Good evening guys to all of you i welcome you all on this wonderful platform that is by juice exam prep please tell me am i properly audible and visible to all of you or not and guys you know uh today we are starting with the very first session of engineering mechanics and the topic for today is trust versus frame i already told you.
Yesterday that we are taking two topics one is stress other is friction because they are the highly weighted high weightage topics so guys that is the reason why we asked we are taking trusses and friction for this series okay so today we will be starting with the trusses so today's topic is truss versus frame so please tell me guys am i.
Properly audible and visible to all of you or not then we are starting the session yes so guys to start the session first of all this is some introduction about me those who are watching me for the first time this is some detail about me i'm having 10.
Plus years of experience written many research and review papers and these are my areas of expertise yes with good evening dear and guys like and share the session so that other student can also join and you know uh now concept capsules are going on which are having some wonderful dose for you guys because they are some.
Wonderful and important topic which are coming in exam as well as interviews and you can see every tuesday and saturday we are having a concept capsule and that is premiere at 9 00 am generally is the timing for mechanical and civil so guys you can go through that then my dear first of all when we are.
Starting this truss and frame or you can say the name of chapter is trust is actually the name of topic is trust versus frame so when i say trust frame generally students are aware of one thing that why trustees are actually required so students are aware that generally.
Trust is and frames are required to bear the load so when my dear when you are saying the trusses and frames are required to bear the load then a doubt comes to my mind to bear the load actually okay so the doubt comes to my mind note my actually it comes to many students mind so it is.
To bear the lord so in my dear the doubt comes to many of the students mind that sir in strength of material you taught us about the beams we have studied cantilever beam simply supported beam propped cantilever beam overhanging beam continuously fixed beam and all those.
Beams were load carrying members only you were having some beams like this and you were applying the forces onto these beams like this is the load acting this is the moment acting you were having some simply supported beams and on that many loads were acting like this udl uvl and all so my dear when.
Beams were already there to bear the load what is the need of trusses and frame when we already had some members which are beams which were bearing the load what was the need my dear what was the need for the trusses and frame so my idea then i would be giving you an example that when we are having the beams and the loads are applied onto the.
Beam so what happened is due to the load you can see this due to this load you can see this this beam is getting deflected so you can see this beam is getting deflected due to this load similarly my dear if we have a cantilever beam like this this is load acting under this this beam.
Will be deflecting like this and this is denoted as y and my dear you already know that if we go for the cantilever beam case for this case you know the y value is coming out to be p l cube upon 3 e i so you can see from this idea that deflection of the beam is directly proportional to l cube and directly.
Proportional to load so the point is if length of the member will be very very big if load applied on the member will be very very big so when load applied will be very very big and when length of the member will be very very big in such cases my dear deflection is also coming out to be.
Very high in magnitude so in such cases deflection coming in the beams is also going to be very very high and my dear you know that in beams because whenever we are having these solid beams we never expect that much deflection because that much deflection if it would be coming into the beam it.
Is going to be very difficult for us because you have seen in the movies sometimes you have seen in some of the movies there are some pathways made between uh let us say there are two uh you can say there are many uh when you are having hilly areas in those hilly areas you must have seen there are some parts.
Made like this they are made up of some kind of you can say stairs like this is it is like that and you have seen many times when the hero or heroine they are going like this sometime their their foot gets slipped from here and you can see there are some chances because it is having deflection and sometimes some part of this is going.
To be effected affected because of many time it is working so sometimes you have seen there is some failure in between so my dear the similar kind of thing you will be having if deflections are going to be more the beams may be.
Failed due to the rigidity criteria when deflection and also if deflections are more it is very difficult to design because we cannot bear more deflection whenever you see towards your roof it looks like plane only it doesn't look like it is deflected so the point is deflections in the beam should be very very small so if you have very big.
Length or very big load then there are chances that you will be having very high deflections so for such cases we need to make some other kind of you can say members which can bear the load without much deflection so trusses and frames came into picture so that is the need of trust and frame that why trusses and frames came into picture and.
My dear now generally students don't have the comparison between trust and friend they feel both are same only so in this session i will be telling you the differences of both and also we are going to see how to determine whether the given truss is a perfect truss or not okay so this is what we are going to see.
