welcome back my name is satiji sahu and we are in your Champion series and Champion Series today we are seeing what the subject still structures in steel structure one of the important topic is what plastic analysis and in that one important topic is what the collapse load of beams so today we'll be seeing how to find out the collapse load in pimps so let us welcome our participants so welcome Ankit swapnil Nikki so let us start the lecture without any further delay okay so before that some small announcements okay and then we will go into the topic okay so something about myself my name is satiji sahu I have done my B Tech and M Tech both from IIT kharagpur I have 10 years of experience in getting ESC domain I have been selected into many of the psus like iocl hpcl rights through gate only okay I have also given ESC and my interview marks was 140 in the year 2016 where it was one of the highest marks in the country okay and I also served as the design manager of Delhi Metro Corporation okay and I teach in both English and Hindi yes and therefore I've taught all across the nation okay in more than 15 states and I teach all the civil engineering subjects yeah I have taken a lot of subjects in the paid course also in the paid course I have taken subjects of strength of material Geotech environment open Channel flow concrete structures steel structures okay so fluid mechanics yes open Channel flow so many of the important topics also I have taken in the paid course okay so let us start with this lecture okay but again some small announcements so tomorrow as you know that we have hpcl bell and tspsc examinations coming up so tomorrow at 11 am not PM am means what morning so morning we will have a session onward your Geotech okay where we'll be solving 50 questions okay 50 questions in the pattern of what hpcl well and your Telangana State Public Service Commission pattern so tomorrow I expect that all the students they join me for this particular session at 11 am in the morning okay and how to manage gate and tspsc attend the sessions attend the sessions we are conducting sessions for both gate and tspsc so keep attending the sessions like yesterday I'm conducting session for Geotech so please attending keep attending the sessions okay you will get better idea of the questions and how to manage okay so as we have discussed yesterday also that before the class we'll be discussing what the number of days left so for SSC je 2022 the number of days left is 47 yes then we have get number of days left is 129 and for EST prelims the number of days left is 144 days yeah yeah same same pattern same thing is there we can say in all this examination the gate one mark or get one more questions is the potential question for what your tspsc okay see I cannot tell everything okay in this lecture so better is what you attend yesterday tomorrow's lecture you will get idea of the questions okay so better is what tomorrow 11 am please attend this session you will get idea of how you know your preparation for gate is helping for your tspsc or not okay so as we discussed the number of days okay so you should be little serious now yes you can see that the number of days for gate and other examination is closing okay so we will be conducting many sessions so keep attending okay also who want to register for our paid courses we have a scholarship test where you're providing what more than 90 not more than around 90 percent okay maximum 90 scholarship yes so if you want to get the scholarship on 1st of October at 11 am we are having a scholarship test also that will be conducted on the by juice exam prep official app so you can download the app you can register for the scholarship test okay so let us start today's class let us start what today's class okay now today's class I will take on scale and Pen I will draw everything I have decided today I will draw everything okay and we will learn everything okay live now many students requested with me to conduct this session on plastic analysis so here it is so suppose we have a beam like this suppose we have a beam like this suppose a simply supported beam suppose this is a simply supported beam okay now when we are applying a load when we are applying a load so what will happen it will deflect right it will deflect it will deflect like this so when it is deflecting like this this is what elastic deformation this is what this is your elastic deformation very good now if you increase the load the deflection will increase and I can say the deflection is still elastic the deflection is still elastic then if you keep increasing the load at a certain load I will call that as w u there will be formation of plastic hinge okay here the Reformation of a plastic hinge and that particular beam goes into plastic Zone at this plastic hinge and after that the beam will not deflect elastically there will not be an elastic curve now since this has become a hinge okay since it has become a hinge it will deflect something like this it will now deflect something like this yes it is a hinge now so it will deflect like this this okay good evening should we okay reflect like this so what we are asked in the examination we are asked that what will be this load at which the plastic hinge is formed and this particular beam collapses plastically okay so this is what known as collabsolute one is what collapse okay so this will be our subject of interest for this particular topic of today's okay so how to find out this collapse load now first of all we will see the possible locations of plastic hinge first we'll see what possible locations possible locations of plastic hinge so all the participant I request today session will be little long okay but if you attend the lecture you know meticulously you will be able to answer many of the questions on collapse routine beams okay I'll cover almost 70 to 80 percent of syllabus so please be attentive now what are the possible location of plastic hinge the first location is the fixed ends the first location is what fixed ends means what if you have a beam like this okay which is fixed at its end then at the fixed ends there is possibility of what plastic hitch it's the first location I can see then the second location is below Point load second question is what below Point load below Point load means what suppose we have a simply support beam like this yes simply support beam like this and suppose a point load is acting like this it might act at the center or it is acting on a different location then the plastic hinge is found below this point load this is another possible location now the Third location is where there is change of cross section where there is change of cross section for example suppose we have a fixed beam suppose we have a fixed beam like this like this okay it's a fixed beam yes the fixed ends and suppose the cross section is changing the cross section is changing something like this you can see the area is changing cross section area is changing so at this location also there is a possibility of your plastic hinge next location is the next location is points of zero Shear Force points of zero Shear Force I can say points of zero Shear Force are also the points of what maximum mining moment for example if I take a simply support beam yes if I take a simply support beam and I am having a URL I am having what and udl right now where the shear force is zero please tell me in the comment section where the shear force is zero please mention in the comment section where the shear force will be zero please tell me where the shear force will be 0 in this particular beam please write in the comment section where the shear force will be 0 at the center yes so here is the possibility of what your plastic hinge there are more possible locations also but for time being we will focus on these four points so at fixed end below the point load where the cross section is changing and point of zero shifts the other possible locations the other possible locations okay now let us analyze okay Analyze This plastic hinge formation and the collapse load with a concept of what that the total external work will be equal total internal work what does this mean let us analyze this so suppose we have a simply support beam let me start with a simple support yes the simplest example let me start with a simply supported view okay so suppose we have a simply supported beam like this yes very nice and suppose we have a load acting like this we have a load acting like this now when it collapses there is plastic hinge formation here okay the plastic is formed here so after this it will deform in this manner right it will deform in this manner yes due to this load it will deform in this manner okay very nice it is deforming in this manner now you can see that this plastic hinge is moving or displacing by an amount what Delta yes so this is the collapse load and this is the displacement Delta is what displacement below the collapsed load so I can say the external the external work done will be what what is work done work done is nothing but Force into displacement right work done is nothing but what it is force into displacement so this will be w u into displacement is what Delta so this will give me what the X external work done to give me what external work now what will be the internal work done what will be the internal work done you see you see these members are rotating right you see these