so, for sufficiently long waves. So, long waves omega square is equal to g k tan hyperbolic of k h for sufficiently small k is just k h. It is just x. This is so, this is an approximation for sufficiently long waves. I am just writing the first term in the Taylor series. And this is equal to k square into g h. Now, notice what has happened for sufficiently long waves the phase speed which is omega y k is just square root g h. This is unlike deep water. This is unlike other all the other examples that we have seen until now where the phase speed until now was a function of k. Now, once the waves become sufficiently long then they effectively behave as pure gravity waves.  This has a lot of consequences for the physics of how these waves propagate especially when there are many of them traveling. We will see some of this later on when we look at shallow water theory. So, shallow water theory is basically a long wave theory. So, you can either say that the wave is long compared to the depth or you can say that the water is shallow compared to the wavelength. Either ways we are meaning the same thing. There is a non dimensional parameter which represents the ratio of wavelength to depth k h is a non dimensional parameter shallow water implies that k h is much much less than 1. So, small k limit or large wavelength limit k is inversely proportional to lambda. So, this is twice by h by lambda. So, shallow water implies lambda is much much greater than h. In that limit surface gravity waves become non dispersive. One can calculate for finite depth instead of taking the shallow water limit. One can stick to pool of finite depth where the wavelength is comparable to the depth and one can incorporate the effect of surface tension. I leave it to you as a homework problem to work out the correction of surface tension on this dispersion relation. So, you have to do is one has to go back to the equations to the boundary conditions and modify the Bernoulli equation. So, you have to modify the Bernoulli equation and you will have one more term here. So, let me write it in another color. So, you will there will be an additional term here which will be coming in because pressure is now not 0. It will be t by rho times divergence of n and then we already know how to calculate that term. So, you have to include this and find your matrix and the determinant of that will give you your dispersion relation. So, this is the dispersion relation for waves, surface gravity waves you know on a pool of finite depth. Obviously, when we go to the deep water limit or in other words when k is very large or for a fixed depth k is very large then we recover the known behavior. So, tan hyperbolic. So, we have we have looked at two limits. So, our general relation is G k tan hyperbolic k h. We have looked at the limit for fixed h. So, h fixed we have looked at the limit k h going to 0. This is the shallow water limit when the wavelength becomes much much greater than the depth. In that limit this is these waves become. So, in the shallow water limit these waves become non-dispersive. So, we have G k into G h. So, tan hyperbolic k h is just k h. So, that gives me a k square into G h. So, this implies C is equal to square root G h plus minus the phase speed C p. Keeping h fixed if we take the other limit k h going to infinity. This of course is the reverse limit. This is the deep water limit. In this limit it is not consistent to ignore surface tension because my wavelengths are getting shorter and shorter compared to the depth. So, my wavelength is much much shorter compared to the depth. But if we ignore surface tension and just look at this dispersion relation, then we have to find out what is tan hyperbolic of k h for large k h. If you plot tan hyperbolic of x as a function of x, you will find that it is asymptote to us to the. So, tan hyperbolic of x as a function of x, you will find there is asymptote to the line y is equal to x for very small argument and then it plateaus at plus 1. So, for very large k h tan hyperbolic k h is just 1 for sufficiently large x. So, this is for k h much much bigger than 1. If you plug that in into the dispersion relation, you can see what do we get? We recover our deep water results. So, this is the shallow water result. This is the deep water result. Very different because in the shallow water limit, the waves are non-dispersive. Cp is not a function of k. All k is travelled with the same speed whereas in the deep water limit, Cp as we have seen is square root g by k. So, every Cp, every Fourier mode has its own speed. So, you can compare this. So, this is the shallow water limit and this is the deep water limit. You can see that in this case, this is non-dispersive. In this case, it is dispersive. Later, we will see that non-linearity and dispersion can compete with each other and lead to a lot of complications which causes a lot of interesting phenomena in the evolution of interfacial waves. Just as we have worked out the formula for the dispersion relation, you can take this and also work out what is the expression for phi. I leave it to you to show that phi can be written as g by omega e cos kx plus f sin kx into cos hyperbolic kh into e to the power i omega t plus pi by 2. Similarly, there is a similar expression for eta. Eta is equal to e cos kx plus f sin kx into e to the power i omega t. You can see that there is a phase difference of pi by 2 between phi and eta. So, that i was absorbed as a phase factor of pi by 2. These expressions can be obtained easily. All that you have to go and do is follow whatever we have done until now and then try to rearrange so that you get these cos hyperbolic factors. Recall the definition of cos hyperbolic which was e to the power x plus e to the power minus x by 2. You have to use that definition and you will be able to obtain these expressions very easily.