Please tell me guys uh are you getting it or not yes fine is it clear for everyone guys great great great so guys let us move further so i was looking at the comment actually i thought maybe the comments are not visible so my dear if you see this if.
You see this here i am showing you a transcend frame if you see this my dear you can see there are some members this is a member this is a member this is a member this is a member this is a member this is a member this is the member and these members are joined together and we have provided the support this is a hinge support this is a roller support.
It is similar to the support we were providing for the case of beams yes very good asif very good uh shah ahmed fine aurangzeb very good okay fine so my team when we are talking about trusses interest is what we are going to do interested in frame both we are going to attach the members like that and we.
Are providing a hinge support and a roller support i feel from strength of material everybody would be aware why we are providing this roller and hinge support because my dear if you will be providing both roller supports like this then in that case you know roller supports are something which can give only vertical reaction so it can give.
Only vertical reaction they cannot give horizontal reaction so if some load is acting like this this load will be giving a horizontal component it is going to give a horizontal component like this and for that there is no reaction coming so beam will start moving so that's why this kind of beam is said to be the unstable.
Beam so that's why we are not providing both the supports as roller support then why we do not provide both the supports to be hinge support if both the supports will be hinge my dear beam is not going to move from this and this point then my dear by chance if temperature is going to increase you know whenever temperature increases.
My dear things are getting expended so my dear when you will be having any kind of increase of temperature you will be having expansions in the member so when expansion will happen you know beam cannot move from this and this point so definitely beam is going to deflect like that so this deflection is coming just because of temperature we have not even.
Applied any kind of load so my dear that is why we never want this because this is said to be a connection where we will be having the thermal stresses to be induced so my dear because of this thermal stresses the stresses will be coming because it is getting deflected so we never uh you can say recommending that we will.
Be going with both of the hinge support so my dear better if we go with one roller and one hinge what are the advantages of that my dear the advantage is first advantage is like if you are going to have hinge support it can give both horizontal and vertical reaction so if some load is acting like this its horizontal.
Component will be balanced by this reaction so that is the first advantage second idea if temperature is going to increase then this beam will be expanding and roller will allow some kind of expansion because the roller can move in x direction and by providing that there will be no deflection of the beam so there will be no thermal.
Stresses induced in the body so my dear that's why we are going to say one roller and one hinge is going to be the perfect combination and that is why we are going to use this combination everywhere whether it is trusses and frames or it is the case of beam so that is something which is there for both the cases so my dear i will be telling you.
One thing whenever you show trusted and frames they are shown in terms of triangles only there is a reason behind that and we will discuss this reason right now okay so don't worry about that so my dear we have already seen first of all i will be showing you some examples that where we are using the trusses actually what are the application of.
Trusses and then i will be telling you about that what is the difference between truss and frame so is it clear yes orange is there an issue please discuss with me so my dear you can see truss is defined as the structure which consists of several member connected together to support the load and you can also see we.
Have already shown the schematic diagram of the trusses now i am showing you the practical application so you can see my idea the first practical application is in front of you this is the example of railway bridge so my deal this is the first example of trusses this is the example of railway bridge and you can see my dear these are the trusses only.
You can see these are the trusses only okay guys so these are trusses only so these are there to bear the loads and you know whenever train will be going on the load will be more and the bridges are having very big length also so in this case of railway.
Bridges load is more because thousands of people are present in the train and length is also very very high so deflection will also be very very high so my idea to avoid the deflection because if deflection will be more fracture will happen failure will happen so to avoid this situation we are going to use trusses and frames in case of.
Long railway bridges the second application my dear is in the stadium because you know in stadium the roof is going to be very very big generally stadiums have the capacity of twenty five thousand fifty thousand one lakh peoples so if that much capacity of people is required so my dear four stadium cases we have.
More length so my dear because of more length for the roof of the stadium we are using the trusses here and you can feel the trusses present here are you capable of feeling or not all these things are very much a practical application everybody can understand that i feel and guys i'm going to teach you this topic not even this topic.
Friction also along with all the practical applications so you would be having a feel of that so don't worry about that now my dear we are going to have the third application this is nothing but the airport in airport also we have very big big roof so here also we are using the trusses and you can feel in this diagram how trusses are.
Going to help us okay so this is the example these are the examples where we are using them and this is my dear the shed of the shed of you can say a service center so my dear in this service center shed you can see the application of trusses you can see that you can see that.
