deflection of space frame in span under gravity by hand calculation

[Kai Wang]

The space steel frame is built by welding many steel tubes. Its global shape is prismatic and composed of longitudinal girder, lateral vertical column, transverse beam, and diagonal brace. It is put horizontally with support at every several meters, maybe can be called continuous beam. Vertical load is applied on it uniformly. I want to estimate its deflection in span under gravity by hand calculation.

My knowledge on mechanics is limited. Does anyone know proper method is on this subject?

Thanks!

 

[klaus.]

My knowledge on mechanics is limited.

well then go to a structural engineer around you......

 

[KootK]

I'd approximate deflection by:

1) Identifying discrete trusses within the spaceframe analytically.

2) Working out a Bernoulli flexure deflection component considering only flexural deformation in the chord.

3) Roughly estimating shear deflection by multiplying [2] by 1.15.

4) Summing deflection contributions where multiple, faux-trusses would contribute to deflection at a particular location.

Depending on the layout, it might also be fun to model the space frame as sort of a two way slab of sorts with the flexural and shear stiffnesses set up appropriately. I've never done it but I don't see why it couldn't be done.

 

[r13]

Do you know how to calculate deflection of trusses? The continuity adds difficulty, but the concept is the same - finding the reactions from global stability/equilibrium, then calculate the internal forces and accumulate member displacement. However, you have to determine whether it is a truss, or a beam, that can alter your results, and the determination is tricky. If this is a practice for learning, it is better start with simply supported truss, and results verified by computer method.

 

[captain_slow]

@OP,

Decent analysis of space frames is a fairly advanced task that requires some sort of finite element modelling for an accurate answer.

Your best bet is to hire a structural engineer with 3D FEA software capability. If you are only interested in deflection estimates (as opposed to signed drawings, signed calculations, insurance and etc...) then I am sure they would charge you a very reasonable fee for a short report with colour-coded diagrams.

 

[Kai Wang]

@captain_slow,

Thank you for your suggestion. I am a FEA engineer with limited mechanical knowledge. I have learned basic beam theory but have no knowledge on truss deflection. I will try to learn it.

 

[GregLocock]

If you can approximate it as a pin jointed truss then first you can figure out the force in each member using the very elegant

https://en.wikipedia.org/wiki/Cremona_diagram

and then there is a similar process for working out the actual displacements once you know the changes in bar lengths, but I've forgotten what that's called.

Cheers

Greg Locock


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[rb1957]

with FEA (since that's your tool) you can easily make models of trusses. use 1D RODs (no bending to worry about) … a little ideal, but a starting point.

Pretty much any strength of materials textbook will show how to analyze trusses. trusses are easy to analyze by hand.

google "analysis of trusses" or "space frames" and you should get something (if you haven't kept your university texts).

another day in paradise, or is paradise one day closer ?

 

[dik]

I used to do a rough deflection calculation for OWSJ treating the top and bottom chord as the resisting areas... and increase it by 20% to accommodate the added deflection due to the strain of the web members (this was generally acceptable)... normally deflections aren't critical and if you need a ballpark deflection you might want to increase it by 25% or 30%... just a WAG...

Hand calcs are a bit out of the question; for space frames... you're looking at some serious calcs...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[dik]

We used to use energy methods way back in sliderule era times... sorry SRE...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[r13]

I think the easiest way for figuring out truss deflection is the unit load method, taught by elementary structural mechanics.