Chapter 2: Part -2 singly Rcc Beam By WSM Engineering |Quick Revision for AE/JE Exams...............

Added: 2026-05-11

[00:00:01]Hello Namaskar friends, I am Arpit Verma, I welcome you all to your own YouTube channel Vidya Pathat Engineers, so today we are starting our single sorry W RCC beam, in this some of your remaining part is left, our actual neutral axis was done, our critical neutral axis is left, okay so let's start without any delay, just wait for the second critical neutral axis AXC, let's put the heading here, critical neutral axis represents critical neutral axis AXC. Generally in Hindi it is called marginal zero force line. Ok? So what is the formula for XC? It is same for everyone, what is the formula of x, mcbc * d upon m sigma cbc + sigma ST xc = m sigma cbc * d upon m sigma cbc + σ Okay, this is your formula, this is your formula of xc.

[00:01:33]Ok?

[00:01:35]And there is another one, XC = KD, I have got this solved also, how does it come in the previous class. So on what does the value of K in your XC depend? On grade of steel.

[00:01:48]Depends on the grade of steel. The grade of steel i.e. the value of K depends on the grade of steel.

[00:02:05]How the value of K is our 40D. It is 40D. For whom? And for Fe 250.

[00:02:16]Our value of K is 289D.

[00:02:24]For whom? For FE 415. Our value of K is 253D. For whom? For FE 500.

[00:02:36]Ok? You all should remember this general value. It is very important because it can be asked directly in every exam and it is also very helpful in numericals.

[00:02:45]Values ​​are very important.

[00:02:48]Ok? Next up is your movement of resistance.

[00:02:56]Movement of Resistance.

[00:03:01]Movement of Resistance.

[00:03:10]Call it MR or MO R, it's okay, you can call it anything, so what is this, movement of resistance, either on the compression side or on the tension side, the load which is applied, is taken on the compression and tension side and into this is your lever arm.

[00:03:30]Ok? So generally we make a diagram of this.

[00:03:35]Like what do we have? is the cross section of the beam. The cross section of one of our beams became wider. This is our cross section of a beam. Ok?

[00:03:52]What is this of ours? is the cross section of a beam.

[00:03:54]What is our concern here? The steel is installed on the compression side, here we have installed less steel on the tension side, what is it called, the steel installed on the top, ASC area of ​​steel in compression side, what is it called, AST means area of steel in tension side, now the ASC which is written on the top, the reinforcement which is given, for this the modular ratio is used, how much 1.5m is used. Ok? And here we just use m for this.

[00:04:31]Why are you using 1.5m for this? Because our concrete is in compression, we use 1.5m modular ratio because the creep effect is more visible in compression. For this reason we use 1.5m.

[00:04:49]Ok? And what is the width of this section? B has been given.

[00:04:55]What is the width of your section? B has been given. The width of the section is B.

[00:05:07]What represents the distance from the top fiber to the center of the steel?

[00:05:10]What do you call this? Effective depth.

[00:05:13]This is called effective depth.

[00:05:17]What does this represent? Represented by D.

[00:05:19]From here, our neutral axis passes somewhere. 1 minute. What is this of ours? There is a neutral axis. 1 minute.

[00:05:31]This is our assumption that some neutral axis is passing through. What are you going through? Neutral Axis. Is it okay brother? This is our neutral axis.

[00:05:38]Now we are making a stress diagram of this here.

[00:05:43]Our stress diagram is formed something like this. Linear is also triangular in shape.

[00:05:55]This is our stress diagram. Ok?

[00:05:58]What is this of ours? There is a stress diagram. Ok?

[00:06:04]This is our stress diagram. Here we have one made like this at the steel level also.

[00:06:09]This thing which is at the level of steel is called stress at the level of steel, it is called CVA, CA, let's call it CB, okay and the one which is at the top bottom is called σ / M, our compressive force is applied here, at what distance, at y1 distance, at what distance y1, it is applied at x /3 distance, this is our y1 distance, at what distance x/3 does our compressive force act. Ok? And this is what our C2 is acting. At what distance is this one of ours acting? This is our y2 acting on y1 distance, sorry y2 distance.

[00:06:53]y2 distance per.