Hello, this is Dr. Mahesh Kalyanshiti, Associate Professor, Department of Civil Engineering, Valchand Institute of Technology, Swalapur. In this session, we will discuss about the analysis of indeterminate structure by moment distribution method, and specifically we will focus on beams. The learning outcome will be at the end of this session, students will be able to analyze indeterminate beams using moment distribution method. Let us take an example. Now analyze the beam as shown in figure one by moment distribution method and EI is constant. So we have this typical beam here where A and D ends are fixed and at B and C we have an interior support and this beam is subjected to loading of UDL 20 kN on span BC and a point load of 250 kN at the center of CD span. Now let us see how to analyze this indeterminate beam now using moment distribution method. We have to start with the determination of the stiffnesses. So we have to find the stiffness of all the members and then we have to find the stiffness of joints. So if I consider joint B here, we have two members meeting here BA and BC. So the stiffness of member BA will be 4EI by L since opposite end is fixed here and for BCL so it will be 4EI by L because C is interior support. So we have 4EI by L for both the spans accordingly we substitute the values and the summation of these two stiffnesses will give me a stiffness of joint B. So the stiffness of joint B is nothing but it is a summation of KBA and KBC. Similarly we determine the stiffness for member CB as well as CD now for CB we have again 4EI by L and for CD since it is fixed end we have 4EI by L accordingly the summation of these two stiffnesses gives the stiffness of joint C. Then we have to calculate the distribution factor as we are aware the distribution factor is nothing but it is a ratio of the stiffness of the member to the stiffness of the joint. So if I consider joint B here the distribution factor BA and BC will be the stiffness of the member divided by stiffness of the joint. So denominator is the stiffness of the joint numerator is the stiffness of the member the ratio is 0.5. For C also we can determine the distribution factor CB again you can see here stiffness of CB divided by stiffness of joint C now the denominator here it comes out to be 0.4 and for CD it comes out to be 0.6. Then the next step is to calculate the fixed end moments. Now we know that for AB there is no load therefore fixed end moment for AB span is not present however for BC we have the loading present and it is a typical case of fixed beam subjected to UDL. So we have a standard case and the fixed end moments are WL square by 12 accordingly FEM BC is minus because it is anticlockwise and FEM CB is plus since it is clockwise so the magnitudes are minus 240 and plus 240. Then for CD also we determine the fixed end moment as the standard case is known to us the fixed end moments are PL by 8. Therefore CD is minus PL by 8 that is minus 250 and DC is plus 250. As per our standard cases we get these fixed end moments. Before we proceed further let us go for some review questions. So I request you to take a pause and answer these questions. Addition of distribution factor of all the members meeting at a joint is always equal to four options are there. The second question is the stiffness of member with far end fixed is the four options. So you think over it get the answer and then resume the video. Welcome back. These are the answers for the review questions. The first question the answer is one because the distribution factor summation of distribution factors at a joint is always equal to one and the stiffness of member with far end fixed is four year well that already we discussed. Let us continue with our problem. Now once we get all the basic data then we have to go for the moment distribution process for that we have to prepare one table here where in all the information are provided joints A B C D so four joints are there member. So A B B A at B we have two members at C we have two members and at D we have one member. Then the distribution factor of all the members are written here as we already determined then the fixed end moments also we determined that is to be substituted here. So fixed end moment will be only for BC span so BC and CB it is minus 240 plus 240 and of course it is for CD also since we have a load over CD minus 250 plus 250. Then after this we shall go for the distribution for that we have to balance the joints first. For example if I look at joint B here the BC and BA it is not balanced. So there is an unbalanced moment of plus 240 so that plus 240 is to be distributed here based on the distribution factor 0.5 0.5 so 120 transfers is 120 transfers here. In the same way here at CL so we have unbalanced moment minus 10 and that plus 10 we have to apply out of plus 10.4 fraction is applied here and 0.6 fraction is applied here. This is how we go for the distribution first and once the distribution is over then we go for a carryover. So from B carryover is possible towards A from C carryover is possible towards D from B carryover takes place towards C and from C also the carryover takes place towards B. So these all carryovers will perform here so this minus 120 sorry plus 120 50 percent transfers here then this 120 60 transfers here 4 2 transfers here then from 6 3 is transferred here. In this way we go for the carryover. Now once the carryover is