Okay, so we're gonna talk about a show that I am loving slash hating at the same time. I started watching Hannibal about a few months ago. I'm still getting through the second season merely with going back to work. It has slowed down my progress of the show. I heard a lot of very good things about this show to the point where I actually regretted having not watched it when it was taken off of Netflix the first time. It's literally been on and off Netflix long enough that I have had a period of time of regret of not watching it and I watched the first season. And the first thing I can say is this show has an impressive production value considering the maturity and the intensity of its content at times. I actually really enjoyed the casting of Hugh Dancy as Will Graham. When I think of the character of Will Graham, I don't think of the Edward Norton character from Red Dragon. I think of the William Peterson character from Manhunter. Manhunter is actually technically the first attempt at trying to bring Thomas Harris' novels over onto the big screen. This film was made in 1987, directed by Michael Mann, had William Peterson as Will Graham and Brian Cox as Hannibal Lecter, which sure it's not as good as Anthony Hopkins. Not in the same realm, but it is still a decent attempt at the character. Will Graham by William Peterson has always stuck in my mind as a very tortured character. That film truly illustrated how far into the means of profiling that Will Graham could go, that he gets so much into the minds of these killers that he's fighting this kind of back and forth of possibly being able to comprehend the means, the understandings, the emotions of a serial killer or the lack thereof. So having Hugh Dancy's interpretation of the character, I thought was pretty spot on at first. It gets a little bit much later on, but we'll talk about that later on. But the other casting choice I really enjoyed was Mads and Mickelson as Hannibal Lecter. I know that Anthony Hopkins is English and Mads is Danish. You know what? I don't care. I actually thought that this was a perfect, perfect casting choice. What we've seen from Silence of the Lambs, Red Dragon and Hannibal and all that, we've seen what Hannibal Lecter was like after he was incarcerated to the point where he doesn't need to hide who his true self is anymore.  What I always wanted to know, and that's what this show is giving, is what Hannibal Lecter was like in terms of a normal society. Hiding who his true self was, but still being able to amalgamate with society and with high class people. And I love that he is dancing around people in this show. I think that his sophistication, his cooking techniques, which supposedly Mads cooked everything, everything that he serves as his character, he actually cooked himself, which is like, damn, you actually get really hungry watching this show, even though you know what he's serving, which again, is so cool that they're committing so much to the material, to the content of what his character is, and to the idea of profiling, to the idea of ritualistic serial killers. However, the show gets a bit much later on. This is the part that bugs me a bit. I'll go from absolutely loving the show with fantastic cinematography, great visual storytelling in terms of Will's insanity, or his drive into insanity. The music is also very unnerving. It never really lets you calm down. It never eases you. It's always putting you on an edge of tension, which is fantastic, fantastic building. And for the most part, I actually like the serial killers that they come across. Sure, it's a bit much that they come across the top 10 most ridiculous and over the top monsters in human society ever, every week. First, that doesn't bother me too much. I enjoy the first person that Will goes after that really bogs into his mind in the form of the stag. It's later on.  And I think the first time that I said that was when the Tower of Human Body Parts was found on the beach.   And there are some parts that worked really well in terms of its visual representation. I found the silo of the people all sewed together. That part was gross. And the guy who got out of it, I couldn't believe that they actually aired this on cable television.  The show just never lets you down in terms of visual entertainment.  Oh, for sure. There was the one where the bodies were kneeling and the backs flesh had been ripped up to be like angels. It's like, oh really? Or like when I'm in the second season right now, the judge who's doing Will Graham's trial, he is found just in pieces in his courtroom. And they're just leaving the door willy-nilly open and one of the lawyers just comes by like, but then there's people behind her just walking normally by like, oh look there, Judge, what's his name got crucified and internally torn apart? Whatever. This is another Tuesday. That's what I mean in terms of how ridiculous the show can be sometimes. Speaking of the trial and Will Graham's thing, I understand that they are trying to emulate Silence of the Lambs with his visual forms of incarceration, but the fact that every time they have to talk to Will Graham, he's in this tiny little box, yet when he's in the courtroom, just handcuffs. He's not in some weird masochistic box, but they have to do it when he's doing these interviews in a secure prison. I understand again, visual storytelling. Give them props for that. Really great job on the production design. It's what slowed me down from watching the second season right now is that it's just getting a little bit too much. It's getting a bit ridiculous. Okay, maybe a bit is a little bit lenient.  