[00:06:57]What do we call this thing that is on top of ours? This is called depth of cover dc. y2 equal to what happened to us? DC happened. What is our width from here to here, what is this width from here to here called? XA We are calling it XA, now when your DC is removed from D, sorry from XA, then what is left for us? XA - DC left.

[00:07:29]xa - dc Now when our total is ad, now x has been removed from this, then how much of our width is left, d - x is left, how much d - x d - x, this width which is left, our d - x is left, okay now here the c2 distance c2 sorry c1 this is our c1 C1 our is being applied at XA/3 distance and our C2 Y here which is C2 is being applied at our DC distance. Ok? On the depth of cover distance, our C1 is the distance from C1 to the top bottom, it is called lever arm, that too lever arm one i.e. LA1, what does it represent? From LA1. LA1 is okay?

[00:08:23]And the distance y2, the distance from y2 to the top bottom, what do we call it LA2 lever arm to LA2, say LA2, okay now this is our C1. This is C2. C1 What is ours?

[00:08:45]C1 is our strength of concrete at compression. C1 is our strength of concrete at compression side.

[00:09:10]Compression side is okay as long as your ASC i.e. Area of ​​History is zero.

[00:09:17]When ASC is 0 = 0 is it okay? Now let us calculate C1. Let's raise it a little higher.

[00:09:29]Correct? Calculate C1. C1 = where is our B A distance B * XA? A one. B * XA 1/2 is becoming triangular. 1/2 * B * XA * CA ok? This CA stress of ours is applying so much compressive force. At what distance is our sight visible?

[00:09:55]Y1 is being applied at a distance. This force of ours is being applied at a distance y1. y1 is applied at distance. So how much is our y1? How much is our y1? Y1 is our XA/3, right? XA/3 Next Next page is being added. We are bringing it down.

[00:10:19]Ok? Y1 is our XA/3.

[00:10:23]Now we are calculating the force of C2.

[00:10:26]How much is C2 costing us? 1 minute down write up will not be visible. C2 C2 Go to our previous. C2 is ours, in this when our steel will also be taken, if steel is taken then 1.5m sorry 1.5mA * CBA wala * 1.5 sorry 1.5 mSC * ASC of CB minus this ASC * CB is it okay? C2 = Write down 1.5m CB minus ASCB ok? Now what is common in this?

[00:11:15]ASC.CB is available common. Take the common.

[00:11:17]ASC.CB What's left? 1.5m - 1 left. So much left. What did we get out of this? C2 force came out. A: At what distance is it appearing? y2 is being applied at a distance.

[00:11:32]y2 distance per. Ok?

[00:11:35]How much is y2 ours? y2 is ours which is dc.

[00:11:39]What is our y2 equal to? is equal to DC. That means effective depth sorry not effective depth DC what is our DC? There is depth of cover. Ok? What are we calculating now? Movement of Resistance. Sorry, without considering the movement of resistance right now, we are first calculating the lever arm.

[00:11:55]Because a lever arm will also be required. LA1 LA1 What is our?

[00:12:00]Look here when A is our 111 force with C1. Ok? So when our AD is, then from this, if XA/3 goes above A, then how much will we be left with? 11 a ones are being written here.

[00:12:16]Only d - XA / 3 will remain. We're going to get 11, which is going to be d - XA/3.

[00:12:24]How much will Aa2 come out? When DC is removed from it, D - DC remains. Did we understand? So how much did our L1 come out to be? D - XA / 3 LA2 How much did we get? LA2 = D - DC D - DC Yours came out. Ok? Now let us calculate the moment of resistance.

[00:12:54]MOR MOR What will come out of us? The force taken in compression or the force taken in tension into your compression in tension, the force couple is into lever R, so you have found the formula of compression now, so 1/2b * not here, first write the formula C1 * LA1 plus C2 * LA2, okay. Now how much is our C1? Put the value of C1. C1 our 1/2b * xa * ca * xa / 3 is 11 of 11 D - xa/3 so write 1/2 b * xa * ca * that is what is your la1? d - x/3 d - x/3 Okay. Plus how much is c2? c2 is our ascb ascb in brackets 1.5m - 1 now what is la2? d - dc d - dc, this is your formula for movement of resistance.

[00:14:18]Ok? Please take care.

[00:14:25]Next comes your tension side. What is your movement of resistance for the tension side?