members were straight they have rotated right you see this member was straight it has rotated right suppose this angle is Theta and suppose this angle is Alpha right this angle is Alpha they are rotated yes so due to rotation this is Theta this is Alpha due to rotation also there is what your internal work done and what is the internal work done what is work done in this rotation when there is rotation the work done is moment into I can say angle of rotation yes the work done when there is rotation due to a moment is what moment into angular rotation yes now you see here suppose this is a these distance is a and this distance is B A and B can we establish a relationship between Theta and Alpha yes we can how you see this triangle you see this triangular you see this triangle this triangle this is a and this is Delta able to see this triangle okay this is the triangle right yes now this is what this is Theta this is Theta now what is tan Theta tan Theta will be equal to Delta by a like Delta by a now for small angles now see these angles won't be very large these angles will be small so for small angles what will happen this Theta will be equal to 10 Theta will be equal to Theta yes Theta yes so from here I can say this displacement will be what a Theta understood now you remember that if we have something like this triangle like this and suppose this is small angle Theta and this is X this will be what Theta into X and therefore if this is a this will be what Theta into a or a Theta yes so I can say this displacement this displacement I am getting how much this displacement I am getting a into Theta yes from this you know we can say 10 to 30. now if we see the other triangle right if you see the other triangle this triangle yes from this triangle can you tell me what will be this displacement from the other triangle this displacement you will get how much can you tell me can you tell me what is the displacement from the other triangle let me see how many are able to answer this from this other triangle what will be this displacement can you tell me delta please write in the comment section Alpha into B S B Alpha yes B Alpha yes so I can say that this Central displacement I can write what the central displacement I can write down a into Theta yes or I can write down what B into Alpha understood B into Alpha very good very good we got this very nice now coming to this internal work then coming to this internal work done okay now you can see that there are two rotations Theta and Alpha there are two rotations Theta and Alpha and the moment developed at the plastic hinges MP the movement developed at the plastic hinges MP so if I ask you the internal work done then what you will say it will be equal to near the plastic hinge you can see two rotations one is Theta one is Alpha so the internal work done will be MP into Theta Plus MP into Alpha so this will be the internal work done now somebody might ask that sir there is rotation at this point also and this point also why we didn't take the internal work done there somebody might ask that there is you know there is rotation at this location also why there is no internal work done there the reason is these are not plastic hinges they are what they are only hinges and at a normal hinge what is the moment the moment is zero na at a normal is what is the movement at a normal hinge the moment is how much it is zero therefore even if there is rotation at those locations we will not consider the internal work done everybody understood this point yes will not consider the internal work done because the moment is zero because those are not what those who are not the plastic hinge those are not plastic hinges they are normal hinges at plastic hinge only we will have the plastic moment capacity as MP and therefore it will be MP theta plus MP Alpha now we'll use the concept of what the external work done is equal to internal work done we'll use the concept what external work done is equal to internal worker so how little patience will come to questions but the concept is important therefore I am spending some time okay so external work done is what w u into Delta Now Delta we saw what it is either a Theta or B Alpha suppose I am writing in place of you know this Del time writing a Theta okay that is equal to the internal work done internal work done is how much MP theta plus MP Alpha now I have to convert the alpha into Theta so what will be alpha alpha will be from this relationship it will be a by B Theta now it will be a by B Theta okay that will be a by B Theta so here I can write down what a by B Theta and this I can take MP Theta common and this will be 1 plus a by B so what will happen you can see Theta Theta gets canceled and from here I'll erase these things I will not erase this thing this thing is what still work done so this is internal work done right in the next page so I can write down the collapse load the collapse load into a is equal to 1 plus a by B into MP yes now this will become what a plus b by B into MP yes now tell me a plus b is the total length now a plus b is total length yes so I can say l total length is a plus b yes so from here I can say that your this is MP L I'll bring this a Down by a b is equal to collapse so it is a very important formula we derived that the collapse load is equal to MP L by a b this is for a simply supported load this is for a simply supported load or load Beam with a load acting in such a manner that a distance from one side and B distance from other side understood this derivation understood this derivation yes internal work done is equal to external work done the derivation is not important but it is important for complicated questions therefore I solve for an easy question now this formula is very important this formula is very important why suppose I tell that the load is acting at the center if I tell that the load is acting at the center now tell me what will be the formula of collapse load then if the load is acting at the center total length is l it is L and this is at L by two tell me what is the formula then tell you what is the formula of this collapse load it will be how many times of M P by L tell me how many times of MP by L tell me if you remember you can tell or you don't remember from this formula only you can find out how if it is acting at the center what will happen a is equal to B is equal to what L by 2. so if you put this L A is equal to B is equal to l by 2 tell me how much you are getting saurabh says writing four others how much are getting others 4 very good yes I'll get a 4 yes in this formula put what MP l then L by 2 L by 2. so what is happening we are getting this LL get canceled 4 MP by L so getting what 4 MP by L now in the examination if you remember this equation you can solve you know many questions let us solve many questions you see suppose I give a question like this it is simply support okay suppose this is L by 3 this is 2 L by 3. and we are asked to find out the collapse load and I am telling collapse load is equal to K into MP by L find K come on give me the answer find K come on give me the answer I am waiting for an answer I'll see comments here also comments are coming double comments now somebody was telling me sir why you see this side you're seeing the answers it's not an answer this comments are coming in the screen here please add parallel answer use the formula and tell me the answer find K 4.5 lavanya and Vivek after very good see write down the original equation what's the original equation the original equation is your MPL by a b here a is what here a is L by 3 B is 12 by 3. so one formula you can see so many questions are able to solve so this becomes m p l by L by 3 and 2 L by three so LL get canceled we get what 9 by 2 MP by L so this will be a one more question in Gate this can be also one more question in your hpcl orbel right next solve this question simply supported beam and then 2 w okay this two w okay nice it is L it is three l okay and I am writing that collapse load W is equal to K into MP by L now tell me find K let us see who finds out this answer find K so so this is our question number one I can say and this is our question number two I can say tell me the answer to this writing to 5.33 so now I will get some different different answers let us see now we'll get different different answers others what others are doing give the wrong answer so that I can correct keep the wrong answers 0.67 okay others six wow four people four different answers let us see some more answer others okay okay okay [Music] um all kind of answers have come let us solve this question okay I'll solve this question don't worry okay you see how to solve this kind of question how to solve this kind of question okay in this type of question write down first the original formula original formula is what it is MPL by a b okay now in the original now what you do you see this is 2W and this is what L and this was how much 2 L right two l or three l it was 3 m but it is 3M so now in the original formula this is the total load right so replace this total load by total load here it is how much 2 w is equal to MP yes this is the total lengthena total length now here total length is how much it is 4 into L right yes total length is 4 into L here this is total length right this is what total length when we derive this was total length now in this question this is the total length 4L divided by a is