complete then the balancing gets disturbed again. You can see here now this 2 is an additional moment come to joint B. So therefore this 2 is to be balanced therefore minus 2 is to be applied out of that minus 2 50 percent is transferred here 50 percent is transferred here then plus 60 is unbalanced moment. So minus 60 we have to apply out of that minus 60 0.4 percent is transferred here 0.6 percent is transferred here. So this is how we distribute it and after the distribution is over again carryover takes place. In this way it is an iterative process once this cycle first cycle is over we have to go for a second cycle third cycle. So number of cycles we have to perform till we get a very small and fractional moment left you can see at this point 0 1 0 1. So at that level we can stop that process and then we can take a summation of all these moments so that we get the final moments of all the members. So here at the last row you can see the summation is taken and these are the final moments of the members. Once the moments are determined then we shall go for the free body diagrams. So using our final values which obtained in the previous slide we can draw the free body diagram AB. So here this is 62.5 AB and BA is 125.2 kilo Newton meter then BC 1 0 sorry it is 125.2 kilo Newton meter only this moment is 281.5 kilo Newton meter and for CD in the same way we draw the free body diagram. And once we get the free body diagram we can draw the bending moment diagram as well as shear force diagram. So with the help of this bending free body diagram see you can see here this bending moment diagram is constructed so here it is 62.5 moment positive is present here. So here it is 125.2 kilo Newton meter at support B so it is 125.2 since it is hogging it is minus here also we get a hogging moment 281.5 kilo Newton meter here and here the last moment is 234.3 kilo Newton meter which is hogging in nature here. So in this way we draw the bending moment diagram from the free body diagram and this is positive this is negative. In this way we can just give the proper label to this. These are the references which are used for the presentation thank you thank you very much.


Rip some packs build the best co-op team that we can and hopefully get a dog online. Let's get it. Hey Kyle What's good my guy? What's up my man? Hey, thank you so much for being here. I'm excited. Of course It's always fun. It's been like what a month and a half How's the game been since our last played dude? I mean the game has been solid man I feel like it's been longer than that because I've been running around.  They just released some good content got these all-star packs They got these new chase packs. I'm gonna be ripping one of those Gives us a chance to add a crazy card to our what's gonna be our new team dude. I'm actually so pumped All right Well for everybody watching we're gonna keep real simple as you can see my team is absolute dog shit Kyle's just fire, but that doesn't matter because we're gonna take the players that we get from these 10 packs We're gonna take the one stud that we get from our all-star and then we're going into co-op So can we pull anything in the game in these like can we actually pull crazy good stuff?  I mean we only need to fill six spots each right that's so true We've already kind of automatically filled one with the all-star pack from you and the chase pack for me So we just got to hope we pull some golds, you know, maybe a diamond out of the standards We'll see what we can do bad. Let's get it, baby. All right first back. Yes, sir See what we got Okay, I got a gold I did get a gold for us. I got a gold shortstop Niko Horner, okay, bet I've got us I think I'm just kidding What is this for I got an absolute bum I get another bum I got a bum. Oh, I got a gold What gold I got Jeffrey Springs. Oh, okay 10 for the odds are a one out of 10 chance to get a gold Exactly and it's one out of 50 to get a diamond damn.  That is a that is a gold glove.  I'm anxious to rip this chase back. Oh, I got us I didn't get another silver though. Yeah, no silver. Okay. Who is it? Oh, you go find out it is Michael Conforto the giant that's that's a solid pick. That's a solid pick for a silver. Yeah, he's got he's got some pop We could we could work with that. Yeah, we're on to the next one. You ready? Yes, sir Let's do it.  Jesus. What is blue? Oh, Jesus Blues diamond. No, no, no, I don't think it was as blue as I was thinking a little blue border I think it's because I was hovering over a okay I got a bunch of bums and I got Joey.  I ain't using who Joey Manessus. No, Joey Manessus is solid as fuck, dude Really? He's a card. Yeah. No, dude. That is solid. He's a budget. Yeah. Yeah, exactly in Battle Royale He's a must pick. Oh, yeah, I'm done. I quit. I'm done. I'm not playing this game All right, let's rip this next one. I got silver. I got silver. Let's go silver too. All right Who'd you get? I got who is an Arizona diamond back baby Gabriel Moreno catcher. Okay catcher. We got a catcher now That's solid. Okay. So Ross tripling and then we got Gabriel Moreno. Perfect. All right. So you got five left I got another silver dude. Your shit's ripping right now. I'm staying with me. I'm juice, bro It's the new account juice man. They know that I haven't spent enough money yet. What silver we get Charlie Blackman That's solid. We got Charlie Blackman. Boom. All right, four more. Oh, no