[00:14:35]σ * d - y bar σ * your d - y bar in brackets y bar now how do you calculate y bar? The formula for y bar is our c1 * x/3, right? + c2 in which is dc up which is up dc/ erase it for one minute.

[00:15:18]C2 / C2 * DC upon which is your C1 + C2 is it ok? Write XA/3 here. Ok? AY will come out. So we will put all these values.

[00:15:34]Our answer will keep coming. We will do it step by step. Ok?

[00:15:40]Next comes your under reinforcement section, over reinforcement section and your balance section.

[00:15:49]In the under reinforcement section, our stress is ductile failure because stress reaches the steel first and in the over reinforcement section, it gives us brittle failure which we avoid.

[00:16:01]So the over reinforced section gives us brittle failure. Ok?

[00:16:06]For that, we use the compression side movement of resistance.

[00:16:10]For the under reinforcement section, the tension side is used. So in the balance section, the stress in our steel and concrete reaches simultaneously. So what do we do about that?

[00:16:23]For that we can solve the question using both the formulas.

[00:16:25]Ok? So, without telling about under reinforcement section, over reinforcement section, balance section, we directly solve one question.

[00:16:34]Because look at our single reinforcement section, the theories for under reinforcement and over reinforcement are the same. There is just a difference in the formula. Because in that we use the formula of single reinforcement section, in this we use the formula of WRC beam. The only difference is this flower. One is d - y times a, there it was d - x / 3, and here we have bx² / 2 = max dd - x. This formula will apply here. This is the only difference between them. So what to write? Ok? So we are giving a question and getting it solved. Like we have a section of a beam.

[00:17:14]What is? a Cross section of any beam.

[00:17:16]This is our cross section of a beam.

[00:17:21]Ok? This is our cross section of a beam.

[00:17:24]What is its width? B. 1 minute.

[00:17:29]Lower it a little.

[00:17:34]What is the width given for it? B = How much is it? 400 mm.

[00:17:41]1 minute.

[00:17:44]What is the width of the section given for us?

[00:17:49]400 mm = 400 mm. Ok? 400 mm, this steel is installed here on the compression side. Ok? Here also we have steel installed on the tension side. How much of this is ours? There are three bars of 25 mm diameter.

[00:18:19]That means there are three steel bars of 25 mm diameter.

[00:18:22]Here our 20 mm gun has been fired four times.

[00:18:32]Four bars of 20 mm by 20 mm dia. Ok? Here we have four 20-minute bars.

[00:18:38]What is its effective depth? Effective Depth What is the effective depth d? We have given 600 mm. 600 mm. Ok? Now let us calculate this. So what is it asked for? And how much will you use the value of m in this? 11 will use it. Ok? And ours is M25 grade concrete. M25 grade is concrete and Fe 500 grade is steel. Fe 500 grade steel. Ok? Now we have all our data. For this we will bring out the Movement of Resistance.

[00:19:26]So what is the value of ASC? In ASC, whatever you calculate your ASC, what is our ASC, how will we calculate it? How many times is π / 4 * D²? It is three times. So we will multiply this by three. So 3 * π/4 π / 4 * d² is three times the 25 mm dia. If we square 25, how much will we get? 1 Minute Calculator. So where did the calculator go? Yes.

[00:20:02]How much is the square of 3 * π/4 * 25 coming to you? 1472 72 is coming approx. Ok? AST will be calculated in the same way. If you have four bars of AST, write four here. 4 * π/4 * d² right? So our AST is to be calculated. We will replace 4 * π / 4 d with 20m. How much will a 20-hole square cost? You can also divide 4 * 5 by four. Square the whole of π * 20.

[00:20:37]How much will 400 pies cost? 1256 is approaching 12564 mm². Ok? Write this down. You might not be able to see it there. 1256 mm² ok?

[00:20:54]Write square here. Correct? Now the actual neutral axis has to be calculated. What needs to be calculated? Calculate Actual Neutral Axis.

[00:21:06]Calculate actual na ana means actual neutral axis. Ok? Writing in short.

[00:21:14]What is its formula? Let's write.

[00:21:18]bxa²/2 + 1.5m x in brackets - dc x in brackets - of x in brackets - dc ok? = mast d - x This is your formula.

[00:21:51]Now we should keep all the values ​​in this.

[00:21:54]What is the value of b given?

[00:22:01]How much do we need to calculate in this one minute 400 * x² x?

