SOM Episode 4 | Self weight Deformation, Bar of Uniform Strength & Compound Bards

[00:00:01]Good evening guys. Good evening everyone.

[00:00:15]Preparation all of you is preparation going well or not a preparation snacks even right so nobody is there okay no one is there why no one is there okay then no problem no issues Right.

[00:00:45]Right. So this is strength of materials.

[00:00:48]Right. Concept booster series. Episode four we'll be doing. Right. Episode 4.

[00:00:53]Right. What is that? Self weight deformations bar of uniform strength and compound bars. Right. So this will lead your confusion to confidence. Right? So those who did not download the rankers per app download this immediately and you can contact this number for any queries. Right? So, Vinod Islav right good evening good evening everyone how are you how are you all right so coming to this self deformation right good evening episode due to the selfweight deformation only Right. And the elongation of a vertical bar due to its own weight. Right? Due to its which one own weight is called as your self-weight deformation, right? Own weight only. What is the meaning of this own weight only? Own weight only.

[00:01:57]Meaning external load external load is not considered here. External load will be considered here. External load is not considered. Right? So what does it mean?

[00:02:09]No external load effect. If you want an external load effect no external load considered, right? No external load considered you can say right.

[00:02:31]Vertically hanging right.

[00:02:37]So selfweight deformation occurs only in the vertically hanging members right only for vertically hanging members selfweight deformation horizontal bars deformation horizontal bars selfweight aial deformation horizontal bars selfweight ate aial deformation will occur or sulfate aial deformation will not occur. Sulfate aial deformation does not occur. Right?

[00:03:20]Why it will not occur for them?

[00:03:22]Horizontal bars. Why it is not occurring for this horizontal bars?

[00:03:30]Self always will be acting in the downward direction. So right. So vertically downg there is no deformation at the length direction because the self of the horizontal bar is acting in the downward direction. Is that clear? Vertically hanging bars clear. Is this point clear everyone?

[00:04:06]Is this point clear everyone? Why we need to consider self deformation only for the vertical bars vertical bars deformation by default meaning okay now right what is W tell me what is W tell me that is your self weight it is not the external load it is your Which one? This is selfweight. You can say right that is your self weight. If you just observe, right? Self weight. Okay. Self weight.

[00:04:45]And here deformation is maximum at the lower end. So lower max right.

[00:04:56]What is the support top?

[00:05:04]Right. Sindu navia.

[00:05:08]Top support, Right.

[00:05:52]Right.

[00:05:54]Right.

[00:06:13]Sulfate deformation delta max.

[00:06:17]At which location? At bottom end.

[00:06:22]Bottom. Which end? Free end free and supportive endu. Right? Is that clear everyone? So always use the total length of this bar in the formula. L is nothing but w by this 2. A is nothing but your area of cross-section. E is in modulus.

[00:06:40]Row is your mass density. Good evening.

[00:06:43]Right. A is cross-section area. E is nom modulus. L is total length. W is a self weight. Right? Is this clear everyone?

[00:06:49]All of you? General formula for this self-weight deformation?

[00:06:55]Is the general formula for the self-weight deformation clear? All of you?

[00:07:00]Is the general formula for the self-effirmation clear? All of you?

[00:07:08]General formula for the self-deformation. Everyone someone respond clear or not? Yes or no?

[00:07:22]Right. Now if you are going for this, right? Uh this is your third one. Right.

[00:07:29]Vertical hanging cylinder. Right.

[00:07:32]Vertical hanging cylinder. This before that what is the relation between this gamma and this rope? Gamma is nothing but your roam.

[00:07:43]What is that? Gamma weight density. Gamma is nothing but your which one density. What is that?

[00:07:51]Row tell me row is nothing but your mass density. Row mass density right? Row is nothing but your mass density. So selfweight is nothing but what is weight? You can say self weight is nothing but rate right self weight formula in terms of density self is nothing but weight density into volume weight density into which one is this volume right row is mass density gamma is weight density g is acceleration due to gravity right so acceleration due to gravity so weight equal to gamma into into that volume right into that volume.

[00:08:40]You can say Winda W by this 2 W gamma into what is the volume of this?

[00:08:56]Tell me what is the volume of this? Tell me what is the volume.

[00:09:05]What is the volume? You'll get tell me what is the volume you'll get. Tell me volume area into the length area into the length. Right? Area into the length.

[00:09:25]Right? Divided by this 2 a.

[00:09:30]Okay. Divided by which one? This 2 a.

[00:09:33]Right? WL by this 2 a e. Right? So there is there right weight gamma into area into length into that length is already there a cancel.