sauce this time. I got all bronzes me neither Oh, Grayson Rodriguez. I got us a good little starter. Maybe okay bet I'll say these names just in case they happen to be good. We got Marcelo Zuna for the break. That's actually solid Yeah, Marcelo Zuna is actually solid. He's got good pop. All right, but and then Josh Zborz Not sure to pronounce that one. It's you rangers. Yeah, really picture. Yeah, maybe pick him for one of your relievers All right, but oh you're carrying us for these packs. Let's go. Three more. Yep. We got two more of the mid ones And then we go for our big boys Willie Calhoun. Willie Calhoun. I think he might oh I got some old reliever who's solid. Hey Yeah, I got a good one. I got us a good one. All right. I got Nick Sandlin relief reliever, right silver silver Oh, yeah, that's that's all it too. So I think Josh Zborz and Nick Sandlin are gonna be your two relievers Not if I pull a 99 All right, I'm gonna rip my last standard pack you have one more to well I technically have one more but we're doing 10 packs. So my 10th pack is gonna be this I'll start you know I mean, oh, just go ahead and rip that one cuz I ripped Okay, let's send it. I like that the more packs the better works for me. Yeah, I got somebody silver It is Matt Moore for the angels another relief pitcher. Okay, it'll be him instead of Josh Zborz But you have Matt Moore and Nick Sandlin you don't open up Okay, I'm gonna rip it you just gotta tell me who's good We're looking for a 99 in the corner though.  I have Elias Diaz and I have Yandy Diaz. Yeah, okay. Okay, so we got to think about this I think we got to choose Elias Diaz. Yeah, that's the guy. That's the guy. We love you both of them You could choose either. They're both really good Look at their hitting stats.  That's so let's go. All right. Now. I'm opening up my chase pack Please something solid. Let's see who is it. Is this Shane McClanahan? I got us a starter. I got Diaz, Cigura, Manessus, Jeffrey Spring, Sandlin, and Matt Moore Oh, they made Manessus like bronze. I didn't know that what are the stats that I'm looking at I want to look at to know who's good. What you're gonna do is go back to Manessus like in the main menu Where you choose him? Press Y and read to me his hitting attribute. I assume those are the contact ones Yeah, contact contact power power. Okay, 86, 83, 50, 60. Okay. Um, read to me Ciguras 64, 82, 40, 60. Jesus.  All right. This Charlie Lackman dude's got 76, 85, but then 59, 37 All right, we're gonna replace Cigura with Marcelo Zuna All right, I'm gonna give you a stacked team based on what difficulty we're gonna be playing on and it's gonna help I'm gonna replace Jean Cigura with Joey Manessus. Yeah, I got it. All right, and then I'm gonna do I got that Niko Horner card He's a gold toss him in there Niko.  That you said that right on the Giants Yeah, I have Conforto. Yeah, maybe replace Marcelo Zuna with Conforto because Conforto solid and that'd be good for our team.  All right. We're good. We're rocking Yeah, this is definitely a gnarly looking team, but we're ready to go you ready.  All right, so we got two rays. Oh stay stay on McClanahan We got to get McClanahan. He's on the right.    He's got that Shohei Otani. Yeah. Yeah. No, it's not a No, but look at that bum. He's got that little 74 overall bum in there.  I always forget that it's two guys. We're basically what a beautiful stadium Where is this Colorado dude? He's two and three me's we got to bathe in this fuckers. You're 117 and 24 Bro, that's with me quitting. That's with me quitting like nine games, too Is this like the co-op record you play co-op lot? No, no, that's my regular record.  We can't let him get one run unique. Okay. Wait. I put you right Yep So I'm gonna turn it all play right here, right?  No, do we not get it? We did not get it I don't know why they made it an error. What's an error? Okay an error means like you were supposed to get it out But you didn't oh, they basically said wow you should have had that but that's pretty exactly didn't get it Oh, that's fucked.   Why did I not relate that to you? That's exact. Oh, I got it I got it. I'm correct.   What do I do again to pitch? I just put it where I want it then hold a Yeah, like there's no other special buttons like I'm so right now. I'm aiming at bottom left and I'm gonna be one classic I feel you mess with all my settings last time.  All right, go to settings settings gameplay gameplay hit RB got it What's it say you're pitching it does it is classic. All right. I want you to go to pulse It's on there. That's it. Yep.  Did you get it a good? I got a good there. We go. That's how you're gonna pitch from now Wait, that's so that's sick. That's all you're gonna do. So what happens if I go early like I just went early here It still ends up being okay. It did work out.  No, I did I did get I did get a good there though I just think I threw a bad pitch to a bad spot. No, yeah, it's all good You're gonna bounce back right you aim those low and out of the zone pretty much.   This is gonna be a ball. Oh just late.   It's all right.  Oh, yeah, that's it. Look at him doing summer salts and throwing me out. Jesus That guy was so mad. We got a lead, baby. We got a hell. Yeah. We got a point.    It's easy. We're good. Is there any like track? Oh, there is track.  So he's cracked right now because in real life.   I'm sorry. That's okay One-to-one is not bad. Why is he fucking? Where am I going with this? Oh good.  