how much L and B is 3L so LL get canceled this and this canceled and I got how much W is equal to 2 by 3 MP by L so those home students found two by Three swap Nils correct we make also correct and Nikki correct Dr engine correct so many people have solved correctly those are not solved correctly hope you have understood how this type of questions have to be dealt okay so last question for this simply support okay so third question so this question will solve easy one I'll give an easy one not easy okay suppose I give like this suppose this is the collapse load given this is the cholesterol given 50 kilo Newton this is what the collapse load the collapse load is given to us okay this is your collapse load and suppose this is your one meter and this is your 3 meter Now find MP the question is to find out MP in kilo Newton meter let us see you will find out this answer first I'll wait okay so sometimes they will give questions like this also and you can easily solve let us see 37.5 others okay that was fast after pen Arsenal very fast very good students very good very good Nikki very good great doing great great that was great very good so you see here I will replace in the original equation I'll replace 50 is equal to 50 is equal to your MP into tal length is 4 a is 1 B is 3. so from here I can say MP will be equal to 150 by 4 and this is how much 37.5 kilo Newton meter so you can see that four questions were able to solve right four questions I would solve from the same formula from the same formula very good let us go to fixed beam let us go to what fixed beam now before going into fixed beam I want to say something about what number of hinges I want to say about what number of hinges now number of hinges formed in a particular beam n is equal to the degree of static indeterminacy plus one now if we have a simply support beam if we have a simply support beam like this okay if we have a simply support beam like this then what happens and we have a vertical load if you have a vertical load in the simplest support beam at the support okay this is a pinned support in pin support will get word only vertical reaction why we are getting only vertical reaction because it is hinged or pinned so it can rotate if it can rotate there won't be any fixed end movement because you can rotate and since there is no horizontal load there won't be any horizontal reaction understood yes see here horizontal reaction also comes but here it won't come because there is no horizontal load yes now the other end is a roller this was pinned this is pinned the other end is Low Roller in the roller support what happens in the roller support only a vertical reactions come into picture right yes because the roller can work it can move horizontally so therefore there won't be any horizontal reaction yes so here if I ask you find out the number of reaction the ramper of reactions is how many the number of reactions R is equal to 2 and if I ask you what is the number of equilibrium equations if I ask you what is the number of equilibrium equations the number of equilibrium equations that is equal to s that will be how much that will be 2 Y 2 because there is no there is no there is no horizontal road so therefore the equilibrium equations will be what summation of vertical forces is equal to 0 yes and summation of moment is equal to 0 about any point yes normally we have three equilibrium equations right summation of vertical force is equal to zero summative moment about a particular point is zero and summation of horizontal forces is 0 but we won't be using the third equation because there is no horizontal load so this equation is not applicable so I can say two equilibrium equations then we know that the degree of static indeterminacy if you don't know I am telling you that will be equal to R minus s number of unknown reactions minus number of equilibrium equations so 2 minus 2 giving me how much 0 and therefore if I ask you in a simply supported beam how many hinges are formed the answer will be 1 because it is 0 plus 1 giving how much it is 1 yes and that particular hinge is formed here below the load which we analyzed everybody understood this number of hinges for a simply supported beam yes now let us go to what let us go to your fixed beam let us go to a fixed page now if we see a fixed beam if I see a fixed beam like this yes if we see a fixed beam okay fixed at the end like this yes fixed at the end now what will happen with the fixed beam you see in a fixed beam suppose a load is acting like this a load is acting like this it's not looking straight let me use my scale suppose a load is acting like this so the number of reactions will be how many if you see the support there will be vertical reaction there won't be horizontal Direction why because there is no horizontal load now this is fixed in fixed end rotation is not allowed since rotation is not allowed there will be fixed end moment also because rotation is not allowed remember that why there is reaction there is reaction when something is restricted you can see this particular point there is no rotation at the fixed end since there is no rotation therefore it will react see when you react at your homes when your parents restrict you from doing something right so similarly when there is restriction there is reaction so your restriction of rotation therefore movement will come in your pinned support there is no restriction of rotation their rotation can happen and therefore no moment reaction okay so here the number of reactions is four equilibrium equations will be two that is the summation of vertical forces zero and summation of moment zero because since horizontal forces are not acting we cannot consider that equilibrium equation so here the degree of static indeterminacy will be 4 minus 2 that is 2. so here the number of hinges will be how many it will be 2 plus 1 d s plus 1 that is equal to 3 plastic hinges are formed so remember this thing we have derived also here that in a simply support pin there is only one plastic hinge formation yes in your fixed beam there are three plastic hinge formation so if you remember the possible locations here we have below the point load and here what at the fixed ends you can see that three plastic hinges are formed here now if I see the deformation the deformation will be something like this right if you see the deformation the deformation will be something like yes and this I can say is the deflection below the load or displacement below this collapse load right so what will be the external work the external work will remain same right you see the external work the external work will be equal to same this collapse load into displacement right collapse load into displacement and the internal work let us see what will happen to the internal work what will happen to the internal work you see here we have Theta and this is what Alpha right so I can say alternate angles so this also will be Theta this also will be Alpha now hinge is here here now here the plastic moment the moment is plastic moment yes now here also the moment is plastic moment because hinge is formed and here also there is plastic movement because hinges from there so if I ask you what is the internal work done the internal work done will be how many you see there are two Theta and two alpha yes and everywhere the plastic moment is MP so 2 Theta so MP 2 Theta or I can say MP Theta plus MP Theta plus MP Alpha plus MP Alpha yes so I can say here you see here MP Theta to rotation of theta here MP Theta here MP Alpha and here MP Alpha understood yes now you might say that this is equal to what 2 MP theta plus m p Alpha and this is w u into T Delta now if you see the difference if I see the difference between the simply support and the fixed then what's the difference let us see I will draw both simply supported and your fixed if I try to analyze the differences you see what will happen in the simply support the hinge is only formed here right but in case of fixed the hinge is formed here it is formed here it is formed here right and therefore you see if you remember there I was taking only MP Theta plus MP Alpha right but here I am taking MP Theta 1 MP Theta then another MP Theta here 1 MP Alpha here another MP Alpha now you might say that here also Theta is there also it Alpha is there but why we are not taking the internal work done because there is where the normal hinges and their moment is what 0 and here at the plastic change the moment is MP but in the fixed here also MP here also MP and here also MP so everybody understood why we have these two figure coming into picture now since this 2 is there you see the internal work done is just twice the internal work done in case of Simply support now yes the internal work done is twice that of what is formed in the simply support now and therefore remember that whatever collapse load you will get for your simply support in the fixed you will just get the double of that so here the collapse load without deriving I can say it is what your 2 MP into L by a b yes because the internal work done is just twice yes if you see the internal work done in case of simple support is what it will be only MP theta plus MP Alpha so from this I get a very nice conclusion which will help you in solving many questions what is the conclusion you see right is getting erased so if we have a simply support and a fixed if I am comparing them if I'm comparing