[00:22:07]In x² upon your 2 plus 1.5 the value of m is 280 up 3 cbc well the value of m is given as 11 m * 11 what is the value of SS given as 1472 which is 1472 one minute let's simplify it further first let's simplify this formula further it will be a little easier. Ok? Stop calculating x here.

[00:22:40]bxa²/ 2 + 1.5m - 1 1.5 m - 1 x - 1 min asc 1.5m - 1x how m s - 1 a c x - dc OK. x - dc 1.5m - 1 x - dc = mst d - x Now put in the values. Ok? So 1 minute will fall short, so I am writing this formula further.

[00:23:53]What did bxa²/2 + 1 5m come to? M - 1 x - dc 1.5m - 1 s How is that done from here? ASC is taken as common here. Then 1.5m - 1 is left out of this. Is any of this okay? 1.5m - 1 ASC XA - DC = MST P - XA Now put all the values ​​in it.

[00:24:31]Well, it was a long formula. Now it has become a little smaller.

[00:24:36]What is the value of B? 400 x² / 2 plus the given value of 1.5m is 11 - 1 SC, how much did it come out to be?

[00:24:51]1472.62 AC 1472 62 in brackets DC of XA minus DC of XA minus how much do we take DC just cover in general? Generally we take 50 mm.

[00:25:09]Ok? They are writing 50 mm. I have assumed it. Ok? I assumed it because I want to tell you how to solve it. Ok? So x is our x - 50 1472.62 in brackets x - which is your 50 equal to m value 11 ST what did you come out to be?

[00:25:33]1256.64 11 * 1256 d in brackets how much have you given?

[00:25:42]Depth of cover sorry depth effective depth is your 600. 600 - x is 600 minus your xA. Now solve this.

[00:25:54]How much will XA cost?

[00:25:57]Use a calculator for a minute.

[00:26:02]cross it out. will become 200XA².

[00:26:09]200X² XA 1.5 11 - 1 Your approximation will come.

[00:26:20]144.11 which is mm should come. 144 will come in 11 mm. Ok?

[00:26:29]You guys can check the approximation by calculating.

[00:26:32]Ok?

[00:26:34]Critical Neutral Axis. Now this is your actual neutral axis. Now what will we do with the calculation? Critical Neutral Axis.

[00:26:44]Calculate actual, okay actual neutral axis, now tell me which steel was used for us, look at the back, which steel was used for 5 bar M25 Fe 500 Fe 500 which is our red of steel, what is the value of K? X = KD.

[00:27:12]What to do? xc = mcbc * d/ mcbc + σd It is easier for us than this, so we are taking it from this.

[00:27:22]So what is the value of k that comes out to be xc? 253d253d So put the value in it.

[00:27:34]What is 2553 * d? How much will 600 mm cost you? 253 * 53 * 600 equal to how much will it cost you? Coming to 151.8 mm 151 8 mm. Correct? Now compare this and this. Ok? So which section will come for us? The XA we have is smaller than the XC. So our under reinforcement section will go.

[00:28:15]Under reinforced section.

[00:28:18]Ok? What formula will you use for this? What formula will we use for this?

[00:28:28]What formula will we use for the under reinforcement section? mr =t * d - x/3 This is what we will use brother mr =t * 1 minute σ * in brackets d - x/ sorry why will d - x/3 come here brother? These single RCC beams are not solving the problem.

[00:29:10]In single RCCB we get d - x / 3.

[00:29:13]Here we will get d - y bar because under is the reinforced section. Ok? d - y times.

[00:29:17]mr = σ * d - y bar because under reinforced section. So for the under reinforced section we calculate from the tension side. How do we calculate the over reinforced section?

[00:29:34]From the compression side. So apply this formula.

[00:29:38]Ok?

[00:29:40]So you guys can do it further.

[00:29:43]Keep the value of σ. Keep the value of ST. d Our 600 mm is given. How will the y bar be calculated? y times that will remove our will be removed. How will ours be removed y times?

[00:29:55]C1 * XA/3 + C2 * BC / C1 + C2 Y times will come out of this. So you guys calculate it. Ok? Please tell me the answer to this in the comments.

[00:30:18]Ok? So that's all for today.

[00:30:20]See you in the next class with our T beam. Ok?

[00:30:27]Thank you. That's all for today.