Let's go.  You ain't just like that. We're out of the You like good you scared me a little bit there. You scared me a little bit on that one I'm gonna be honest with you. I thought we had two outs already. So once he called it I was like okay sweet. Where was it too early? Okay? I'm gonna wait a little bit It's okay. We're fine, bro. We are fine. We got him right where we want him, bro Let's see what you've been pitching with bullsnow. This one was good. It's gonna be a ball.   Oh my god. Why is he so slow?  Oh, no I'm gonna put this I'm gonna give us a better picture. Yeah, that's just not ideal Here we go Give me that nice play How'd you die? It's rent. Yeah. Yeah, I know that one. Oh my god. What is he doing?  It's alright. It's alright. What do you mean by that?   It's alright though.  I was like I'm a little behind that I gotta jump. No You just gotta run to it. Oh Okay, that changed this a little bit.  Let that drop. Let it drop. Let it drop. Let it drop.  I tried to let it drop. I know you did. I know you did. I thought they were gonna let it drop What's the what's the rule if it dropped he'd have to go back to third base and we just put a runner on first, right? No, no, no, no if it dropped it was gonna.   All right. Come on. Let's go, baby. Let's go. We're starting it off right here I'm gonna get it either a double or a Homer right here. How's lean door?  All right. Hey, that's awesome. Yeah. No, we take it. We take it. We take it man.  Oh, wait. No, no, it was a good pitch on this part.  They can't stop me. Oh, no, what was I supposed to do? You were supposed to go back to first. You didn't tag up. I'm gonna be honest. I don't even know how to do that.  I hear you. Let's try this Turn it turn it. Let's go Good kid. I had to control. We don't want to put curveballs where we were initially put in them That's how like those get killed got you got you.  Oh my it's literally in the corn. The corn has physics.  Oh my god That was impressive.  Oh, where do I go home? First first first.  Oh, I had already pressed it. I know I know it's okay. Good luck, sir Thank you Good. All right. All right. All right.  Please. Did he just fake show it? I think you know, but dude our guy almost got thrown out at second cuz you so I know okay I thought he used to have a cutter There we go.    Yeah, that's what I was telling you dude.  That should have been an owl. You made a good pitch dude.  There we go Redemption and then adjust to the off-speed Come on.  Let's go. Can it bounce out? Yeah. Well, it doesn't matter regardless. Oh, you get you only you get two Yeah, yeah, if it went over he'd be on second to go.  I do not swing at it. No matter what I see what you're saying See what you're saying See and I tell you see me. Yeah, the chances are he's probably not gonna throw it there See all right now you swing come on ball. Where are you going buddy?  Come on.  I feel like you tracked it. Well, there's nothing you can do there. Let's go Where do I go? Oh? Yeah, you just got to run the it's it's just about the route you'll get used to it as you play I gotta take a better angle on the ball there. Yeah. Yeah, exactly. If you ran more out towards the outfield He grabs that Oh, and then that's Can we get six runs in an inning? We can That is so tough. So we're down five right now.  How's that sound right here right here though Just to get us in a group do not swing until we have a strike on our counter That's such a good piece of advice. I love it's because it's it works.  No, dude. We're still gonna win.       All right.    That's crazy.  We really didn't get through it. That shit's fun, dude I can see I get so addicted to this game.   It's so fun Oh, it's not about winning.  You know what I mean? It ain't about the result It's about the process and when you get some processes smooth. We're gonna get you to the right spot We're gonna beat some heads and we're gonna be alright. That's fire. Hey, well, thank you so much again for doing this Me that was so fire. We're gonna win next time, dude We got many more wins ahead of us and I promise you hey if you boys love MLB make sure check out Kyle's channel It's your friend Kyle on YouTube. Huge shout out to him.  I get so mad huge out to him I guess I got on base twice. I made some contact, but never had a playable ball kind of sad dude Hey, it's like 2k man. It's like that 2k shot release. How long it took me to learn that either way? Hey, I love you guys. Thank you for watching as always. I'll see you in the next video. Peace


What's going on everyone? Sam here with late in sports cards. I've been 22. Panini Flawless, football hobby, one box break, number nine, random left side serial numbers. So look again at your random results as always. You can find these on the website under the results tab as well as the link in chat. Good luck everybody. Okay, here we go. I see something huge showing. Another shield inbound. Well that's nasty. All right, here we go. Empty lid. Going to the six spots, six to 15, Josh Jacobs, Bo Jackson, two color patch on Jacobs, one on Jackson. Player one on Bolt, very nice. Oh, you like this one, Sean. Congrats to the six spot is Thomas Jay. Going to Aaron M at the two spot, two up two, dual laundry tag, two up and Tyreek Hill. That's nasty. Player one, two up. Let's go. You're an empty lid. I'd take him back that one, why not? Going to 22 spot, 22 of 25, Alshon Jeffrey, Star Swatch signatures. All the way back from 2020 Flawless. 