[00:09:54]So what is that you are left with finally gamma l² / this 2. So square by this is clear how we have got that is clear all of you how we have got that is clear everyone everyone it is clear so similarly you'll be getting same w by this 2 a right w by this 2 so similar right if you are using similarly Right?

[00:10:30]What is that you'll be getting for this?

[00:10:32]If you are using similarly for this con also, right? What is that you are getting? Tell me. For con also, what is that you are getting? Tell me. Simple.

[00:10:41]That is your gamma l² / this 6.

[00:10:47]Since volume of this cone will be equal to/3 of this volume so 1/3 of this volume of this cylinder volume of the cone equal to/3 of this volume of the cylinder right so simple volume of this cone equal to/3 of this volume of the cylinder right soind volume formula WL by this 2 is same W by this 2 A volume of the cylinder right became which one this six is that clear everyone So volume of this cylinder volume of this cylind P<unk> R² into right what is that so volume of this of this P<unk> R² into that is what right gamma L² by this 2 E change L square by this 6 G L square by this 2 E to G L square by 6 Okay, clear everyone. This is about your self deformation. Okay, general formula by this material same formula. Right. General formula.

[00:12:38]General formula irrespective of this shape. Okay. Shape. Cylinder shape is the ro g l square by this 2 a cone shape is ro g l square by this 6 a or gamma l square by this 6 a right everyone it is clear the self deformation out of you everyone the self-way deformation is clear everyone is clear right if it is clear we'll just move on to the bar of uniform strength okay bar of uniform strength Right. Shall we move?

[00:13:21]Shall we move on to the next everyone?

[00:13:23]Right. Now, okay. Yeah. Okay. Before we go into that, uh, APSC, TGPSC, L8 batch, AW8 batch has started on 20th July. We have started RCC, right? Don't miss that all of you. Any doubts, any uh questions regarding uh any queries regarding the subscription, you can just contact this number. Okay, KBR number. So, AW officers batch also started. So, without mentorship, this technical will be there, right? Elate batch means same features of this officers batch along with which one this one is one mentorship will be there. Right? So these are the prices and test series also we have started and tomorrow at 700 p.m. I am taking a class showing how the test series looks like and how many questions are still there. How many questions are going to come right? Like that how many tests are there? Right?

[00:14:14]Like that. Now bar of uniform strength.

[00:14:18]What is the meaning of this bar of uniform strength? Tell me.

[00:14:22]What is the meaning of this bar of uniform strength? Everyone is the meaning of this bar of uniform strength. So it is the bar with what conditions tell me. It is the bar with what conditions?

[00:14:39]Same intensity of stress. Right? With what conditions tell me bar with the same intensity of stress.

[00:14:51]Bar with the same intensity of stress.

[00:14:54]At which location? Tell me. At every point.

[00:15:01]At every point. Due to which loads? Tell me. Due to which loads? Anyone tell me?

[00:15:09]Which loads?

[00:15:14]I'll be just waiting for your comments.

[00:15:21]Anyone?

[00:15:34]Tell me someone anyone any idea Idea, right? Due to axial load. Okay. Due to that due to self weight. Right. Due to self weight plus which one? Axial external load. Right. Axial which one?

[00:16:25]External load. Right. So right both will be there. Right. Both will be there. Right.

[00:16:54]effect right that is what we need to do okay is that clear everyone so now so prismatic shape will give that or it is a non-prismatic shape we need to get it nonprismatic shape we need to get it non-prismatic shape tell me why we need to go for this non-prismatic shape tell me why we need to go for this non-prismatic shape tell Why prismatic shape will not be given?

[00:17:26]Because so why why it is like that right? What is the reason? Tell me.

[00:17:31]Since P is same right what is that P external aial load P since that is self that is W right W right since P which tell me since P since P is conant everywhere since P is conant everywhere but constant but Self weight is not constant right. So but is nonuniform right? Not constant.

[00:18:19]Self weight is not constant throughout.

[00:18:21]influence.

[00:18:36]Self is influencing it.

[00:18:42]Right?

[00:18:44]So if you are taking this bar, right?

[00:18:46]What is that bar? This is your bar. If you just observe right this is the bar if you just observe right what is that you can say A1 A2 right what are these A1 A2s you can say right this is your bar and what is that shape you'll be getting this is the shape you'll get right this is the shape of this bar you will get right this is the shape of this bar you'll get right so at the top right what is the cross-section that is your A1 is the cross-section. So here what is that external load that P is the external load we are having and along with that what is that you are having that P plus selfweight W is also acting or not along with that P self W is also acting you can say right is now what is that you can say that that is your A1 and this is your A2 if you just observe right what is the relation between this A1 and this A2 so L is which one this length of this bar okay L is the length of this bar so what is that tell me sigma Sigma is the uniform strength required. Right? What is the sigma? Sigma is the uniform strength required.