You can see that okay so this is how the trusses are used there so my dear this these all are the practical applications only so there is nothing like theoretical only now my dear i'm telling you about the types of trusses when we are talking about types of trusses there are two types of trusses.
First type of trusses are said to be plaintras as the name suggests in engineering mechanics in strength of material wherever you see the word plane it means two dimension wherever you see the word space the meaning is three dimension so plane truss means 2d truss so my 2d trusses are those in which all the members of a truss lying in a same.
Plane in a same plane and my dear on the other hand when we are going for the space truss it means the three dimensional stresses so my dear when we are saying three dimensional stresses trusses they are members which are in different planes then it is said to be 3d truss so my dear 2d truss is a plain truss 3d truss is a space truss now my.
Dear whatever the application i have shown you can you tell me which type of truss it is if i show you railway bridge my dear what you will call it 2d or 3d i am waiting for your response very good pawan kalyan bahati badia yes so my dear when we are talking about this railway bridge this is the example.
Of 2d truss so i am mentioning it it is an example of 2d truss then my dear you can see the next example is nothing but the stadium this is an example of what this is an example of what yes anybody anybody this is stadium.
This is an example of what okay so my idea now if i show you this this is an example of 3d truss you can feel it and also i will be showing you more example for 3d this is once again 2d you can say they are in all one plane then my dear i will show you the 3d example now these are 3d example this.
Mobile towers these mobile towers they are the examples of three dimensional trusses okay so they are 3d or space truss so my dear very good i feel you are capable of identifying it that whether the given trust is a 2d truss or a 3d truss.
Whether it is going to be a space truss or plain truss so in a good manner you guys are doing it it's really great guys next let us move guys we are going for the plane truss assumption when we are going for the plane truss assumption idea plane truss assumptions my dear i would like to identify actually what is the difference between trusses and frame.
So i am starting with the first point all members are connected only at the end so my dear first of all i would like to tell you that if i am having a trust like this if i am having a trust like this you can see if i am making it in this way then my dear you can feel one thing.
You can feel one thing that here all the members like a b is a member bc is a member cd is a member d e is the member so a c a b b c c d d e b d all the members are corrected at the joints only all the members are corrected at the joints only there is no member which is.
Joined in between but my dear so when i am we are going to say this this is the example of trust when we are talking about the frame in frame idea you will be having the connections in other way also like when i am going to make it in this way so if you are saying we are going to make a frame.
Then in frame you will be having this type of connection also my dear you will be having this type of connection also so there is a member this member is attached at this end at this end and also in between so my dear when this kind of connections are there it is said to be framed so as i said members are connected only at the.
Joints in case of trusses but they will be present they will be joining in between also in the cases of frame so i feel you got the first difference between trusses and frames sir is this high extension tower to transmit yes yes yes uh jack.
Just mobile tower was on the left hand side you are correct sorry actually this was mobile tower this was for electricity sorry i have written in both the ways okay this is for a high tension electricity wires you you are correct check this sorry for that okay so this.
Is for the mobile tower okay so this is correct so my dear when we are talking about the second second point what is the second point of difference now so my dear if you see we when we are talking about the trusses on the trusses you will find out the forces will be acting only at the joints you will find out the forces acting only at the joints you.
Will not be having any force acting in between whereas in case of frames you can have force acting in between like this also like this also you can have udl acting like this also you can have a force in between like this also so my dear in case of frames forces can be present other than the joints also but in case.
Of trusses forces will be present only and only at the joints this is the second difference between trusses and frames okay guys so my dear now the third point the third point if you see when we are talking about trusses as the forces are acting only on the joints forces are acting only on the joints.
So because of that my dear because of that when forces are acting only on the joint all the members in the trusses will be two force members so when i will be making any member of the truss that member either will be in the tension or this member can be in compression.
Or it will be a zero force member so my deal this can be in tension this can be in compression this can be a zero force member but only either tension or compression will be there so we always call that every member of a truss is a zero force member so as my college has started so i watch.
Recording classes okay fine fine fine great channel so whenever you find any difficulty do be come in contact and also uh get the handwritten notes which i am sharing okay i feel you have also made yours also and on youtube also try to attend the practice session whenever you are free because i have taken a marathon.
