## Statics: Lesson 58 – Shear Moment Diagram, Graphic Method

okay everybody here we're going to talk about shear and moment diagrams okay so he talked about we're talking about shear moment diagrams this is kind of a preview for solids but it is contained in the statics course and so let's see if we can solve one of these okay so these are shear and moment is is what we're talking about is the shear force which is represented as a V I tell my students was if I sent you to the kitchen for the the shears what would you come back with pair of scissors what's the International sign for scissors yeah the okay that's where that comes from but it works for me okay so V is the shear force and the shear force is like I have one force I have an oval this trip going this way so it's trying to tear the beam in half in this direction okay you also have the normal force but a normal force is trying to pull or push the beam okay and then you have M which we call the bending moment Hey and that is a force that's trying to bend the beam one way or the other way and make the beam into a smiley face or a frowny face depending on which way it bends right so we're going to say what if I wanted to know the shear force or the bending moment for every single point in the beam how would I do that well the only way to do that would be to plot all of those forces and then I can see what it's doing throughout the whole beam this is important to me as a designer as an engineer to know what is the maximum bending moment in that beam because that's going to define like what kind of material I use how thick my eye beams are going to be how heavy they're going to be and so I need to know what these values are all right so what I'm going to do here for this problem is going to be called the graphic method that's not because there's blood and guts okay because we're going to be using some graphs okay okay another method we'll talk about a little later maybe in another video would be the equation method but for this one we can do it with a graphic method I think okay so what I'm going to do here is I'm just going to draw a line down the page now I'd like to always start these at the top of the page because this is up here this is the load diagram the next thing I'm going to have down here is going to be the V diagram the shear diagram and it's the integral of the load curve and the next one down from that is going to be the moment diagram guess what it's the integral of the V curve and so these curves are all related so if I'd wrong kind of in order it makes things nice and easy I'm going to draw something we call discontinuities here I'm a little bored I'm going to draw like everywhere where I think something's going to be happening I'm going to draw me a line I think there's going to be some change to my graph at all those different places there okay so for step one for solving these problems we're going to do this in red I'm going to have to find my reaction forces now I have a B Y and over here I have an a why and maybe I have an ax now this particular load scenario I have no forces in the X direction which means that ax is there if I needing but for this particular load is zero okay he's not there so for these problems step one is always find global equilibrium find those reaction forces where this thing is is hooked to the world if you will alright so what I'm going to do is just sum the moments at a okay and I'm going to fund this being positive and I'm going to find I'm going to find B Y okay now I didn't put one load on there did I that is a three kill names per meter and so this load up here is three kilonewtons per meter so what I need to do is convert this distributed load up here into a concentrated load and I didn't put dimensions on here I left all kinds of stuff off for you guys this is three meters six meters and this is three meters okay if you got it all on here so if this is three kilobits per meter times how many meters of it six and so what we're doing is finding the area of this curve here so it's three tall it's six wide and so it's 18 kilonewtons okay because if I multiplied meters times that the meters cancel it out and leaves me with kilonewtons okay so and of course I put it right in the middle because that's where the centroid of a rectangle is okay so let me go back to my equation over here and what I'm going to do is I'm going to take the whole matinee okay so I have this 18 force it's rotating me clockwise will call him negative so negative 18 times 3 and then I've got this 18 here so minus 18 more times 3 and 1/2 of 6 which is another 3 so that's 6 and then I've got be why he goes in the other direction so plus b1 times mmm 9 right it's 6 and 3 to get over here B Y and then I've got one more load over here which rotates me also negative so I'm going to call it minus 6 times 3 9 12 okay so there's my equation the only unknown in this equation is B Y so when I solve this I'm going to get be Y so B Y is equal to oh but let's see I don't think I can do that in my head let me get my calculator my calculator okay let's see here 18 times 3 plus 18 times 6 plus 6 times 12 equals 234 divided by 9 equals 26 so B why is 26 and that would be kilonewtons the total downward force I have is 36 plus 6 that's 42 so if I subtract 26 from 42 I'm left with 16 so a y must be equal to 16 kilonewtons okay so it by this point and statics you guys should be getting really good at calculating global equilibrium this is back in chapter 5 stuff okay so in the Hitler book at least we should be getting really good at this okay so the V Y is 26 and a y is 16 okay now any time if you have a mistake on these problems your graphs don't come out this right you probably should go back to this step right here I find this is where most of the common mistakes occur okay here we go so we're going to plot this order to plot it in green okay and so what we're going to do is really the V diagram it's going to be based on for this diagram so what what you think about is is you got a backpack on okay you got we'll call it your load backpack and as I get on to this beam I'm going to start walking across the beam and unstuff is going to start going in my backpack okay so as soon as I hop on the beam now IV here and V is going to be in kilonewtons okay these shear force it's a force and then this is down here M is going to be in kilonewton meters okay so the first thing I do want to hop over the beam is I get 16 Q moves in my backpack but it's going up isn't it so it's going to make a lighter by 16 counters so that's right there okay it's sixteen then what's going to happen as I start walking across the beam any change in the force yeah nothing nothing nothing nothing BAM I get to this line here what happens I get 18 kilotons in my backpack well I'm at sixteen right so that's going to take me to negative two there I am negative two okay now I have that distributed load up here now don't think of this as a concentrated load we can only use that concentrated load for finding global equilibrium I can't do that anymore okay so here I go I'm at negative two what's going to happen is I take a step what's