[00:20:00]So same intensity into the sigma uniform strength required strength and gamma density of the material.

[00:20:10]Right? So what is the relation we are having? If you just observe that a1 will be equal to right what is A1 will be equal to A2 into what is that? E power gamma L / this sigma like that we need to go for right so shape so log ln A1 by this A2 right ln which one this A1 by this A2 equal to what is that gamma L by this row that gamma L by this row is also written as ro G L by this sigma right row gamma L by this sigma or GL by this sigma A2 into e power what is that ro g l by this sigma. So tell me which shape it is following tell me is it a straight line or it is which one? This exponential one it is following.

[00:21:05]Which shape it is following? Tell me which shape it is following tell me everyone.

[00:21:10]Anyone tell me right which shape it is following? It is that exponential or this logarithmic variation.

[00:21:20]Exponential or you can also call it as which one?

[00:21:23]This is a logarithmic right exponential or this is logarithmic right any shape you can call it as right this is your bar of uniform strength right so bridge bridge bridge peers Right. Bridge peers are this fly over peers.

[00:22:00]Fly over.

[00:22:11]Right.

[00:22:30]Is it not the shape you are having?

[00:22:32]Everyone fly of uniform strength bar of uniform strength. Right? So that is the story of bar of uniform strength. Right?

[00:22:52]First part of uniform strength. Next we are left with which one? This compound bars. Right? We are left with which one?

[00:23:00]is compound bars. One topic.

[00:23:04]Okay. Right now we'll be going for this compound bars. Right. What is the meaning of this compound bars? Tell me.

[00:23:14]What is the meaning of this compound bars?

[00:23:18]What is the meaning of this compound bars? Tell me. I love you. Everyone compound bars.

[00:23:33]Two different cross-sections of which one tell me two different cross-sections of same material or this different material right two different cross-sections of same length right same length but what happens to me right but what happens right but With a different but with which one? Different materials.

[00:24:06]But with different materials, what will happen to them? Subjected to a common load. Now subjected to which one? This is subjected to this common load. Okay.

[00:24:21]Subjected to which one? is a common load by a plate.

[00:24:29]By means of a plate they are subjected to which one? This a common load you can say right? By a rigid plate right which type of plate it must be that is your rigid plate it must be right. It must be which one? This rigid plate if you just observe right. Okay. So for example, Okay.

[00:25:06]One second.

[00:25:15]Right. So let us take this as which one? Let us take this as which one.

[00:25:23]Right. Let us take this as which one?

[00:25:25]two bars right.

[00:25:39]So both are of this same material or both are of this different material.

[00:25:43]Both are of this different material.

[00:25:45]Both are of this different material and we are applying right there is a common plate we are having plate external load.

[00:25:56]So let us take it as this as aluminum.

[00:25:59]Let us take this as which one is this?

[00:26:02]uh steel just for an example right steel, aluminum, copper, anything right whatever it is right so like that we are having okay now same right both are different right like that different material should be there right so then what is that you are having this is your length L same L is the same for the first member as well as for the second member or not. So this is your first member. This is your second member. Right? So then what is that load shared by this part one?

[00:26:47]So they will be sharing the loads or not? They will be sharing the loads, right? load shared by this part P1 plus this P2 will be equal to what you can say that externally applied first part second having idea Anyone having idea?

[00:27:29]Someone tell me.

[00:27:32]We will be distributing the P in which ratio? Anyone?

[00:27:42]We'll be distributing the P in which ratio? Tell me someone.

[00:27:53]So that the load distributed in proportion to what? In proportion to anyone having idea in proportion to their respective respect to which one tell me in proportion Someone tell me we are applying which load? Tell me we are applying the load.

[00:28:53]We are applying the load. Aial load.

[00:29:13]Axial rigidity will be resisting or not.

[00:29:15]Right? Axial rigidity will be resisting.

[00:29:19]Right? So what is that? Axial rigidity will resist it or not. Axial rigidity will resist it. Right? Bending member bending rigidity, right? What is the flex rigidity right? What is the flex rigidity? Tell me. Ei G right force a rigidity, right? Aial rigidity will resist right.

[00:29:45]First member load A1 E1 divided by total total total resid A1 E1 plus this A2 E2 right is that clear so load is distributed in proportion to their respect to which one this aial rigidities right so aial force bending It won't happen right.

