Statics: Lesson 41 - Trusses, Method of Sections, Truss Tips and Tricks

[Music] hey my friends I've got a video for you here on trusses a few tips and tricks a little secrets of the pro it's okay so after this maybe we'll be pros - okay so I've got a different kind of truss here instead of this one being typically they're anchored to the ground but this one's anchored to the wall right so they want us to find four send members b c d e and f e so where is that let me let's highlight i'm good okay so here is f e down here and then b e which is this guy and then bc which is this guy up here okay so and the reason i do that is because i want to see those members that I'm going to cut through remember how do I know the difference between the method of sections in the method of joints method of sections if they ask me for specific members I'm going to go do the method of sections if they ask me for every member in the in the trust then I might as well just use the method of joints okay I have left up here the recipe for how to solve these problems number one find global equilibrium cut through the members of interest which we have highlighted don't cut through more than three unknowns and then draw the Freebody diagram the easiest side now this is the this is an important step this time okay we'll put a little star there because that will change our mind about step number one okay tip number one of the pros here you go today if we cut through the members of interest okay if we cut right through there okay it says draw the Freebody diagram the easiest side so we can draw the free by an eye on that side or this side now if we draw this side the left side then we're going to have this global equilibrium stuff on it right but if we draw a left the right side rather there's no global over there so step one should say find global equilibrium when necessary okay yeah students are like okay I memorized your your recipe and I'm gonna do it on every problem think with your brain here okay if I do this side over here I don't have to do step one I can skip that that's tip number one okay so here we go big triangle not ice free bodies big nice for you guys oh this is a different angle than that is a different angle than that okay so we got a little angle ISM we have to contend with so we've got a vector a vector lets you draw that more more steeply okay this pin does not erase very good okay and then one here okay so this is BC this one here is B e and this one down here is f e okay now I think before we get started let's do some let's do some angles okay so I'm just gonna make myself a couple of triangles here well this triangle is three this way three that way so that is 45 degrees okay that was pretty good and then this little trying run here is three on this side and one on that side so we're going to do what the tangent on that guy okay so let's see what we get here we get 2 inverse 10.3 oh goodness clear inverse tan a point opposite over adjacent 1 over 3 is 0.33 3 and that's eighteen point four two degrees okay so eighteen point four two degrees all right now I think it's important now to look at some we can put some arrows on these and I'm thinking most of these method of section problems I've told you this before is just guess everything in tension just guess it in tension and if I get a negative I guessed it wrong okay no big deal all right now one of the things we do at the foot of this free body diagram are these external loads and so we've got six kilonewtons here and a three kilonewtons there okay this is point D point C and point E okay all right so there is we're all the way up to step three the next step is solved right and that's a statics promise the regular Oh statics problem so here's here is another thing another another row another secret for you okay now to solve this I think it's pretty easy to do the regular way but I want to I want to show you one more trick you know the next thing that I would do is I would go to the moment equation right and you want to take the moment somewhere that I'll knock out some unknowns and I only have one unknown left right and that way my moment equation I get something right away right that's what I want okay so where can I take my moment to knock out a whole bunch of notes well the obvious one is B II I mean at Point E right the obviously the the play here is to take the moment at Point E okay and and that's that's good but there's one that's not so obvious and that would be this if I extended this line up and extended this line up then this they intersect over here at point B can you take the moment at the at a point that's not even on your free body diagram the answer is yes you could take the moment about the end of my nose if you want to you get the same exact thing okay so if I took the moment at point B then I would get Fe if I take the moment at E I'm gonna get BC okay so there's more than one way to skin a cat and that's tip number two is don't forget about points that are off of your free body that can knock out some of your unknowns that's a that's a good tip okay put that went away all right so I'm gonna take the moment at E and what do I get well actually the six kilonewton it goes through point e as well those two guys are knocked out so I get BC which rotates what positive BC times how far away from E up to there is three okay and then I got the three over there which rotates me negative so minus three times how far away is that guy three okay if the forces and the Y then the distance is in the X you know what that's it isn't it the three divide everything by 3 B C equals three killa Newtons and I'm driven tension I got a positive answer which means he really is in tension right if I would have got a negative answer men well he's actually in compression how nice is that y'all that's so easy okay now the next thing I could do okay here's what I could do I could go up here and I could take a moment here right and then with another moment equation I get Fe and then I can come back with a sum of the force in the X or the Y either one and get B eat and be doing this problem okay but I can also I'm telling you this is so important man if you have one of these little calculators right this ti 36 Pro if I write this sum of the force in the X and the y I'm gonna get two equations with two unknowns right those two unknowns and I can just put it in my system solver done with this problem okay so why would you go into a test with a calculator that doesn't have a system solver and it makes no sense okay so let's do that right quick some of the forces and the X is equal to not in the X Direction what do we have we have BC which is three oh but he's going in the minus direction everybody's one of the minus direction so I know somebody somebody's not right here okay - be e Coase 45 and then minus F e cose 18.4 - okay and then the sum of the forces in the Y what do I get in the Y direction I get this guy going uphill so be e sine 45 and then minus f.e sign 18.4 two and then -9 right 6 plus 3 is 9 going downhill -9 right so real quick let me rewrite those equations so that they're in kind of my system solver format here okay so point 707 be4 less what is the cosine of eighteen point four two point nine four nine point nine four 9f e is equal to negative three okay and then the other equation here I'm just going to move the nine to the other side so that equals nine and what's that number eight sine of eighteen point four two there's point three one six and then see that would be a minus and then this guy would be a positive so 0.707 be e okay so there's equation number one equation number two and of course this one came from the X that one came from the Y now it's just a matter of putting my system solver and I'm done with this problem so in our system solver here point 707 enter 0.94 nine enter negative three enter 0.707 enter and then negative 0.316 enter and then finally nine and so i'm one of these is going to be negative right because you can't have an equation like this you can't have a negative a negative and a negative equal to zero that just doesn't work okay so one of these backwards who is backwards okay and it gives me that be e the first one here be e is equal to eight point four nine and that's kilonewtons and it's a positive number right so I assumed him intention for B ESM team intention so he really is intention hey there's one and then the Y I got a negative for the Y I knew one of them was negative right so it's y so Fe alright Fe I got nine point four nine okay but I got negative nine point four nine from when I saw these equations so that means that I assumed Fe intention well he's really in compression excuse me so it'll be a C there okay and done so a few tips right you didn't we didn't have to find global equilibrium we can take the moment off the part that's one that not not very many people understand so but we got it now and then system solver is such man it just makes this problem so much easier that's supposed to be a star that's the worst star in history okay sorry okay gang so there you go I hope that makes your life easier solving these trusts problems check it out I'll see you next time

Channel: Jeff Hanson

Views: 45,449

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Id: E0eXgTXZ554

Length: 12min 44sec (764 seconds)

Published: Fri Jun 19 2020