going to happen every step I take work three killings in my backpack no step three more killings about X oh I'm getting heavier and heavier and heavier and buried okay so I'm going to be going down and I'm going to go down how much 18 but I'm going to go down linearly okay I'm going to go down here too I'm at negative two I went down eighteen more so I'm not negative twenty okay now another way you can kind of think about how these lines go well talk about that just second okay now here I am at negative twenty and look here now I met this b1 now I get 26 off of me so what is that going to do to me make me lighter right I'm at negative 20 I go up 26 that puts me at six and then what no change no change no change am I to the end and then six kilonewtons group takes me back home okay now on the beam what's the sum of the forces zero so if I don't want backup at zero I've done something wrong and they always these graphs always come back to zero okay always if you know that's a good check step because if you don't come back to zero you say mom messed something up and it's probably this one here okay so notice that I have these different shapes this one's flat this one's got a linear decreasing and this was flat remember what I told you that these graphs are related by the integral list thing about this I call this the order of the lines order of the lines okay and order the lines is like it goes like this if one of my graphs has a concentrated load on it then the next graph is going to have a flat line right so here was a concentrated load look at this graph it's flat across here here's the concentrated load the next graph flat across there okay this would be like one equals five so what happens if I integrate y equals five I get y equals five x and that's what if i graph a 5x it looks like that right if I take the integral of 5x I would get a squared right the X would go into a square which is a parabola which looks like that and if I integrate a square I get a cube which looks like I've learnt that right so if I can remember these order of the lines like an arrow then a flat then an angle then a parabola than a cubic I can go over here and look at this if I have a flat line the next line down right the next graph is going to have a slanted line right i linear decreasing line what's the next graph damn going to have well the next graph down is going to have a parabolic curve for that okay so let's see if we can calculate the last one now by the graphic method I can use these areas to calculate where I'm going to go down here on my moment diagram okay so here's one thing I like to do is positive area here is a positive slope down here a negative area here is a negative slope down here and again this is no yet another positive area so anywhere the graph my V graph goes from a positive to a negative what's going to happen on am graph I'm going to have a positive slope and then negative slope I'm going to have a little help you do on my graph there right I'm going to have a local min or max so I know that I'm going to have a min or max here and I'm going to have one here because this thing changes slope at both of those places all right so and this is this height here is in kilonewtons and the width here is in meters and so when I multiply the height times the width what do I it I get kilonewton meters I get a moment so I can just calculate the area of this shape to give me the value of my moment curve down here okay so this guy this area here is what 16 times 3 it's 16 tall and 3y okay and that's going to give me my slope down in the bunker now I'm going to calculate all these areas this is a rectangle and a triangle that's what 2 times 6 so this part is 12 and this part is let's see 18 it's 1/2 the base times the height which is 18 right so what is that 9 times 6 54 ok and then let's add these together let's see I'm not sure going to put my head 6 times 18 8 holes divided by 2 equals okay before Plus that 12 plus 12 equals 66 right so the total area of this shape here is 66 and then the area of this guy what's that 6 times 3 18 okay so let's see if we can plot this there we go ok so the first one I start off at 0 the only time you don't start off as at 0 is if you have a concentrated moment on your load curve and we don't have a concentrated moment anywhere so we're going to start off at 0 and I'm going to go up 16 times 3 I should calculate that right 30 plus 18 it is 48 okay so I'm going to go from 0 to 48 and how am I going to get from 0 to 48 right this is flat so what's the next one right linear increasing here and then what a negative area I'm going to know negative I met I meant go up didn't label that that's important that you label these okay okay because we may ask you what is the maximum moment of the whole beam if you don't label your points you won't know okay so I'm going to go down over this area I'm going to go down sixty-six but I'm at 48 so what's 48 minus 66 over 48 minus 6 18 negative okay so here now I'm going to be down here at negative 18 here we go how do I get from there to there oh this is the hard part this is where people get lost okay I know the neck this is linear decreasing so I know the next curve down is going to be parabolic but I have two choices here's a parabolic curve and here's a parabolic curve so how do I know which one to choose is a concave down or concave up I don't know here's how you do that again think about that load backpack okay over here right as I take a step I'm getting little short stacks of load there okay as I take that same step over here what am I getting whoo I'm getting fat stacks over there right so this is like a slow accumulation of load this is a fast accumulation of load imagine these like stacks of bricks but take a step I get a short stack but over here if I take that same step I get a big stack okay so my load is going is increasing slow then fast and you can kind of think about that as the size it's small here it's big they're so slow fast and if you went skiing what would slow and fast be so it would be like bunny slope that's like splat slope and fast would be like black diamond that's steep slope right so look here slow then fast here slow then fast this is fast and then slow at the end I don't want that one so the correct curve to choose is this this is the slow then fast curve like that negative 18 okay and now we're a man may be negative 18 this is a positive area I'm going to go a positive slope I'm going to go up 18 guess where that's going to take me right and notice this is flat this is angled order of on lines alright the next one takes me back to zero so just like the shear curve the moment curve has to return you to zero okay if you don't come back to zero you know you did it wrong so what's the maximum shear force on the beam well if I look at this the maximum shear force on the beam this was six this was minus 20 that's 16 that's the maximum shear force 20 kilonewtons okay if I'm designing I'm going to design for that what's the max bending moment okay well this is 48 that's 18 the max bending moment occurs right there and it's 48 kilonewton meters okay Sharan diagrams

