How to identify zero force members in trusses

hey welcome back in this video I just want to talk about zero force members in trust systems so it's possible that in some of these trusses that some of the individual members will actually have no internal forces depending on the configuration of the externally applied forces some of the ways I guess before we start talking about that I want to talk about these kind of three types of joints we can have or joint configurations with other members so imagine looking at this top one imagine if there was some internal force in this member here there's two members connected at one joint they're collinear they're both in line with each other for this joint to stay in static equilibrium this other member has to have the equal and opposite force in it so if it's compression on this side it has to be compression on that side if it was tension on this side you would also have to be tension on this side right for this thing to stay in static equilibrium otherwise if these were unbalanced or not equal magnitudes this thing would end the joint would actually have the tendency to translate along one of these lines so the first thing that we can get the first situation we can have with a zero Force member is if there's actually zero forces inside this and there's zero external forces applied to this kind of setup we have here imagine there's no internal force here but there is an internal force here if with nothing to counteract that and there's some tension here or something and this joint we want to translate up this way so in the case of this in the case of these two collinear members with no external forces then they have to both have zero force if this guy has zero force this guy has to have zero force as well for this thing to still be in static equilibrium another situation that we can get a zero Force member is imagine we have this set up here where we actually have three members connecting at a joint where two of them are collinear so imagine again we have some amount of compressive force like this for this thing to be in static equilibrium we have to have the same compressive force resisting that if it was tension this cyber just have to be tension as well but if there's any amount of force and this let's say this let's say this is tension there's nothing else to be able to pull on this because these guys can't support a lateral load and so this thing would just start translating or drifting off in this direction making it not in static equilibrium because the sum of forces in this direction would not sum to zero so in order for the sum of forces in this particular direction to sum to zero there actually has to be zero internal forces in this guy so whenever you see something like that for example I'm seeing something like this we have we have a joint here with three members two of them are in line and one of them is not in line well this member here has to be a zero Force member because otherwise if it was pulling or pushing it would make this joint out of equilibrium so that's something that we can look forward to force for zero force members okay the other kind of situation that we can have is imagine if we have again let's say we have a compressive force in this member and we have a compressive force in this member there x-components might be balancing each other out but no matter what their Y components are summing up to some positive force in the Y direction in this thing this joint would have the tendency to translate upwards same thing if these guys were tensile then their net force then that Y force will be negative and this thing would have the tendency to translate downwards so the third case is when we have a joint with two non collinear members so just two members that aren't in line and no external force then they both have to be zero force members otherwise this joint will not be an equilibrium when we're going through analyzing for zero force members if there is we do it we do a joint by joint kind of and if there is an external force applied at add a joint for example here I'll draw a straight line we have some external force you know acting like this at this point we can no longer just say by inspection that this is a zero Force member actually it wouldn't be because again we would have these guys would be these guys would be doing their thing in this plane but this force would actually be introducing a force in in the plane of the two collinear guys and also in the plane that's perpendicular to that and so this would indeed have to have some amount of force to kind of counteract whatever that force is and is when you see an applied force at a joint you can't immediately start saying that things are zero force members at that joint using these three definitions so let's go through these two examples and pick out all of the zero force my that we can find we already mentioned this one so we have to collinear members with a third member that's not in the same plane is them or not the same line as them obviously if they set any tension or compression in it it would be making this joint out of equilibrium so this guy is a zero Force member let's put a little circle around that knowing that this one is a zero Force member we we can look at this and so if this is zero force it might as well not be there and here we have another two collinear forces with a third member I start to collinear members with a third member that's not in the same line as them acting at this joint and so by this definition here this member also has to be a zero Force member now when we look at this joint we actually can't say anything based on this joint because it hasn't applied force at it and so we're actually not sure we can't you know we know that something in the plane here that's perpendicular to these two collinear members will actually have to take some of the load of this force so we're not actually sure but what we can do is we can come down and look at this guy it's not the joint with the applied force on it so we're good to go we can analyze it independently we have two members collinear one it's not collinear and that means that otherwise if this had any amount of force in it it would be making this joint out of equilibrium so this guy is also a zero Force member now when we look at this joint we can see that that this member here will take all of the component of this blue applied force that's perpendicular to these two collinear members okay is anything in here zero Force member well no when we look at this joint this force is going to air this member is going to introduce some amount of some amount of force in that the y-direction and this guy here is going to have to counteract that so we found the three zero force members in this diagram something that we can do just so you can wrap your head around it is we can just show you what I can just show you what the equivalent is so basically if we just erase the zero force members like that that and get rid of that guy you could solve this problem analyzing it as if these three zero force members didn't even exist and these are equivalent systems basically with the current loading obviously if the loading changed we would have to reevaluate but these are the only members here that actually have internal forces in them all right let's go down here and look at if we can find any zero force members in this guy so again here we have two collinear members a third one that's not in the same line this guy is definitely going to be zero Force member otherwise it would be pushing this joint up or down once we knock that one out we can see here that we have two collinear and the other potential guy here again that would you be pushing out of the plane that these two are in or out of the line of those two forms this one is the zero Force member actually I think what we should do is I'll erase them as we go and it'll be easier for us to kind of track the the progress that we're making in this equivalent system so I'll come in here and I'll erase the two zero force members that we found so far now the next thing that we want to do is let's look at this so we have a member here a member here collinear a third member here obviously if there's any amount of force in here pushing it it would translate this this joint here in this direction or this direction so this guy also is a zero Force member and we can go and erase that just like this all right so knowing that this one is zero force we've erased it here other thing we can look at now is the situation here well now we have two more collinear guys and definitely we can't have any force in this one otherwise it would push or pull this joint so this is also zero Force member and we can come in here and erase that guy there we go and there's one more zero Force member in here it's kind of hard to see but if we think about this this reaction here can only provide a reaction force that's normal to the wall right because it's on a roller so if we're providing a normal force here and then this has zero force in it this will have to be equal and opposite and then looking at that it looks like we have two collinear forces so there actually can't be anything in here because if there was some amount of force in here it would make this joint fall out of equilibrium so this guy also zero Force member and then we can come in and erase it out of here so there you go this truss had five zero force members in it this truss had three zero force members in it and if you just want to solve this problem now if you were given the applied the applied force and you're asked to find all of the internal forces of all the members this would actually simplify your process quite a bit when you're going to find those because we'd actually we already know that a lot of them are zero

Channel: Engineer4Free

Views: 489,369

Keywords: free, engineer, engineering, math, university, science, tutor, tutorial, lesson, online, learning, mathematics, engineer4free, worked, example, statics, mechanics, AP, physics, static, equilibrium, truss, trusses, zero, force, member, zero force member, members, tension, compression, joint, joints, pin, pinned, connection, colinear, sum, of, forces, net, free body diagram, method, sections, analysis, structural, civil, bridge, crane, design

Id: xSEScMN6bpo

Length: 9min 42sec (582 seconds)

Published: Tue Jun 21 2016