[00:30:21]Is the point clear everyone? Is that point clear all of you?

[00:30:26]Right. No. So similarly right what is that load shared by this part two?

[00:30:37]What is that load shared by this part two? Tell me.

[00:30:44]What is the load shared by this part two? Similarly that P2 will be equal to how much? P into what does it tell me?

[00:30:50]That is A2 E2 axial rigidity of the second part divided by sum of the aial rigidities. Right? A1 E1 plus which one?

[00:31:00]This A2 E2 right? A1 E1 plus which one?

[00:31:04]This A2 E2 you can say right like that.

[00:31:12]stresses same do we have same stresses or we'll be having the different stresses delta in the first one is equal to the delta in the second one but the stress in the first material and the stress in the second material both are same or both are not same stress in the first material and the stress in the second material both are not same right how can you get that now tell me stress in bar one stress in the bar one.

[00:31:45]Stress in bar one sigma 1 not to bar sigma 1 P1 / this A1.

[00:31:54]Similarly, what is the stress in the bar?

[00:31:59]stress in the bar 2 that is sigma 2 equal to that P2 area P2 by this A2 is the stress in that bar 2 P1 by this A1 is the stress in that bar one right so now what is delta 1 is equal to that delta 2 so delta 1 is equal to delta delta 2 P1 right P1 PL by this a PL by Say so P1 L by this A1 E1 equals to right what you can say P2 L2 / this P2 L2 L2 identity L2 same length same length right P2 L divided by which one P2 L divided by which one? P2 L divided by this A2 E2.

[00:33:02]So strain in the first bar is equal to that strain in the second strain compatibility.

[00:33:11]Right? What is that? You can say strain compatibility satisfy strain compatibility satisfies strain compatibility satisfies right strain compatibility satisfy right is that clear everyone is this clear everyone another example one more example if you just observe So what is this one? Tell me what is this one? Tell me if you just observe. There is a tube you are having.

[00:34:03]There is a tube you are having right and inside that tube right what is that will be there inside that tube there will be a rod you are having right inside that tube right what is that you are having there is a rod you are having right inside that tube there is a rod present right there is a rod present right inside the tube if you just observe right And there and there is a plate you are having right.

[00:34:47]So there is a plate through this plate we have applied which one tell me we have applied this external load right.

[00:34:54]So this is your which one? Tell me. This is your outer tube.

[00:34:59]This is your outer tube. Right.

[00:35:12]So what is this one? Tell me this is your inner core rod.

[00:35:20]Inner core rod tube rod combination property right steel tube outer steel aluminum tube for an example.

[00:35:37]Just for an example arrangement.

[00:35:43]Tube and rod arrangement is also can be considered as which one? This compound bars, right?

[00:35:49]Same we need to use or different we need to use. Tell me.

[00:35:53]Same we need to use or this different we need to use. Tell me.

[00:35:58]Same procedure we need to use. Now it's no same pro procedure for which one? for stress and this deformationation calculations.

[00:36:10]Is that clear everyone?

[00:36:15]Is that clear everyone? Right? Same procedure we need to use for this stress calculation as well as which one? This is the deformation calculation. Right?

[00:36:22]Stress calculation as well as which one?

[00:36:24]This is deformation calculation. Right?

[00:36:26]Like that. Is that clear all of you?

[00:36:30]Is it clear everyone?

[00:36:34]Is this clear? Someone tell me this one is clear?

[00:36:48]Anyone having any doubt in this?

[00:36:51]Everyone it is clear or not? All of you?

[00:36:55]Right. So this is how we'll be having this is how we'll be having this you can say right. So class so uh we have completed with this in tomorrow's class what we'll be doing is tomorrow what we'll be having is test series right test series uh right test series right test series dashboard Test series dashboard of these rankers pro and number of questions number of tests. Right. Next onst 23rd 23rd stresses thermal stresses topic discuss both are at which one? 700 p.m. only, right? Both are at which time? 700 p.m. time only.

[00:38:02]Right? Anyone having any doubts now?

[00:38:04]Anyone having this any doubts?

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[00:39:27]First, simple stresses and simple stresses and complex stresses and strains, right?

[00:39:38]Complexes and bending stresses.

[00:39:45]Okay. Yes. Yes. I'll be covering them, right? I'll be covering them. All concepts will be covered. Right? All concepts will be covered. Right? This is a concept booster series. Right? All concepts will be covered. You can say, okay, don't miss that. Right.

[00:40:00]Right. Anyone having any doubts? Any doubts you are having, you can just contact this number, download the ranks pro app and uh join this telegram channel. Right. Okay.