22 spot is Aaron M, grads Aaron. It's a cool little throwback Alshon. Player one on that as well. God, 10 of 15. Going to the 10 spot, Thurman Thomas. 10 is going to be Daniel K. Congrats, Daniel. Nice one there, buddy. Well, I got you all here as well. There's just 14 to go in the next break, everybody. One pen. God, going to the four spot. Four spot, DW, Eli Manning. Congrats on that. Nice one there, D, Eli on the honoring. Going to the two spot, Aaron M, how about a Brian Erlocker. Two of five, Patch Auto. So cool, dude. So cool. And of course, my guy going to the 10 spot, Daniel K. 10 of 10, Ray Lewis, Flawless, honored Inc. Got the Jersey Mojo today. Congrats on that. There you go, Daniel. 10 spot. All right, we're starting off with A.J. Brown. Two of 15. Going to the two spot, Aaron M. We've got five of 10. Going to the five spot. That's going to be Cooper Cup for the five spot, Zach H. One of the 12 spot, Jeremy J. Desmond Ritter. On the signature gloves, RPA. The pattern on the gloves is sick, dude. Good stop there. Congrats, Jeremy. Empty. Not going to do a recap, guys. That'll do it for the break. Thanks again for the fill. Number 10, coming up next.


How to spot a high value woman, fellas, if you're watching this video and you're single or you're dating somebody right now, I'm gonna teach you how to be able to identify if the woman you're seeing is high value. And if you're single, I'm gonna teach you how to find this one. One of the things to look for to make sure that this woman is gonna be a high value woman. Okay, so stay to the end, because I'm gonna talk about what the biggest thing out of all of these is that you should be looking for when deciding whether to get with somebody. Okay, number one is a willingness to apologize. Okay, that's the first thing. I put it first because it's not the most important, but it is up there, okay? The last one that I'm gonna give is gonna be the most important, but this one, dude, there's a reason why I put it first. If you find someone who does not have the ability to admit when they are wrong, then you can't work on things and you can't improve as a couple, okay? If you admit when you're wrong and she admits when they're wrong, then guess what, y'all can grow together and you can work on things as a unit.  If you have someone who never admits when they're wrong and always thinks that they're in the right, you're not gonna have a great relationship with them, okay? So you might not always say I'm sorry, although if she does say I'm sorry, that is so huge, because most women can't do that.  For instance, me and my girl, we were talking one time and came to find out during that conversation, she doesn't do nearly as many things as she thinks she does for me. And because of that, she just got kind of quiet for a little bit, we changed the subject. So she didn't apologize then, although she has no problem apologizing when she feels like she's in the wrong, which is one thing I love about her. But in this case, she just slowly changed her behavior over time, which is great.  And I find that that's better. You might not always get the I'm sorry and the big apology that you want, although it is important to be able to have that with somebody, okay? Number two, she takes care of her health, okay? Fellas, you want someone who takes care of her health because if she doesn't take care of your health, then your health is gonna get worse around her, okay? You're the average of the five people you spend the most time with, you're gonna be spending a lot of time with this person if y'all are in a relationship, okay? Again, I don't care what type of relationship it is, you're gonna be spending time with this person if she is being really unhealthy with her body, with herself. And above all, I'm thinking about having kids with this woman. How do you think she's gonna treat her kids? She's gonna have those kids, right? And she's not taking care of her health and her body. Like that is a huge concern, all right? You want someone who eats well, okay? She doesn't have to never drink alcohol or party or do any of their, never eat sweets, okay? But everything is okay in moderation. If she's doing that seven days a week, that's not someone that you want to be getting into a relationship with, okay? Now, a lot of times women can get away with this when they're young, okay? If they're in their early 20s, sometimes even in their teens, they can get away with partying seven nights a week and still look good, okay? Doesn't mean you should get with them, but it is something that you wanna watch out for because that is not maintainable. When they hit 29, if they keep doing that, they're gonna get really large and really gross and they're just not gonna be a healthy person to be around. They're gonna have all these health problems, okay? So make sure that the woman you're dating takes care of her health. Number three, she pays attention to you. Guys, this is super, super important, okay? If you told her something several times and she's forgotten it, if she doesn't remember what you do and you guys have been dating for two months and she still doesn't know and you've told her multiple times, like, guys, like, she is not paying attention to you. Clearly there are other things that are more important going on in her life that she thinks are more important and you aren't one of those things.  