Analysing a 3D truss problem

[La82]

Homework Statement

I am trying to analyse a 3D truss problem (attached). The idea is that when you pull with a force F in the direction of the arrows, the pin in the middle will be pressed downwards, decreasing the length of p2. In general the overall structure will be consistent of a series of these in both directions.

I am having some difficulties getting started with this. As far as I can tell I should be ok to only analyse the section shown in the bottom picture?

Homework Equations

I wish to get some sort of solution that relates the length L1 and L2 to p1 and p2.

The Attempt at a Solution

My first attempt at this is to use simple statics in 3D:

Point at top of pin:
Sum(F_y) = 0
0 = - F_(BE) - F*sin(Beta)*2 (symetry)

Sum(M_top) = 0
0 = - F * sin(Beta)*2*p_1 + F*cos(Beta)*A_1-F*cos(Beta)*A_1+F*sin(Beta)*2p_2

So something clearly goes wrong here since I just end up with p1 = p2?

Can anyone help me in the right direction?

 

[BigJDubs]

Thanks in advance! The solution to this problem can be found by using a 3D truss analysis. The first step is to define the structure as a set of nodes and elements. Each node will be assigned a set of coordinates (x, y, z) and each element will be defined by two nodes and the length between them. The next step is to analyze the forces acting on each element. This can be done by finding the force vector acting on each element, which will be the force due to the external load (F) multiplied by the unit vector of the element. Once the forces are determined, they can be used to calculate the reaction forces at the nodes.The last step is to solve for the unknown displacements of the nodes. This can be done by setting up a system of equations for the unknown variables (displacements) and solving it using matrix methods. Once the displacements are known, the final lengths of the elements can be calculated. This will give you the solution that relates the length L1 and L2 to p1 and p2.