Tensions, forces, and moments for an A-Frame crane

[x86]

Homework Statement

I have to solve for legs AB, CB, and the tension in DB. The weight of the fish net is 200 kg.

Homework Equations

Sum of moment = 0
Sum of force in x,y,z directions = 0

The Attempt at a Solution

I have no idea what to do. I've tried using AB and CB as two force members but this doesn't give me any information. The only thing that I really know is the weight of the fish net, which basically means that I know the tension in DB has to be equal to this weight. I've solved one part of the problem, but have no idea about how to determine the force along the legs of AB and CB

 

[SteamKing]

One property of this system which is to your advantage is that the problem is symmetric about the y-z plane, which suggests that you can determine certain relationships between the forces acting in legs AB and CB.

As always with these types of problems, a systematic approach to determining the solution is recommended. First, draw a free body diagram which isolates either leg AB or CB, and start writing equations of static equilibrium.

If you need more detailed help, please show your work.

 

[x86]

One property of this system which is to your advantage is that the problem is symmetric about the y-z plane, which suggests that you can determine certain relationships between the forces acting in legs AB and CB.

As always with these types of problems, a systematic approach to determining the solution is recommended. First, draw a free body diagram which isolates either leg AB or CB, and start writing equations of static equilibrium.

If you need more detailed help, please show your work.

Okay, just one quick question. Is it okay to assume that the legs AB and CB equally contribute to resisting forces? For instance, if the weight causes a -x N force in the +z axis, then can I say AB_z = CB_z so 2 * AB_z = x Newtons?

How would I go about justifying this? Because if I am unable to do this, I don't think I'm able to solve the problem.

 

[SteamKing]

Okay, just one quick question. Is it okay to assume that the legs AB and CB equally contribute to resisting forces? For instance, if the weight causes a -x N force in the +z axis, then can I say AB_z = CB_z so 2 * AB_z = x Newtons?

How would I go about justifying this? Because if I am unable to do this, I don't think I'm able to solve the problem.

Well this is Physics, not metaphysics.

There's a big difference between not being able to solve the problem, and not caring to solve the problem because you might have to make an assumption or two. Assumptions are made all the time in the world outside of the classroom, and most of them are not made with certitude beyond epistemological doubt.

If the system has geometric symmetry, it is reasonable to assume that symmetrically applied forces will distribute symmetrically into the system, especially if the system is in static equilibrium, as this one is.

The fish net is hanging over the apex of the A-frame, and it appears to be static, so there will be no side loads generated by the non-existent dynamics of a swinging load, i.e., there is no evidence that the weight of the fishnet is producing any net force in the x-direction, positive or negative.

 

[haruspex]

If the system has geometric symmetry, it is reasonable to assume that symmetrically applied forces will distribute symmetrically into the system.

I would go further, and say that symmetry is an entirely valid argument, not just an assumption. Moreover, it is perfectly possible to solve the problem without employing that argument, but unnecessarily complicated.

 

[gneill]

I notice that no one has asked whether or not the legs AB and CB have mass. So I shall do so :)

Are the legs "light, rigid rods" or real-life weighty material? If so, what's their masses?