You want a woman who really takes the time to pay attention to you, not just what you mean for her, but you, okay? And you should do this too, because she's looking to see if you're doing this as well. Women are very observant to this, but you gotta give them the same energy back sometimes because if a woman's not giving that to you, then guess what? She's not gonna be there for you. She's not gonna be a good partner, okay? They know, statistically, whether a couple is going to break up or not, by 90% accuracy, if they are willing to observe how the other partner is looking or feeling in the moment. So if they're in a room and one person is clearly angry and the other person just doesn't see it, very high likelihood that that couple is gonna break up, okay? So find someone who pays attention to you. She can tell when something's on your mind and you're really upset about something or she knows a certain things about you and she's willing to learn and remember those things, like that is gonna be a good partner for you. That's a high-quality woman for yourself. Four, takes care of her appearance, okay? You want someone who takes care of their appearance, you want a good-looking wife. I don't really know what else to say this, okay? If you have a wife who's comfortable, just walking out and not looking good, then you have a wife who doesn't respect you, okay? Now, I'm not saying 90% of the time she can't be in her sweatpants without makeup on and her hair all messed up and some weird kududile like little thing that she's got. That's fine. My girlfriend wears comfy clothes 95% of the time, but when we go out, when I'm with other people, when we're in public or when it's date night or when at certain time she is taking care of her appearance. She's making sure she stays in shape. She has your body looking good, okay? She's making sure she gets her hair done, right? This is stuff that sometimes I pay for because I know how important it is. For me, I want someone who tries to look good. Fellows, I don't know if you understand this, but looks are basically a measure of how much you care. Some people are born with looks and everyone says that looks face. You shouldn't judge for looks. No, you should judge whether somebody cares about their look. If they do not care about their look, they are going to look ugly. If they care about their look, they're gonna stay looking good for a really long time. You ever seen a woman in her 40s or 50s? She was like, you're like, damn, man. She's one of her 40s and 50s. Well, this one looks good. It's cause she tries. She tries to look good. She stays in shape. Again, this is part of being very healthy, okay? She knows how to take care of herself, right? Her hair, makeup, lotion, all of those things to keep her skin looking good, to keep herself looking good. And on top of that, if you even want to get the bonus requirements to this, you can even get plastic surgery, okay? Like there's no excuse if you have money for looking bad in today's day and age, all right? So find someone who takes care of their appearance. They don't have to go overboard. Like I said, plastic surgery is optional. All doing those crazy, you get those nails done that all that's optional, but she should care about her appearance and take care of it, okay? If she doesn't care about her appearance, she looks up dressing like a slob, you know, with barely any effort in, that makes you look bad. Number five, she lets you take charge, okay?  She becomes feminine, all right? She's willing to do this. Now, a lot of women in today's day and age have a lot of trouble stepping into their feminine, allowing you to take charge, okay? We have a lot of women in the workforce, a lot of boss babes, and so they spend a lot of time trying to be the man all the time. And if they do this, they might have trouble allowing you to be that man.  So you have to step up as a man and take charge, but also at the same time too, she has to allow you to take charge, right? It's a two-way street. There are some women that I have dated that were just never comfortable with this, all right? I did what I had to do, and the only thing that I can do as a man to respect myself was to walk away from that relationship.  Most of the time, if you are willing to take charge, they should be willing to let you do that. They're gonna be all the time, you don't always be taking charge, you just wanna chill and hang out, that's fine. But in order for sexual attraction, desire to get created, there has to be a man to woman or masculine and feminine connection in there, okay? And that happens when you lead and she follows. Number six, she has goals, all right? She has goals, she has some sort of responsibility to herself. Those things are really important. Not as important as your goals and your ambition, okay? Not to say that we put hers to the side, but when it comes to raising a family, for the very long term, those things are gonna be really important, okay? When we talk about like long-term in terms of the relationship, okay?  So you gotta be that person who has that ambition. Women care about a man's ambition, more than men care about a woman's ambition, but you should care about it, okay? Because if she doesn't have any ambition, she's one of these do-nothing babes that just has everything handed to her, that's gonna be annoying to deal with.  