them it's a simple support okay and it's a fixed if I am comparing them yes so here the collapse load is what it is MPL by a b and here it will be how much here it will be 2 MPL by LP just remember it will be twice just remember it will be twice why I just explained to you now if I tell that the load is acting at the center in case of a simply support then what was the collapse load here the collapse load was 4 MP by L we derived right so now if I tell us load is acting at the center of your fixed beam then tell me what will be the equation of your collapse law tell me what will be the equation of prolapse law tell me then butter 8 MP by L very easy very easy okay so now you see so many formulas you remembered by some basic concepts so just remember this one just remember this one yes and remember that in case of fixed you just get two times yes and therefore this is the case understood let me give you a question whether you solve it okay let me give a question so question number five I think right question number five so we have a fixed beam like this we have a picked beam like this so they will frame questions like this only in the examination and if you are smart and you know the basic formulas you can easily solve suppose this is L by 3 this is 2L by 3 right and this is w u find w u if sorry if the find K if w u is equal to k m p by L will be the value of K so first fast is telling nine very good others nine very good you see use the formula it is 2 MP right it is 2 MP 2 MP total length here also is L divided by L by 3 and then 2L by 3. so 2 2 get canceled LL get canceled I am getting what w is equal to 9 MP by m if you remember same similar question we solved for the simply support right similar question we solved for the simply support that time we're getting 4.5 right but here we got 9 because we'll just get that twice so that means you see from one equation you can remember many equations right that is the key that is the way you study for competitive exam you have to be smart students are very smart they are smart like me yes students are very smart so you have to be also smart let me give another question then let us see who will solve this question first question number six so any type of question they ask you can easily solve if you know these basic things this is 4 by 3 of w and this is your L and this is your 3L and they're writing the collapse load W is equal to k m p by L find K so such kind of questions they will ask in the examples question number six what is the value okay please solve and tell me two okay others two very good others two let us see so here write down the original equation original equation is this right original equation is this yes and here you see in place of collabs load I will write down four by three W just replace 2 MP in case of length I'll add down 4 L A is L B is 3L so this is 3 3 get canceled this 4 4 get canceled this LL get canceled I am getting what w is equal to 2 MP by L where is K is how much getting two easy so if I ask you from this last 45 minutes if you can just remember this formula you have you can solve all these questions now if you just remember this formula okay if you just remember this formula that collapse load is equal to m p l by a b right MP L by a b and remember that in the fixed we get twice of Simply support we get twice of Simply support then actually you can solve all the questions which we have solved till now right yes because if you know this you know that it will be 2 MPL by a B for fixed and then the load is acting at the center it will be 4 MP by L for the simple support beam and for the fixed beam it will be 8 MP by L so you see this is what is Smart studies yes this is how you study for competitive exam for gate examination yes you remember one formula you remember one formula and from that one formula you are able to what derive other formulas or solve in the examination this is smart stories this is what's smart let us go to the next type of thing that is what that is the propped cantilever that is what profit can tell you let us understand for profit cantilever what happens in a propped cantilever okay in a propped cantilever we get something like this you see here it is a cantilever only what is a broad cantilever it is a cantilever only okay with one end is pinned one end is what it is pin this is one end split so if I ask you the degree of static indeterminacy if we have a load acting like this this load is suppose W you suppose and acting okay suppose this is a this is B this is a this is B so here number of reactions will be only one you see there can be a horizontal reaction also but since there is no horizontal Force only one vertical reaction and here one vertical reaction and one fixed end moment because of the fixed end no rotation so there will be reaction so number of reactions here will be three right and equilibrium equation will be two so here the degree of static indeterminacy will be 3 minus 2 that is how much one that is how much one and I can say number of hinges will be how much d s plus 1 that is how much it two yes so very important Point very important point that in case of your simply support one hinge is formed for prop cantilever two hinges are formed and for fixed three hinges are found right now you see this propped hinges can form where below the load yes and at this fixed end at this fixed end right so now let us analyze and find out the collapse load expression for this let us find the collapse load expression for this so here you can say operate is formed it will deflect like this so I'll draw the deflected shape like this yes and hinge is formed here yes and I can say that this is the displacement below the load this is what the displacement will the load Delta again this is Theta this is Alpha this is Theta this is Alpha yes and I can say the in external work done I can say that the external work done will be equal to Wu into Delta it's our W Delta yes but if I ask you internal work done tell me what will be the internal work done I will wait for a reply tell me what will the internal version come on write down in the comment section what will be the internal work done write down in the comment section what will be internal work done write down in the comment section let me see that who are solid understanding the lecture properly and waiting for answer come on very good 2 MP theta plus MP Alpha yes here you see we have plastic moment here yes we even have plastic movement here yes but we don't have plastic movement here it is a normal hinge because no plastic sorry sorry what happened so sorry sorry for the sound something some notification came in the mobile okay I didn't silent let me silence sorry okay now it is fine so here what happens this is a normal hinge only so here moment is what 0 so we won't be considering the rotation there right so internal work done will be you see MP Theta this one right again another MP Theta this one and then MP Alpha very good very good student so 2 MP theta plus MP Alpha very nice yes so now if I equate the internal work done external work done yes external work done is W into Delta this Delta can be written as what it can be written as a into Theta right yes we have discussed already this point right it can be written as what you see this is Theta this is a this is Delta so this can be written as what a into Theta so w a into Theta will be equal to I can write down 2 MP Theta plus MP Alpha we know this relationship right which relationship Theta into a is equal to B into Alpha that is equal to a Delta we derived it right initially yes and I can say from here Alpha is equal to Theta a by B so we'll use this relationship so here in place of alpha at and what MP Theta a by B yes so what will happen w u a into Theta will give me I'll take MP common MP Theta common so it will be 2 plus a by B right Theta Theta get canceled and this will be m p a plus 2 B by you see this a I will bring down so it become what a b right yes already B is there so it become a b and this is your collapse load this is what this is your collapse level everybody understood so in this case of a propped cantilever so I can say the collapse load is equal to how much we got MP a plus 2B by a b now this can be written as MP a plus b plus b a plus b plus b by a b and this is what MP this a plus b is L total length now yes so m p l plus b by a b so you can see that this equation is also similar to the equation it is also similar to the equation which we got for simply support now that it was only MP L by FB here it is what MP L plus b by a b yes yes so now if I say if I say that the load is acting at the center if I say that the load is acting at the center something like this sorry fixed end and here it is acting at the center L by 2. then tell me what will be the expression for your collapse load here what will happen a is equal to B is equal to L by 2. so what will be the expression for collapse node how much MP by L this will be MP L plus n plus of B I can write down L by 2 divided by L by 2 A and B is L by 2. so how much I am getting this we are taking so much of time how much I am getting 6 MP by L yes I am getting 6 MP by here so this becomes 6 MP by here yes so if I summarize now see it's very easy I'll compare three of them I'll compare three of them and you can see that you can easily remember the equations I'll compare three of them you will see that you can easily remember the equations