Last sunday okay so my dear interest is all the members are going to be zero force member they will be either in tension or in compression because forces are acting at the joints only so when the forces are acting on joints only if even these members are going to have some kind of buckling then my dear buckling whenever.
It is coming in the columns we consider those member to be under compression actually so when i say there will be no shear forces actually there will be no effect of shear there will be two force member either in tension or in compression and when these members are in tension they are given the name of tie members or thai bars and when they.
Are in compression they are given the name of strut bar so these are the name givens but my dear when we are talking about the frames as you can see forces are acting like this also so they will be creating normal as well as shear effect both so in case of frames my dear it is not necessary there will be two force member they can have.
Shear forces also my dear one more difference is whenever we are talking about the trusses we have already seen forces are applied on the joints only so these joints actually the joints actually they are pin joints and my dear in case of frames the joints are generally welded joints.
The joints are generally welded joints so my dear this is one more major difference which is there between truss and frame okay guys so these are the differences we have discussed and now when i say this many students have two kind of doubts one sir is it really feasible to have member.
Joint with the pin joint we have never seen that second out is sir we have never seen roller support our roller support theoretical only or practical also they are possible then if you remember some days back i have put it a shot on this channel and in that short i was there at the bangalore airport and there i have just took the.
Video of the truss and there i have shown how the things are connected with the roller support okay and i am having the diagram today also i am showing it to you so these roller supports and pin joints are the reality you can see how the members are joined with the pin joints so my dear this pin joint no doubt we are making those assumption but.
They are reality also so in reality also members are joined with pin joint like that so pin joint is not a theoretical thing it is a practical thing only so you can see here this member this member and this member they are connected with the pin joint and similarly roller support is also a reality i will be showing you that.
My dear you can see these are the examples where big big highways big big bridges they are they are on the roller support so whatever we study roller and hinge is the best combination we are using that practically also so my dear you can see these are the roller supports okay so.
They are the practical figures they are not the animations of you can say they are not something made this is just a photograph taken okay so i feel you are very much clear about that so guys all these things are reality only.
So my dear now uh this was the first thing we have discussed and there are the assumption as i already said all the joints are pin joint in trusses loads are acting only at the joint all members are subjected to axial loads only as i said there are only two force member and the weight of the members will be negligible because if weight of the.
Member will be more then my dear weight of any member would be acting as udl and if you will be having high loads udl will be present then it will not be a two force member so these are the assumption under which we need to work for the trusses chapter so guys now what kind of questions are coming in the gate in gate they will not ask you difference.
Between trust and frame in general yes they can ask this kind of thing in hcl hal and such kind of exams but they will never be asking this in the gate in gate what are the types of question they are asking so my dear first type of question they are asking where they will be asking you that what is the force acting in this member.
What is the force in bc member what is the force in cd member and you will be having options this much newton tensile this was newton compressive so how to find out magnitude that we are going to start from tomorrow but today we will see how to find out the direction that whether the member is under tension or the member is under.
Compression how to search that so let us start my dear that whether the member is under tension or compression how to check that so my dear i am going to tell you with a normal example only we will be considering a spring for that okay so my dear let us consider a spring this is the spring and my dear let us say you are applying.
Some tension force on this spring like this just imagine someone is taking your hands and pulling from both the sides so when someone is trying to pull you from both the side for the safety of your arms and body and joints what you will try to do you will develop some internal forces and try to take your.
Hands back so when you were under tension you applied the forces away from the joints joints where these hands are being connected so you are saving your hands and your body by applying the force in this direction means inside means inside inside means you can say if this is a joint.
If this is a joint this is a joint when the member is under tension internal force will be generated inside inside means away from the joint away from the joint so my dear if forces are coming away from joint it means the member is under tension so this is how we are going to.
Identify tension and compression in any member then my dear if we have just the opposite case the spring is there and this time some compression is applied so now imagine someone is going to compress me like this so to save my hands and my body i will.
Try to resist like this like this means this time if something is joined with my hand i am trying to go away from the up sorry towards the joint because we are saying this is the joint so my dear this time you will say the forces will be generated outside resistance will be generated outside or you can say.
This is towards the joint because this is joint so resistance will be developing towards the joint here resistance is developing away from the joint so if resistance develop towards joint then the member is said to be under compression so my dear this is the trick to know.