I'm going to finish it. At least that's my intent. I'm going to finish it. I find that the show is just kind of going into the realm of Sherlock Will's ability to think like a serial killer has gotten to the point where he can now just look at a photo, look at some notes for about five seconds, and then he puts himself into the mind of the killer and he's there. I was like, okay, whoa, whoa, whoa, whoa. It made sense the first time because he was standing in the room. Yeah, okay, maybe it isn't really realistic at all, but at least it was established that if he was at the scene of the crime, everything around him, he could kind of reinterpret it, the crime himself. But now you apparently could just look at a photo and be like, yep, I know exactly what happened. I even know details of the room that I'm not even told from this photo. That's what I mean in terms of its overextravagancy. I'm hoping that maybe it tones itself down. I can't wait for Jillian Anderson to come back in the third season. Apparently, she's a regular in the third season. So that's been my major motivation. I love me, Jillian. She's so damn cool. I'm not going to give a review of the show until I'm done. But if I were to give like kind of basis reviews, I would give the first season a five out of seven for sure. Second one, I don't know. I'm a little bit on the fence right now. But anyways, guys, I hope you enjoyed this video. If you did leave a like and if you're interested in more subscribe, if you haven't seen Hannibal, I would definitely at least say watch the first season if you are a bit queasy. It's a bit much. At least doing a pretty decent interpretation of silence of the lambs if with the extravagancy of Hannibal. Anyways, that's all for me. See you guys next time. Thanks for watching the video. My name is Nitz and you might remember me from the animated cult classic TV show undergrads. It's been a while, but I'm happy to say the click is finally getting back together in an all new movie thanks to a successful Kickstarter campaign. But we are still asking for your support to see any and all updates about the upcoming undergrads movie. Be sure to check out and like the bring back undergrads Facebook page. And with any luck, we'll see you guys soon.


Friends, myself Prashant Vishwanath Dinshati, Assistant Professor, Department of Civil Engineering from Valgen Institute of Technology, Solapur. So, today I am here to explain you about slope and deflection of a cantilever beam with point load by double integration method. So, today's learning outcome is at the end of this session students will be able to understand and find the values of slope and deflection of cantilever beams with the point load having following conditions. So, before going with slope and deflection we will see what is beam and its definition. So, beam is a structural element that primarily resist load applied laterally to the beam axis. Its mode of deflection is primarily by bending. So, this is the beam and the load applied is laterally and the beam is having a bending shape it resist by bending. So, beams are classified based on its support conditions. So, why we require slope and deflection? So, we will see. So, design of beam is frequently governed by rigidity rather than strength. So, every building course specifies the limit of deflection as well as stresses because due to excessive deflection of the beam it is not only visually disturbing but it may also damage to other parts of building. So, each building course limit the maximum deflection of beam. So, we have to see what is the deflection and slope of the beam. So, we will see the definition for the deflection of beam. The deflection at any point on the axis of the beam is the distance between its position before and after bending. So, this is a cantilever beam it is straight and when load is applied the beam bends in this way and this is the deflection. So, wherever you take the section. So, the deflection is greater at the free end and it decreases to the fixed end. Slope of the beam slope at any section in the deflected beam is defined as angle in radiance which is the tangent at the section makes with the original axis of the beam. So, this is the curvature where the beam deflects and this is the line tangent and we are having this reference horizontal axis of the beam. So, this theta b is the slope of the beam cantilever beam it is a beam which is fixed at one end and free at the other end. So, one end is fixed other end is free. So, we are seeing by double integration method. So, now what is the equation by double integration method? So, when the beam deflects this way. So, it has a curvature and here is a center point of that curvature and this is the radius of that curvature. So, the radius of curvature of the deflected beam is given by the flexural equation that is m upon i is equals to e by r. Therefore, m upon e i is equals to 1 upon r. So, we will treat it as equation A, but for a practically beam or mathematically it is 1 upon r is equals to d 2 y by dx square that is equation B. Equating this equation A and B we get m upon e i is equals to d 2 y by dx square. Therefore, m is equals to e i d 2 y by dx square this is the equation for the double integration method. So, this is a cantilever beam which is having length L and load W is at the free end. Due to this load there is a deflection