see we are not able to remember the equations because we are not logically understanding them okay so we have to remember yes we have to remember but with certain logic with certain logic you can easily remember you can easily remember and all these standard cases I can say they can be asked in the examination and you saw that the variation of certain cases also yes that can be also asked in the examination so you see if a load is acting like this a b load is acting like this a b yes and load is acting like this a b so I can say here here it is how much m p l by a b yes or no here it will be how much just the twice of that so 2 m p l by yes and here what here it is MP by a b l is there just additional this p is there can you remember now these three formulas right can you remember now these three formulas easily yes you can easily give another formula yes now if I tell you if I tell you that a is equal to B is equal to l by 2 means what the lower is exactly acting at the center when the load is exactly acting at the center you see here I am getting how much 4 MP by L right and I can say you see only one hinge is formed only one hingest form I am getting how much 4 MP by L here you see two hinges are formed yes so you got increased to how much 6 MP by L yes and you see here I am adding one more hinge so three hinges are formed here yes and here it is how much twice of that it is what 8 Amp by here so it will vertically remember also you see here it is 4 MP by L then one hinge got increased becomes 6 MP by L then one has got increase become 8 mph you see all this logically you can remember yes all this logically you can remember and if there are some variations of this then also I can solve the questions right like we solved in the previous questions you see all these questions are what variation this is we can say the variation on the standard question right it is the variation of standard question so let me give you some more questions let us see how you're able to solve or Not by using standard results so sixth question we solved seventh one okay so today I decided that I will solve the questions without any PPT work yes so today everything I am writing okay everything I'm writing hope you are enjoying the lecture okay so I'll give you a question like this let us see who will solve this question first okay and you can see that these stations are designed in such a way that it will be helpful for SSC exam for your gate for your ESC hpcl okay Rahul are you there Rahul are you there so people ask that how to study for gate and um exam they come to the accessions people always come to session and ask how to study how to study how to study how to study but when we teach then people run away so I always feel that how to study for gate exam attend the classes that's it it's very simple right attend the classes that is the way to study if you don't attend the classes then how you will study yes okay now I'll give this question yes this is your L this is your 2L and this is your 3w so collapse load W is equal to K MP by L yes so please find out K here see in the examination they will ask these questions only okay in the examination they will ask these questions only this year already 5 000 vacancies were filled from psus and state exams combined it is 10 000. so next year it will be expected 15 000 vacancies so please attend the classes please be sincere for one year don't be distracted by anything one year just sit with your notes five by six is the Arsenal's answer one year just study your notes attend the classes don't listen to anyone okay people are just you know distracting you so just focus on studies okay five by six others five by six okay I done the original equation w u is equal to your MP L plus b divided by what a b so in this original equation you will write down three W is equal to MP then l total length is not L here total length is 3 l here and B is how much B is 2L here divided by what is l b is 2L right so I can say this will be 5 MPL by 2 L Square so L got canceled and from here W I will bring this down and getting what 5 by 6 MP by L so again you can see that you can easily solve this kind of questions by just remembering what the standard cases by just remembering standard cases next question you solve for me and for yourself for one and a half years don't let anything affect you attend the classes okay study your notes all the questions will be from notes only don't waste your time here and there please find out K here so only these questions they not only the question these are the prominent type of questions they ask okay so you need to be little careful please solve this question let us see who will solve this question I'll have more water after some time 7.5 um seven point five fifteen by two seven point five Fifteen by two seven point five fifteen by two seven point five fifteen by Twenty what is a here what is B here tell me what is a here what is B here what is a here what is a here let me see and I can see in the comment section here what is a here a is L by 3 B is 12 by 3. okay so you didn't get confused by the question very good you didn't get confused by the question very good very good smart students yes a is your L by 3 B is your two L by three remember that it is not by order that this is a this is B this is wrong in case of word your prompt cantilever see in simply support and your fix doesn't matter A and B how I will define B is the distance of the load from the propped end so this is B and this is a so smart students okay smart student so didn't get confused very good I am very happy that we have understood the concept very nicely okay you see here in the previous question this was a this was B because this is the distance from the propped end right yes so always remember that this A and B in the prompt cantilever the B is from the prop tent distance of the load of the property see if you take this as a and this has B then the answer would have been wrong but you didn't do very good so the collapse load is equal to your MP L plus b which is 2L by 3 then your L by 3 and then 12 by 3. 3 so I can say this will be MP Type L by 3 and then 2 L Square by 9. so this got canceled this got canceled I got 15 by 2 MP by L which is 7.5 MP by so you can see that all these questions you are so easily solving right you are easily solving these questions without any major hiccup right by just understanding basic concepts by just understanding basic concepts let us go to the next type of question that is what the cross-sectional change if there is change in the cross section how to solve those kind of questions okay let us see suppose we will start with the fixed beam where the cross section is changing okay now there is no standard formula for this type of questions for this type of questions you have to do proper analysis means what you have to do internal work done is equal to external work done okay in this type of questions we don't have any options so we have to go for this good job so it is fixed like this okay and here there is cross section change somewhere the cross section change won't be always at the middle right it won't be always at the middle it can be anywhere can be anywhere suppose I am telling it is somewhere here suppose and when the cross section changes what will happen the MP will change why the MP will change because the MP depends on the cross section the MP will change so suppose this is your 2 MP I am giving the data and here it is MP and suppose this length is l yes this length is l and suppose this length is 2 L very nice and suppose here now in this type of questions the first thing is where the load is acting the load can act in two locations either they will give the load at where at the junction you can see the junction the load is acting at the junction yes or it can act some other point let us analyze when it is acting at the junction it is acting at the junction now tell me in the fixed beam how many hinges were formed tell me in the fixed beam how many hinges are formed tell me in a fixed beam how many hinges are formed three we have found out right DS was 2 so d s plus 1 d s was 2 so 2 plus 1 3 hinges are formed yes and in this case one hinge will be formed here one hinge will be formed here one hinge will be formed here okay now this Beam with the cross section is changing let me represent it with a single line for you know simplifying purpose I am representing this with a single line let me represent as a single line okay just for representation and simplicity packaging of the question a single line I'm telling and I am telling that hinges are found here here and here and since load is acting at this Junction I will say that I will get a deflected shape like this I'll get a deflected shape like this sorry that I just he came I just see where are you I was waiting for you yes so the hinges here okay now you see this is the displacement below the load Wu and this is the displacement below the load this was l i told and this is 2L I told right if this is Theta and this is suppose Alpha can you give me the relationship between Theta and Alpha come on can you tell me the relationship between Theta and Alpha what is the relationship between Theta and Alpha letter c will tell what is the relationship between Theta and Alpha tell me Theta is equal to 2 Alpha yes you see the central difference displacement you see this is if you consider this triangle it is Theta