Dude, you are a legend. I haven't been to class for a while which means I have no idea what was going on. I watched your videos in one day and I got a B in my exam:)

Excellent job!!

Watching this in the 11th hour before an exam and finally understanding. 🙌🏼🙌🏼 Thank youuuu.

Sir I may say you are the doctor of the statics every body can understand this easily by your language your teaching method you are the king of statics .. may God give you more and more love you sir..

te amo brow <3

As usual, amazing…

So the sign convention for the bending of beams is opposite the sign convention used for moment forces?!

You managed to give the information that my teacher took a total of 8 hours worth of lectures in 17 mins.

Thank you from the bottom of my heart ❤

The OG

Awesome explanation.

So funny definitely explained it better then my professor.

Wow the order of lines really made this click for me. Amazing lecture

so clear

god bless

OMG this is the easiest class ever. After watching this video I do not even understand why I struggled with this in last semeter that much. Thank you professor! I appreciate for all your effort of making this video.

يخي انت في قلبي سكنانا

That is the best explanation ever. I've been wrestling with this stuff for I don't want to say how long. That was excellent. Bravo!

Thank you!

thank you so much Dr. Jeff Hanson. This was so very well explained!

ref 16:30

Very gud

i really liked the way you solved problems, simple and clean. if i can get an aa, i will come back and reply this comment :d

Great videos!! Thank you for helping me out of my statics final!

saatler olsun hocam

You are the goat my friend. 🐐

Order of the lines needs to be taught! Dude you are so smart and your little sound effects honestly help too for some reason. Thank you so much.

God bless you.

This guy is a legend

Missed the class my professor taught this and I feel like I can teach it to anyone just from watching you.

Shouldn't By be equal to 30? Since the sum of the negative factors is equal to 270.

I wish you were my professor.

Thank you for this video! I missed the lecture for this, so in the next class day I was totally lost! I was nervous to start my homework, but I think now I'll be able to do it 🙂

You. Are. Awesome!!!!!!!! And thank you for using metric units 😀

Why don't more people teach like you….

Fat Stacks

LIKE A BAWS!!!!

You really are the best

I like the idea of slow and fast … thanks, easy concept.

Merci beaucop

Thank you, aewsome.

Magnificent 😍🙏🏽✌🏽

I'm a EE background student now getting a ME PhD 14 years later…needless to say I've forgotten everything and didn't learn other things I'm needing now. These lessons have been immensely helpful in getting me up to speed quickly. Appreciate your time and effort.

That Slow and Fast Tip for the Moment's bend is such a great way of looking at it! Great Video on breaking shear moment diagrams down easily

It never gets easier we just get better because of God and Professors just like YOU