Whether the member is under tension and compression and this is really very important for all of you this is the point from where questions are coming that whether the member is under attention or compression so guys please tell me jack jess janil asif pawan yes shaha emma are you clear about this.
Or not if i give you any question can you tell me whether the member is under tension or compression and yes there are some zero force members only but about zero force member we are not going to study today that we will be discussing tomorrow that is a different study where we will be finding out that how many zero force members are.
There and how to find out the zero force member all these kind of things we are going to see tomorrow yes but we are definitely we have not started yet okay this is just i'm giving you introduction today but still for the direction i am giving you some examples let us say if we have a trust like this.
If we have a trust like this okay let us see right now we are not talking about the magnitudes but if i give you the direction can you tell me that a b member if the force is developed are in this way then a b member is under tension or.
Compression let us do that much practice that you will never be doing mistake at least in the direction part please tell me away from the joint these are the joints so to wash the joint or away from the joint asifally don't worry you will feel right now.
I said that whenever you will be in tension you will try to save yourself by doing that doing that means away from the joint inside and when you will be compressed like this you will try to resist like this means towards the joint this is away from joint this is towards the.
Joint so here you can see whether it is towards the joint or away from the joint towards the joint away from the joint it is towards the joint you can say forces are going towards a and towards b a and b are the joint so when forces are acting towards joint first of all write this when forces are acting towards joint.
Towards joint means this internal forces are going towards joint towards joints means member is under compression so you will say that member is a struct member a struct bar and if you see away from the joint if you see away from joint then you will call it as tie bar.
Please tell me now uh asifali you got it or not so when we are talking about this a b member a b member is a strut compression means strut tension means tie compression means strut tension means tie and guys do like and share the sessions.
Whether you are interested in the session or not okay so now i am showing the forces in this member let us say bc member forces in this bc members are acting like this let us say it is acting like this is it tension or compression bc member you need to tell the name strut or tie.
Strut or tie yes strato tie strut or tie once again towards the joint towards the joint it is struck okay let us take another example this time it is.
Away from joint cd cd is away from joint cd is away from joint so you need to tell what about cd what about cd what about d e you need to answer all of them in the comment section.
Okay this is about be and this is about ec okay and this is about a tell me guys.
Cd if you see cd cd is away from joint because d is a joint c is a joint they are coming away from joint away from joint means it is a tie d e towards the joint strut b e b e away from joint.
Away from joint tie ec away from joint sorry e c towards the joint e c towards the joint means struct a a away from joint means tie is it clear for everyone.
Great so guys this is how we can find out whether the member is under the tension or under the compression i feel now any student who understood this will never be doing any kind of mistake okay so that is what i was expecting.
Okay so this is how we can find out the ties and struts everybody got it so guys now we are moving to the frame if you see this is the example of a frame structure so if you just try to identify this frame so you can see this member this complete member.
Is joined with other members here here here here so that's why it is a frame because in trusses joints are the members are joined only at the joint joints are these two but members are joined in between that's why it is a frame so my dear this connection is a kind of frame.
And i would like to tell you in engineering mechanics we need to study only about the trusses we need not to study about the frames so that is the thing we need to go only for the trusses so my idea now when we need to study only the trusses i am coming on to the next topic for today and this is the last topic of today.
From which one mark question is going to be framed sometime two marks question is also going to be framed and this is the first topic from trusses where questions are there okay then second topic is method of joint and method of section which we will be starting from tomorrow so let us have.
Discussion on perfect trust so my dear when we are talking about perfect trust what is that actually my dear when we are talking about perfect trust for any trust to be perfect there are some conditions the very first condition for perfect.
Trust that it should be statically determinate it should be statically determinate it should be statically determinate the first condition then my dear second condition it is statically determinate second condition is my dear it is non-collapsible.
It is non-collapsible non-collapsible means motion should not be possible okay when applying the forces motion shall not be there so these condition must be satisfied then only a truss is said to be a perfect truss first of all we will try to identify this condition than this condition so this is said to.
Be the necessary condition for any trust to be a perfect truss and but this condition when it is satisfied then also we need to have a second condition this is necessary condition this is sufficient condition until and unless any trusts qualify both the condition we will not be saying that trust to be a perfect trust it is.
Similar to when you study cochi riemann equation there are two conditions one is necessary other is sufficient so it must satisfy both the condition first we will derive the necessary condition actually okay let us say my dear there are m number of members.