into L and if you concept this triangle it is 2 L into Alpha right you see this thing now see Theta into L is this one Center one right Theta into L this also 2 L into Alpha yes so replace this relationship I can say Theta is equal to 2 Alpha I can say very good now very interesting thing we have three hinges hinge number one hinge number two and hinge number three now tell me what is the plastic moment capacity at hinge number one what is the plastic moment capacity at hinge number one is it 2 MP or is it MP at age number one what is the plastic moment capacity is it MP or 2mp please write in the comment section is it MP or 2mp it is 2 MP at the see here here it is 2 MP right here it is 2 MP here it will be 2 empty yes now in hinge number three in hinge number three tell me what is the MP hinge number three what is the MP hinge number three what is the MP yes it is MP only yes because this engine is in empty now hinge number two hint number two what is the MP hinge number two Hill number two it will be the minimum of both since hint number two is at Junction you will take the minimum and here it will be what MP only everybody understood how we are finding the plastic moment capacity at different hinges so I will turn again here you see here it is 2 MP here it is MP and since this particular point this particular point is at the junction so I will take the minimum so here it will be MP okay now let us study the rotations and then find out the internal work done okay let us study the notation and find out what the internal work done so in this case so it is kinematics or you'll join relative see it is kinematic method or static method don't matter it is just a method it is just a method I don't go into so much into kinematic or static this is method of what the internal work done is equal to external work done and I only follow this method I don't follow other methods if by following kinematic or static you are getting the same answer then better is what just remember one method this is the one method I will not tell the name and confuse I'll don't tell the name and Confused I am teaching only one method that is sufficient for your examination okay now here you will study the rotations now we will study the rotations okay this beam is looking straight this is not looking straight let me make it straight oh nice now what is happening yes there is rotation here Theta here also Theta yes and here plastic hinge is formed with capacity MP yes here plastic engine is formed with capacity 2 MP yes therefore this internal work done will be what it will be 2 MP into Theta over here for this rotation and for the this rotation it will be MP into Theta right not this rotation this rotation against yes for this rotation to MP Theta the other one MP Theta right this is Alpha so this to this rotation it will be MP into Alpha and this is also Alpha and here yes the plastic moment capacity is MP so therefore for this rotation it will be how much plus MP into Alpha everybody got cleared how to find out the internal work done here everybody got cleared how to find out the internal work done here any doubt any doubt how we found out the internal work done yes so I can say that the internal work done so whenever you're finding the internal work done now I will give you a simple hint first for every hinge write down the plastic moment capacity like we did here without the plastic movement capacity then what we did then we just multiplied the angles this was Theta so 2 MP Theta this was Theta so MP Theta this was Alpha so MP Alpha and this was Alpha so amplifier very easy very easy yes so the internal work done is equal to I can say 3 MP Theta okay plus 2 MP Alpha and this 2 MP Alpha can I write that as MP Theta can I write that as MP Theta because you see Theta is equal to 2 Alpha so 2 amplitude 2 MP Alpha will become what MP Theta so this will become 4 MP Theta understood here in place of two alpha writing Theta so this become what MP Theta okay so this is your internal work done easy now what about the external work done I can say the external work done will be equal to Simply external work done will be simply equal to the collapse load here right w u yes L and then Theta yes because this Delta will be what L into Theta right so I can say this will be equal to I can say your w u l into Theta w u l into Theta Now ladies and gentlemen can you give me the extra the plastic is a collapse load tell me how much it will be the collapse mode will be how much tell me find out equate both of them and give me the load the collapse load for this thing so I can say this is your question number eight nine nine I think I am excluding standard cases also why are taking so much of time it is very straightforward now equate this external work done internal internal work done external work done we have taken so much of time um slept wake up I think some malfunctioning has happened in the comment section in the comment section I am not able to see the comments so please write down the comments I'll see the mobile IP mobile moments are coming I think some malfunctioning has happened here okay now it came very good right cam 4 MP by L yes 4 MP by n understood how we are solving for this case everybody understood so question number eight this was question number nine so I'll give a question now now I'll give a question your question okay solve this very good good students sorry you see if you are attending these sessions now in a very short time you see hardly for simple yes so everything is done before okay so everything is done before you can go to the initial part of the lecture I have taught for simply simply supported I have taught for cantilever prop cantilever I have taught for fixed so all the simple cases I have completed so now we are going to cross section changes okay so if you want to see this you can see you can just go to the initial part of the lecture you can see ah everything I have taught first we saw all the simple cases now we are going towards complicated ones okay hmm very good okay now this question you will solve okay so I will give you some time to solve take your time to solve this is L this is L both are L okay frames no no frames today will not teach some other day will teach otherwise it becomes 2 am and you know some of my friends were telling they were opening YouTube they were watching movie trailers they saw Saturday at 12 o'clock so they were telling satyajit you have gone crazy I told no I was already crazy W yeah this is 3 MP okay and this is MP okay so find collapse load this is K MP by L so find K 1 apply the same method and find out K here you see there is no shortcut right see here there is no shortcut you have to properly analyze for this type of questions there is no shortcut you have to properly analyze the question okay so there is no shortcut for this you have to properly analyze so first what you can do is that you can take this as a single line okay I'm giving you hint start solving you will only solve while would solve oh you've solved also so fast okay let us see might be wrong cross check cross check once six five all right there is no standard formula for this you have to find out okay oh that's fast that's very good great others also please see are you solving okay oh oh that's great nice great you see since this is L and L this also will be Theta this also will be Theta right because the load is acting exactly at the center yes therefore the both the angles will be same yes so this also will be Theta this also will be Theta because the load is acting exactly at the center there will be symmetry right it will be symmetry now coming to the movement capacity here the moment capacity will be 3 MP right here the moment capacity will be MPE and at the junction the moment capacity will be how much the minimum that is MP right so if I ask you the internal work done the internal work done will be equal to I can say the internal work done will be equal to you see 3MP Theta yes yes for this angle then plus MP Theta for this angle plus MP Theta for this angle plus MP Theta for the center this is giving how much is giving 6 MP Theta okay it was easy actually very good and then the external work done you see such kind of questions you can easily solve if your Basics are strong external work done is this into Delta and Delta I can say is your L Theta it is what L Theta is and from here I'll equate this to the internal work done the external work done so from here I can say Theta Theta get canceled I get the polar flow is equal to 6 MP by 3. so hope everybody understood this particular thing where the load is acting at The Junction now if the load is not acting at the junction okay load is not acting at the junction suppose it is acting like this question number 11. and the last question for the day no homework today is a question okay very good everything is easy only when we know the method everything is easy if you don't know the method then everything is tough now what we will do will apply the load not at the junction okay not at the junction suppose same question let us let me take the same question so that there is ease of understanding but I will not apply at the junction the Lord is not acting at the junction so this is L this is l okay and suppose the load is acting at L by 2 from here the load is acting at L by 2. so in this case what to do let us see in this case what we will do first of all the number of