Determining forces in members of a structure

[question dude]

Homework Statement

I want to find the force in the vertical purple member.

Assuming I know the forces in all the other members, there's a problem with working out the force in the purple member.

(Bear in mind, I'm using the method where I assume equilibrium at each joint in the structure, and then resolve the forces vertically and horizontally)

If I look at joint A and resolve all the forces horizontally and vertically, then I would find that the vertical purple member must have a force in reaction to the vertical component of the force carried by the diagonal member. But if I look at joint B, it would be found that the vertical purple member has zero force, which contradicts what was found in joint A. I'm stuck on this.

 

[PhanthomJay]

Homework Statement

I want to find the force in the vertical purple member.

Assuming I know the forces in all the other members, there's a problem with working out the force in the purple member.

(Bear in mind, I'm using the method where I assume equilibrium at each joint in the structure, and then resolve the forces vertically and horizontally)

If I look at joint A and resolve all the forces horizontally and vertically, then I would find that the vertical purple member must have a force in reaction to the vertical component of the force carried by the diagonal member. But if I look at joint B, it would be found that the vertical purple member has zero force, which contradicts what was found in joint A. I'm stuck on this.

Firstly, you don't have a pure truss the way you have drawn it. Maybe you omitted a member or incorrectly drew the figure. Where are the applied loads? That makes a difference in your analysis.

 

[AlephZero]

If I look at joint A and resolve all the forces horizontally and vertically, then I would find that the vertical purple member must have a force in reaction to the vertical component of the force carried by the diagonal member. But if I look at joint B, it would be found that the vertical purple member has zero force, which contradicts what was found in joint A. I'm stuck on this.

There is no contradiction. You have two equations $T_1 = 0$ from joint B and $T_1 + T_2\cos\theta = 0$ at joint A, and the solution is $T_1 = T_2 = 0$.

But as PhantomJay said, there is probably something wrong with your diagram, because the members to the right of the purple bar form a four-bar linkage, and can't support any applied loads or reactions to constraints. In most truss structures, The bars form a network of triangles.

 

[question dude]

Firstly, you don't have a pure truss the way you have drawn it. Maybe you omitted a member or incorrectly drew the figure. Where are the applied loads? That makes a difference in your analysis.

This is actually half pf a complete structure (which I have designed and built), so I have omitted the rest of the right hand part in my diagram, but let's assume that we know the forces in the other members (caused by the applied loads). What I want to ask is, whether there's a way to work out the force in the purple member? Or is it statically indeterminate?

There is no contradiction. You have two equations $T_1 = 0$ from joint B and $T_1 + T_2\cos\theta = 0$ at joint A, and the solution is $T_1 = T_2 = 0$.

But as PhantomJay said, there is probably something wrong with your diagram, because the members to the right of the purple bar form a four-bar linkage, and can't support any applied loads or reactions to constraints. In most truss structures, The bars form a network of triangles.

edit: sorry, to clarify to you both, here's the situation:

the dotted lines to the right show the rest of the structure

I assume you're referring to the diagonal member as T2.

T2 can't be zero though, because I've already worked it out to show that its carrying a compressive force.

 

[PhanthomJay]

You need to rebuild your truss such that the solid right side diagonal connects to joint A and not to the right of A as shown. Also, you don't show where the supports are located. On the assumption that there is no applied force at B and no support at B, then the vertical purple member must be a zero force member. Joint equilibrium at B demands it.

 

[question dude]

You need to rebuild your truss such that the solid right side diagonal connects to joint A and not to the right of A as shown. Also, you don't show where the supports are located. On the assumption that there is no applied force at B and no support at B, then the vertical purple member must be a zero force member. Joint equilibrium at B demands it.

there's no rebuilding, I've built the thing, and now I've got to analyze it as it is (terrible situation I admit). The whole structure is supported at its two ends. One is shown on left of my diagram, hence there is a 4KN arrow, and the other is the right hand side of the structure which isn't shown.

And you've assumed correctly, there's no applied force at B (i.e its not resting on anything at that point). I see how you've concluded from joint B that the purple vertical member must have zero force, but there's still the problem at joint A - which shows that the purple member must be carrying a force, because the diagonal member connected to that joint is calculated to be carrying a force (unless I'm wrong here?).

 

[PhanthomJay]

there's no rebuilding, I've built the thing, and now I've got to analyze it as it is (terrible situation I admit). The whole structure is supported at its two ends. One is shown on left of my diagram, hence there is a 4KN arrow, and the other is the right hand side of the structure which isn't shown.

And you've assumed correctly, there's no applied force at B (i.e its not resting on anything at that point). I see how you've concluded from joint B that the purple vertical member must have zero force, but there's still the problem at joint A - which shows that the purple member must be carrying a force, because the diagonal member connected to that joint is calculated to be carrying a force (unless I'm wrong here?).

If you had correctly built the truss such that all 5 members met at joint A, then the diagonals on either side of A share equal but opposite load, and the vertical has no force in it. You don't show where the applied are, but if your 4 kN traction load on the truss is shown correctly, the diagonal we are calling T2 is in tension, not compression.
Now since the rightmost diagonal does not frame into A , you no longer have a pure truss, and instead, you have introduced shear force into the horizontal top member that the diagonal frames into. This shear force maintains the equilibrium of joint A when combining it with the vert comp of the left diagonal. No such shears exist in pure ideal trusses.

 

[ScientificMK]

If you already built it, the problem you have is that (as previously mentioned) your structure is not a truss. What you have built is a frame and thus its members support shear and bending in addition to tension/compression. Equilibrium at the nodes is no longer the way to solve the structure. If you don't know structural mechanics, the only way out I see is to add a diagonal bar in your quadrilateral portion of the structure. It would not require a lot of work, and then you would be able to compute using equilibrium of nodes. If you have an iPad or iPhone, you could easily visualize how your structure would behave if it were a truss using this program:
https://itunes.apple.com/us/app/truss-me!/id732367282?mt=8

 

[AlephZero]

If you already built it, the problem you have is that (as previously mentioned) your structure is not a truss.

And the take-home lesson from that (which is a very important lesson in engineering!) is "don't design (or make) something that you don't know how to analyze."

Best to learn that lesson early while you are still at college. Sometimes teams of engineers only learn it the hard way, on a real life project.