M number of members in a truss if there are m number of members in a trust you know every member is a two force member two force member means either it will be in tension or it will be in compression so it will be having some unknown force so my dear every member is subjected to some internal force you have seen in the.
Previous figure and here you have seen that every member is having some force into that let us say in this member force is f1 this is f2 this is f3 so this is f4 this is f5 this is f6 and this is f7 you can see the member one two three four five six seven so the number of members all the members.
Will be having some unknown force so all the members have some unknown force so my dear if i want to find out the condition of statically determinate so everybody will be aware that there are two condition one condition is said to be statically determinate statically determinate.
And other condition is statically indeterminate other condition is statically indeterminate so when we are talking about statically determinate what do you mean by that if number of unknowns if number of unknowns are equals to the number of equations.
Number of equilibrium equations this is the condition of statical determinacy and my derived number of unknowns if number of unknowns are more than number of equilibrium equations this is said to be statically indeterminate.
So my dear when we are looking for statically determinate these two conditions uh this condition must satisfy because you know number of unknown should be equal to number of equilibrium equation if you see the previous stress if there are seven members there are seven unknowns if there are seven members there are.
Seven unknowns so we will be writing the number of unknowns the number of unknowns the number of unknowns will be equals to the number of members m are the number of members m are the number of members but if you see properly there are two supports also and for that two reactions will be coming.
For hinge one reaction will be coming for roller so these three reactions this is ha this is va and this is vd so we have m plus 3 this 3 is coming because of support reaction so these are the number of unknowns these are the number of unknowns so we.
Already calculated the number of unknowns okay so my dear now we are going for the number of equilibrium equation so my dear if you are going to see this truss in this truss if you take any member let us say i am taking a member bc this is b this is c.
You are very well aware that in any of the member in case of truss forces will be acting only on the joints so my theory for bc forces are acting on the joint what do you mean by that forces either will be acting on the b forces either or will be acting on the c and my dear let us say a number of force.
Acting on this b let us say this force this force on c also there are multiple forces acting let us say okay let us say these are the forces if you see at b all the forces are coplanar and concurrent if you see at c all the forces are coplanar and concurrent and when the forces are coplanar and concurrent my.
Dear there are only two equilibrium equation that is summation f x 0 summation f y 0 because when all the forces will be passing from single point how the moment will be generated so that is the reason for co planar and con current cone current means they are starting or ending at one point coplanar means they are in one plane so when they.
Are coplanar and concurrent there are only two equilibrium equation so two equilibrium equation for one joint two equilibrium equation for another joint so whatever be the number of joints into two will be the number of equilibrium equation because every joint will be giving you two equation summation f x zero summation f y zero how to use this.
That we will understand tomorrow today i am just deriving this equation otherwise i could directly give you equation but i am not doing that i am deriving it so that you can understand they are not difficult things they are very easy so my dear if you see the number of the number of equilibrium equation it is 2 times j so if you.
Satisfy this condition it is said to be statically determinate so statically determinate means m plus 3 is equal to 2j and this condition is said to be the necessary condition if this condition is not satisfied you can say it is not going to be a perfect truss even with your closed eyes.
Okay so if you want to identify whether the truss is statically determinate or indeterminate first you need to check this non-collapsible if you want to see it means it should be it should be made up of triangles only.
Made up of triangles only here you may have some doubt so i will be starting with first truss if somebody asked you how you can make a truss with minimum number of members so minimum number of members to make a trust are three because one member cannot be a trust and if you have two members my dear let us say you have two.
Members like one and two then my dear if you have two members only applying the forces here there will be a motion possible and because of this motion it will not be able to withstand the load in the stationary condition because on applying for this is going to you can say rotate about this point so.
Minimum number of members possible for interest are three so now we are having this truss with three members so if you see this trust my dear one member two member three member so you can say left hand side is m plus three it is coming out to be six if you find out the number of joints.
Joint number one joint number two and joint number three so 2j is going to be six you can see left hand side equals to right hand side so it is statically determinate and if you apply the force in theory of machine you have already studied that whenever we have three members on applying the force it cannot move it.
Will be withstanding the load only so my deal that's why when it is in the form of triangle it is a non-collapsible thing and that is why i said if it will be made up of triangles only it is non-collapsible so we will call it as a perfect address this is the example of perfect truss what if we have four number of members.