hinges is how many number of hinges is three only it is three only but what happens here you see if I take the line diagram let me take the line diagram here always do the drawing diagram so that it is a little easier whatever question they have asked you do the line diagram yes and I'm you know carrying the scale and all because I wanted to teach you how to do properly okay see structure one of the important thing is what you should be structured in solving question of structure even in any you know engineering thing you should be many structure you see here the possible locations are the fixed end you see the junction also there can be a moment there can be a hinge because we have discussed that whenever there is change in cross section there is a hinge formation there and below the load also there can be hinge so there are four possible locations there are four possible locations but only three can phone yes only three can form therefore it will lead to two mechanisms it lead to what two mechanisms so I can say two permutations or two possibilities right two possibilities it will go to what two possibilities I will say mechanism one yes mechanism one and mechanism two why because the number of hinges formation is three only but the possible locations are 4 and therefore we will have your in mechanism one at the fixed end always there will be the hinge formation remember this and one hinge will form just below the load this is mechanism one this is mechanism one and you can see that there are three hinges and then in mechanism 2 in mechanism two what will happen in mechanism 2 what will happen the hinges will form in the fixed end and one hinge will form at the junction understood understood so two mechanisms are happening why because we have three hinge formation possibles that is the three hinge can only form but possibilities are four therefore we have to go for multiple mechanism yes so now we will find out the collapse load from mechanism one and then collapse load for mechanism two and then we will take what we will take the minimum one yes so let us find out using both the mechanisms so let us first study what the mechanism one okay so I am giving you time solve and tell me how you how much you're getting from the mechanism one I'm just drawing the diagram I am drawing the diagram solve and tell me how much collapse load you are getting from mechanism one start solving you will solve I will not solve you know the method now right mechanism one means below the load yes L by 2 given come on tell me what is the collapse load from this mechanism let me see who will solve first which is the same method of what external work done is equal to internal work done I'll wait for answer okay take your time take your time take your time 10 MP by L others very good after let us see you see this hinge will have moment capacity 3 MP right this will have MP3 ampere 2 MP what was there we are not given in the early data is right down here to our confusion so swapnel is also writing 10 MP so writing 10 MP okay so now tell me here it is MP what will be at this Junction what will be the MP at this hinge tell me what will be the MP at this hinge tell me what will be the Ampere at this hinge what is the MP at this hinge it is 3 MP or 2 MP or MP it is 3 MP why you can see that this particular hinge is not in the junction it is formed below this load and this load here in this point the MP is 3 ampina yes so here also this is what 3 MP so if I write the internal work done if I write the internal work done ah that was the mistake the internal work done so you have to be careful you have to be careful therefore the sessions are conducted right so see where the hinge is formed the hinge is not at the junction the hinges inside the beam where it is 3 MP so the plastic movement will be 3 MP there yes so here the internal work done will be for this Theta it will be 3 MP Theta yes for this Theta also 3 MP Theta yes for this Alpha it will be 3 MP Alpha and for this Alpha it will be what MP Alpha understood everyone yes so this will become I can say 6 MP theta plus 4 MP Alpha this is the internal work done this is the internal work done right now the relationship between Theta and Alpha I can say Theta into L by 2 is equal to 3 after selling 12 MP corrected so others what they are doing others are watching highlights of India versus South Africa India has already won you can watch later okay what are others doing yes so from here I can say I am late okay no problem you can see the recorded also yes so from here Theta is equal to 3 Alpha right Theta is equal to 3 Alpha and I can write down this as 6 MP Theta S Plus this will be 4 this will be 4 by 3 MP Theta while getting 12 getting 12 let me see and the external work done will be equal to the external work done will be equal to Wu into your Delta that can be written as what w u L by 2 Theta this is the external work done you can see this triangle right this triangle if you see this is L by 2 so taken L instead of three L by 2 okay so say how many mistakes You are conducting that means lack of practice Delta will be equal to Theta L by 2. yes how you are getting this I am feeling some mistake you are doing so from here you will take 22 MP Theta by three now yes yes Arsenal correct now not practicing all students not studying so from here w u is equal to 44 MP by L 44 MP by L understood what mistakes you did what are others doing eating badappa and why you are unable to solve this why you took so much time and even after solving also you are not that means you are not practicing things yes so no problem we will therefore conduct sessions therefore we are conducting sessions so that you get a reality check right and also you see that your practice is less understood everyone this particular mechanism this only mechanism one mechanism two is still remaining okay mechanism 2 is still remaining okay you can just take every calculation is correct I might be also I might have also done some calculation error you just check that everything is fine or not everything is fine or not 3 MP theta 3 MP theta 3 MP Alpha MP Alpha 6 MP theta plus four MP Alpha here Theta is equal to 3 Alpha yeah yeah 22 MP Theta by three yeah yeah correct y w t g of Steel in Gate huh what is wtg of Steel what is wtg ISO don't know what is wtg because what is the what is the question because I am not able to get it can you just elaborate what is this question okay now mechanism to you do weightage oh my God okay sorry oh sorry I am very poor in shortcut Ok sorry what is the weightage okay see other students are very smart so students understand student language and teacher has grown old better teacher okay better teacher okay no problem what is the weightage of Steel you can get three to five marks in your gate examination okay in a gate examination three to five marks and in ESC you can expect in ESC prelims you can expect eight to ten questions from steel prelims in men's also you can get around 50 marks from in the mains in sscj you can expect around 10 questions from steel structures okay but then we can say 6 to 10 it varies okay 6 to 10 okay okay let us go to the mechanism to hope you are understanding and enjoying the session so mechanism two now mechanism two you do let us see what mistake you will do let us see what mistake you will do in mechanism two then I'll correct it I Am Legend no no no I am not Legend I am I am teacher I don't want to be Legend I want to be teacher let me teach okay so you also learn you are also not Warrior you are student so study tell here hinge is formed here he also hinge is formed here and one hinge is formed here here okay at the junction if you see like this see Legend is who you know Legend is Abdul Kalam yes Legend is Abdul Kalam Legend was Madame Curie yes legendary all the noble laureates who are scientists Legends are the big scientists who are working in ISRO in NASA yes Legends are you know the soldiers who are working in the front legendar the numerous doctors okay nurses who are always working for the betterment of society Legends are who you know Legends are the people who are cleaning our gutters also they are also Legends okay so I am not a legend I am okay I am trying to follow the legends okay the load is acting here to tell me you're getting 6 MP by L 4 MP by others others what you are doing others what is the answer for others let me throw the deflected shape yes the deflected safe hinges formed here hinges found here hinges found here okay now you see since the hinge is formed in a symmetric way this is L this is L so Theta will be same Theta Theta Theta Theta because I wrote the hinge is formed at Center hinge is formed a center okay so now here the moment capacity will be 3 MP now yes this is 3 MP so this is 3 MP this is MP so this is also MP and now this Hint it at Junction so it will become what MP so when I get the internal work when I get the internal work I'll get what I will get 3 MP theta plus MP theta plus MP theta plus MP Theta right I will get how much I will get 6 MP Theta now what about the external work can anybody tell what is the external work here what is the external work done tell me what is the external work done what is the external button Anu you have committed a small mistake a small mistake you have taken this displacement this is not the displacement we have to take the displacement below the load load is acting here so this displacement I will