Complex frames - analytical calculations

[FEAnalyst]

TL;DR Summary

How can one solve complex frames, like those shown in the post?

Hi,

I came across some interesting frames recently. Here they are:

I wonder if all these frames can be solved analytically. If yes then how to do it ? Examples a) and d) are planar frames with diagonal members while b) and c) are spatial frames: b is subjected to uniformly distributed load while c) is subjected to remote loads (forces acting at a distance $r$ and transmitted to the frame via rigid links). How can I solve these examples ? I guess that at least some of them are statically indeterminate. Should I break them into individual beams and solve their members separately ? Is there a book or online source where I could find similar cases ?

Thanks in advance for your help

 

[Dr.D]

Where you show dots, are those pin (revolute) joints, welds, or what?

 

[FEAnalyst]

I should have drawn them better. All of these are not hinges but rigid connections of the beams.

 

[tech99]

I think there is a difficulty here because the joints are not hinged, so the members are subject to bending. As a result, the elasticity of the members will affect the result. For instance, in (d), the lateral load on the top support will depend on the rigidity of the bottom support and vertical member in bending.

 

[FEAnalyst]

I should have mentioned what these frames actually represent:
a - workshop crane
b - curtain rod
c - support of a seat in a bus
d - different type of crane

 

[Dr.D]

I have solved similar systems analytically,, but it is a whole lot of work. I would think and FEAnalyst would simple to a finite element model.

 

[FEAnalyst]

Sure, it’s very easy to solve these models with FEA (even using some free online apps) and I already did that. But I would also like to learn how to do it analytically. Since these are statically indeterminate systems, it seems that, apart from FEM, only flexibility or stiffness method can be used to solve them.