What if we have four number of members like this then my dear once again you know number of members are one two three and four so you will say m plus three is equals to seven if you see the joints one joint two joint three joint and four joint then my dear two j will be eight.
So you can see this time m plus three is less than two j it means the number of members are less you know on left hand side we have the number of members so when left hand side coming out to be lesser it means the number of members are less than the required so it is said to be deficient deficient trust or free.
So if left hand side coming out to be left less than right hand side it is said to be deficient and even my dear it is not a perfect trust if you will apply the force it is going to deviate because there will be a motion possibility so that is why this is not at all a.
Non-collapsible thing it is collapsible also very good so it is non-perfect okay we can have another example where we will be having the five members like this okay y5 let us have six members connection is at this position only joints are these four they are this is not a joint member is one two three four.
Five and six so m plus three will be nine joints are one two three four two 2j is going to be 8 so this time m plus 3 is going to be more than 2j means number of members are more even if we reduce the member we can make a perfect truss it means this is a.
Redundant frame or redundant truss redundant means which can be reduced into perfect truss because here the number of members are more here something less was there here something more is there and what if we have this kind of structure this if you have this.
I'm making you clear each and every concept member one two three four and five if you find out m plus three you will be having eight if you will find the joints they are four only two j is equals to four sorry eight you can see left hand side is equal to right hand side necessary condition is satisfied then you will see.
Whether it is made up of triangles or not if you see this carefully my dear this is one triangle this is another triangle so as it is made up of triangles only my dear you will be calling it as a perfect truss because both the conditions are satisfied so my dear it is required that it it should be made up of triangles.
Only so first condition is m plus 3 is equals to 2j second condition is it should be a non-collapsible for that it should be made up of triangles now i am showing you one more good example by which you will be more clarified we are having this time a member like this we have this and this.
So with these two questions guys everybody will be clear how to understand the perfect and known perfect okay one roller one hinge this time we have this and this if you see both the cases my dear always.
Remember when i'm saying trusses it means members are joined at the joints so these are the joints if you see member 1 2 3 4 5 6 7 8 and 9 so m plus 3 is going to be 9 plus 3 as 12.
The number of joints 1 2 3 4 5 6 2 j is going to be 12. you can see necessary condition is satisfied m plus 3 is equals to 2j necessary condition is satisfied if you see properly it is made up of all triangles so it is going to be a perfect truss sufficient condition is also satisfied.
But if you see this case this is rather than this very important and interesting case here also the number of member is this is joint this is joint yes are safe are you getting it or not please tell me that so this is one two three four five six seven eight and nine.
So m plus three is going to be twelve one two three four five six the number of joints are 2j 12. so my dear if you see this m plus 3 is equal to 2j necessary condition is satisfied and now comes the important point.
Whether it is collapsible or not whether it is made up of old triangles or not so my dear this is a triangle this is a triangle yes no problem this is a triangle but is this a triangle this is not a triangle so if any force would be applied here this is going to have motion like this.
So because of that it is going to be not a perfect truss so as i said one condition is satisfied this is necessary condition but what is sufficient condition all triangles if there is a possibility of any.
Geometry other than triangle like rectangle is there it is going to be a non-perfect us so guys now please tell me everybody if i give you any question by looking at that can you tell me whether it is a perfect trust or not you can have this type of question in gate exam esc exam hcl hbcl types of.
Exam and tomorrow we will be starting tomorrow we will be starting the method of joint and when we will be starting method of joint there you will find at least 20 30 questions are there from the previous year's gate.
So method of joint method of section these we are going to start from tomorrow and this is the starting class first class so today i try to give you some basic concepts what are trusses and frame and if my dear you will be giving this type of support to this series i am promising you that this is my.
Promise i will be completing the entire engineering mechanics on youtube so i want that kind of dedication from your side also so guys just like the session share this with your friend and also subscribe the channel it would be great if you share this with your juniors who are in first and second year.
Of engineering because they would be also getting some help because these are the things which are coming in their university exams also and i will be sharing this pdf on my telegram channel so just you can download the pdf from that okay yes.
So goodbye for today guys so today's topic is over so we will be meeting tomorrow once again at 6 00 pm fortress using method of joint so goodbye guys for this session thanks for joining