consider understood I will not consider the central displacement I will consider the displacement below the load here the hinge is not formed below the load yes therefore this displacement I will not take always the displacement should be below the load in the previous cases everywhere the disc the hinge was found below the load yes the hinge was formed at the load therefore the displacement we are taking but here you see hinge is not formed below the load and therefore I will take this displacement this is L by 2 so this will be w l by 2 Theta so this is the concept this is the concept so from here I can say these are liquid to 6 MP Theta and your W will be w u will be equal to your 12 MP by L yes so from this mechanism I am getting 12 MP by L and from this mechanism I am getting 44 by 3 what is 44 by 3 by the way what is 44 by 3 by the way what is 44 by 3 will get 11 point no no no he will get 14 point something 14.67 right yes you will get 14.67 MP by so ladies and gentlemen yes by the narrow stop margin this is the collapse load because this is the minimum one is the minimum and this becomes what the collapse so yes we solved so many types of question yes this is the end of the class hope you enjoyed this class okay so we solved so many types of question yes we solved so many types of question okay and the most critical was when the cross section changes other things were easily solving other things were easily solving because there what was happening many things were from standard formula now when the cross section change there are two cases one case when the load is acting at the junction when load is acting at the junction there will be only one mechanism right when load is acting at the junction then only one mechanism if the load is not at the junction like this there will be two mechanisms and in both the mechanisms what we'll do first mechanism below the load yes and here you have to be careful below the load this is not Junction so don't take Junction minimum one okay yes this is not the junction below the load is not the junction it will be inside some beam take the moment of that beam take the plastic moment of that beam yes this is the critical mistake we students do but you understood and when the hinge is formed at the junction there don't take this displacement people commit this mistake will take the displacement below the load yes so all the mistakes which we do that also have taken care so one homework I will give homework okay homework yes so homework there will be cross section change okay you do it and write down the answer in the comment section okay I will answer to that comment section okay today I will set an answer to the previous questions also don't go don't go away I have some announcements for you don't go away okay highlights can wait I have I will also see the highlights I have also not seen the highlights I'll also go and see the highlights so please wait please wait for me we'll see highlights together so this is 2mp this is MP okay this is l this is sorry this is L suppose and this is 3 l and load is acting at 2. that is okay load is acting at we're not not at a junction okay so the collapse load w u here is equal to k m p by L so solved by both the mechanisms and find K okay hope you enjoyed today's lecture a lot many of your Concepts got cleared and you saw for the standard cases also how you were able to solve and for clock section change also so tomorrow ladies and gentlemen tomorrow so many webs oh where is the end of the PPT oh yes so last announcement so we have the scholarship test on 1st of October if you can get the scholarship tomorrow time yes and that's what I was going to announce so this is the scholarship test where you can get so like this I have taught many of the subjects on the by juice exam prep app in there I have taught strength of material fluid mechanics Geotech environmental open Channel flow concrete structures steel structure fluid mechanics so all these things I have taught if you want to attend those all lectures you can download the app give the scholarship test and you can Avail all the lectures and tomorrow 9 00 a.m 11 A.M okay we have this session on what Geotech where we'll be solving 50 questions 50 questions from all the topics of Geotech I have originally framed those questions okay so 50 questions you all attend it is am not PM okay PM we will have some different class so morning 11 am we have session for hpcl well tsp it will help you in all the states exam exam sscj the night okay 10 45 night we have an important lecture on what your riveted and bolted connections so so many questions are asked in riveted and bolted connection okay so rebated is as per the old code and voltage is but as a latest code so all the possible small small questions we will see in repeated in bolted connection tomorrow 10 45 so tomorrow we have two lectures yeah after after some lecture you have to stick the subscription okay you have to take subscription okay so if you want to take subscription you can click on what talk with counselor they will tell you the course costs okay and suppose you want scholarship if you want scholarship you can register for this particular scholarship test so in the app you register for the scholarship test on 1st of October there will be scholarship test you can attend the scholarship date you will get concession up to 90 percent concession and if you want to do good in the scholarship test you keep attending our sessions so this is how you know we are giving scholarship but not to everyone we are giving scholar tips to the students who are serious in their preparation if they are serious in their preparation they will give the scholarship test they will get good marks and then they can Avail the full courses and if you are facing difficulty in attending the scholarship test then you can attend the lectures on our YouTube channel we are conducting many sections in the YouTube channel from the YouTube channel you can attend the lectures then you can perform good in the scholarship test and then you can take the full course so this is we can say is what helping students also and then not helping everyone yes we should help students who are willing to study and work hard so if you are willing to study and work hard then scholarship test is there but you have to register for it there is no cost for the scholarship test scholarship test is free for everyone and if you are facing difficulty in the scholarship test you can always attend the YouTube sessions okay very good so tomorrow 11 am Geotech and then your 1045 your steel so we have more session coming up after tomorrow I will be taking lectures on hydrology then I will taking lectures on irrigation then Highway engineering so lot of lectures will be following now so keep up to date so for that what you can do in the description you can see there will be link for what the telegram group you can join the telegram group in the telegram group daily you will get what you will get the notification or in this particular YouTube channel you can subscribe and then in the YouTube channel you have this word if you see there is something a community the channel there is community so every day morning you can see the list of lectures which will be there in that particular day so then you can attend those lectures also there are lectures on aptitude the lectures and Mathematics right okay okay so thank you very much if you're liking my lectures you can like this session uh I will not suggest you to share the video because why to share with opponents don't share you study yourself okay so but like the lecture and okay so I like the lecture and leave your valuable comments in the comment section and yes solve this question this question is not for fun that question I gave na that question you solve okay so let us submit tomorrow at 11 am so you study something yes studies Geotech whatever you have studied whatever you know study that and come to the class so that it will help you okay so Geotech now also it's 12 40 okay 12 40 is there so you can study half an hour and sleep or you sleep also you can study okay imagine okay see dreams of Geotech or morning you can wake up in the morning and uh study for two hours and then come session don't wake up at 11 am and you know half sleep you are seeing the session in the bed that won't help morning wake up at eight o'clock or nine o'clock okay wash your face brush eat food one hour one half hour revise your Geotech notes okay 11 M sit with pen and paper okay and obviously more will be objective oriented because this is for hpcl well okay so meet you tomorrow okay it is happening now no no no if it's happening well good see there are three stages one stage is no studying second stage is sleeping and watching that is also fine that is better than no studying that is better than no studying yes and the best Stage is what table chair pen and paper you see how I am teaching see I'm teaching from last two hours am I sleeping am I really no I'm active right I'm active I'm not hyperactive I am active hyperactive is also very dangerous to health right ah no no no no no calm down come down hyperactive is not required just to be active alert and then study yes thank you very much tomorrow we'll meet at 11 am we'll have much for phone thank you very much for attending the session hope you enjoyed the session see you tomorrow at 11AM bye bye bye huh I love you I know