Okay, so you wanna have a woman who has goals, wanna have a woman who has some sort of responsibilities, and one of the things about my girl that I love about her is that she does have goals, but the other thing that I love about her as well is that she really takes care of things, you know? Just animals that she takes care of. She's a good parent to those animals. She's a good person to be around. She treats her family and everybody really well, all right? Maybe we can add another one in there where, you know, how she treats other people, right? Not just you, okay? That makes a huge, huge difference. All right, now the underlying thing for all of this is a high value woman for you who helps you achieve your goals. A high value woman is someone who helps you achieve your goals. Some people might have a woman that helps them achieve their goals, but it doesn't help you achieve your goals, okay? So that's why a high value woman isn't the same for everybody, right? Maybe a high value woman for a guy is he wants to move up in society and, you know, this woman is really rich and so she helps him get to the upper echelons of society, so he marries through that, okay? That was actually a common way that men and women used to advance through society in the olden days, mostly a lot of times women, but men would do this too, especially if she was widowed and George Washington did this, but like that would be an example of somebody who's helping you achieve your goals. Now that's not my goal. I don't wanna date some rich girl who, you know, is making it all about her. I wanna date someone who likes me. That's what I want. I want someone who helps me achieve my goals, who's supportive of me. Not every woman is gonna be good for you, you guys, all right? And it's really important to be able to recognize this. If she is not helping you reach your goals, you have to break up with her. I don't normally say this, but if she's not helping you reach your goals, you have to break up with her. Now this doesn't mean if you've had a 20 minute argument or something like that, you immediately gotta break up with her. Well, that's 20 minutes that could have been working. No, that's not a good enough reason, okay? A good partner provides a lot of good things to your life, but if she's not helping you reach your goals, then you have to leave that person. It's a harsh thing. Now, let's say you're watching this video and the person you're dating, you're not sure if she's helping you reach your goals. Well, does she do these six things? Let's solve that question. If she's not doing those, how can you get her to do those things? Let's take an example for maybe your girlfriend doesn't spend a whole lot of time on her appearance, right? She doesn't really care about it that much. What are things that you can do to maybe get her to try a little bit more? Well, you can ask her, but do it the right way. Be like, hey, babe, when you wore that wet red dress and you had that red lipstick on, I love that outfit. You look so hot then.  You're embarrassing me, okay? She's probably gonna resent you if you do stuff like that. Okay, don't say that. All right, positive reinforcement is good, but just generally asking, if it comes down to it, you say, hey, babe, I love you to death and this is great, but I really wish that sometimes you'd be able to say I'm sorry. That would mean a lot to me if you said that, okay? Because I'm willing to say I'm sorry when I'm wrong and when you don't say you're sorry, to me, it makes me feel like you think that you're never wrong and I'm the only one who's wrong, right? You do that whole proper way of communicating, right? There's a whole strategy to be able to do this, right? Now, if you're not seeing somebody and communicating like this is not the right time. If it's early on, it's probably not the right time to be making any of these demands, okay? This is only if you're currently dating somebody. If you're not dating somebody, what are the things that you can look for? I would say you probably should be able to identify these things within the first couple months of dating somebody, okay? In the first few months of dating somebody, somebody's gonna make a mistake and you're gonna see how they're gonna react to it. You should be able to see them in a lot of different environments. Do they actually take care of their health? Are they actually having goals or did they just put a front on you for the first couple of days and say they were doing all of these crazy things? It's easy to talk, talk is cheap. You gotta pay attention to their actions, all right? So in my program, basically I break down and I help guys be able to identify whether this person is a high quality woman. I can usually tell by the way that they're paying attention to the person, whether the person's paying attention to them, the things that they're doing, especially when it comes to is she letting you lead? Is she actually paying attention to you? Very easily able to identify those. So that's something that you get alive in my program. So if you wanna get coached by me, you wanna get access to my program and go to getcoachedbyloy.com. Links in the description box below. First one, book a free call with me or a member of my team and we'll see if you're a great fit. Thank you so much for watching you guys. This is how to meet a high quality woman. This is how to identify a high value woman. Good luck out there. We'll talk soon.