of the beam where yB is the deflection and theta B is the slope. So, now we will consider any section in a beam that is at a distance of x from fixed end and the remaining part is L minus x. So, total length of beam is L and the W is acting at free end. So, at this section the moment mx is given by minus W into L minus x this is load into distance of the load from the section where you are going to take the bending moment. So, the minus sign is due to hogging bending moment. So, as per the equation 1 m is equals to e i d 2 y by dx square. So, putting the value of m. So, we get e i d 2 y by dx square is equals to minus W into bracket L minus x is equals to minus W L plus W x. So, integrating the above equation we get e i d y by dx is equals to minus W L into x plus W by 2 into x square plus c 1. So, this is equation number 3 where c 1 is the constant of integration. So, again integrating that equation 3 we get e i y is equals to minus W L into x square by 2 plus W by 2 into x square by 3 plus c 1 x plus c 2. So, where c 2 is the again constant of integration this is equation 4 where c 1 and c 2 are constant of integration. So, these are obtained by boundary condition. So, what are boundary conditions for cantilever? So, you are pause the video and try to get answer for the boundary condition. So, at the support is fixed the values obtained from the boundary condition are at x is equals to 0 that is at fixed end deflection y is 0 and at x is equals to 0 slope d y by dx is also 0. So, by substituting the value of x is equals to 0 y is equals to 0 in equation 4 we get c 2 is equals to 0 and by substituting x is equals to 0 and d y by dx is equals to 0 in equation 3 we get c 1 is equals to 0. So, now putting this value c 1 is equals to 0 in equation 3 we get e i d y by dx is equals to minus W L x plus W x square by 2. So, plus c 1 that is 0 is equals to minus W taking common we will get into bracket L x minus x square by 2. So, this is equation number 5 this equation is known as slope equation. So, we can find the slope at any point on the cantilever by substituting the value of x in this equation. So, we will get the theta b that is at free end where putting x is equals to L in this above equation we get e i theta b is equals to minus W into bracket L into L minus L square by 2 here I am replacing x by L. So, we will get by solving it is minus W L square by 2. So, therefore, theta b is equals to minus W L square upon 2 e i that is equation 5 a. So, this negative sign shows the tangent at b makes an angle in anticlockwise direction with line a b. Substituting the value of c 1 is equals to 0 and c 2 is equals to 0 in equation 4 we get e i y is equals to minus W L into x square by 2 plus W by 2 into x cube by 3. So, again the two terms are next two terms are 0 as c 1 and c 2 are 0. This is equals to taking minus W common minus W into bracket L x square by 2 minus x cube by 6 this is equation number 6. This equation is known as deflection equation. We can find deflection at any point on the cantilever by substituting the value of x. So, we have seen that the maximum deflection is at free end. So, we will substitute x is equals to L and the deflection at free end is y b. Therefore, e i y b is equals to minus W into bracket L into L square by 2 minus L cube by 6. Here I am replacing x by L. So, solving this we get is e i y b is equals to minus W L cube by 3. So, therefore, y b deflection is equals to minus W L cube upon 3 e i it is equation 6 a. Here again negative sign shows the deflection is downward. So, now instead of this load acting at the free end it is acting at somewhere at a distance a from the fixed end. So, this is L. So, this is a and this distance is L minus a. Now, let theta c is the slope at point c. So, now here if I draw a tangent here that will be having a theta c that is dy by dx at c. So, y c is the deflection point at c and y b is the deflection point at b. So, now the portion ac of the cantilever may be taken similar to a cantilever which is having a load at free end. So, now I will discard this. So, if I assume this only. So, now this is W is acting in a cantilever at a distance a that is at free end. Therefore, theta c as we have derived it is W a square upon 2 e i. So, here in the equation 5 a we have already derived that equation. So, instead of L I am putting it as the distance at a. So, y c is again W a cube upon 3 e i. Here I am not mentioning the negative sign because here it is anticlockwise direction and here the deflection is downward. So, I am only taking the values. So, I have not put negative sign there. So, now to find the theta b and y b. So, now beam will bend only the beam will bend only between a and c. So, here in this only portion the beam will bend as c to b there remains straight since no bending moment occurs in c b portion. So, now if no bending moments occur this will be a straight line. So, this straight line if I continue that will give a theta c or theta b will be same. So, theta c is equals to theta b is W a square upon 2 e i. So, y b is equals to y c. So, this deflection plus this deflection. So, here I am knowing this angle it is theta c. So, from that distance L minus a and theta c I will get this deflection b b dash. So, y b is equals to y c plus theta c into bracket L minus a. So, putting y c I will get y b is equals to W a cube upon 3 e i plus W a square upon 2 e i into bracket L minus a because theta c is W a square upon 2 e i. So, these are the references which I have used. Thank you.