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