# Analysis Of Statically Indeterminate Structures By Hand

When double-checking/confirming results produced by structural analysis software, many engineers recommend verifying and spot-checking key or critical members if the entire structure is not analysed.

However, for rigid jointed structures with sway, it is not possible (at least in my understanding) to analyse individual members. This means that hand calculation methods such as moment distribution or slope deflection cannot be applied directly.

How would I go about analysing those members in a sway frame?

Also, to what storey of an indeterminate structure would you analyse purely by hand calculations without computer software when considering code requirements?

In my professional experience, I've found few opportunities to perform literal "by hand" verification.

Unless you're dealing with simple structures (or structures which can be simplified as such), it gets quite complicated and if you perform any mistakes you won't know if it's because of the model or your "by hand" calculation. And I personally have a hard time identifying (non-obvious) mistakes in my own calculations when I'm not even sure they're there.

That being said, the hard part of "by hand" verification of non-trivial structures is the actual structural analysis. Thankfully, the world has many different computer programs that do this exceedingly well.

So I check my work in one structural analysis program by creating another model in another program. This other model, however, is usually much simpler: hell, my tool of choice was Ftool, which only does 2D frame analysis. So if I was trying to double-check a 3D program, I'd have to recreate the model in Ftool using slices, manually calculating the applied loads (usually using simple distribution areas), considering the support conditions (it's much easier to be explicit and intentional about your supports and hinges in 2D than 3D), etc. It's important not to get too detailed in this model: don't try to model a complex support condition using master-slave relations or whatever; make the best simplification you can: fully hinged or fully fixed (or if absolutely necessary, do both and get an average of the results).

And then I let Ftool do its job and give me the internal forces, which I can then compare to the 3D model.

If they're close enough, great. It's much harder to get the boundary conditions wrong in a 2D model (where you explicitly define what they are at a single point, while the 3D model may require you to apply conditions to multiple points to represent the same effect, giving you room for error), so if they're close but actually wrong, it's because you explicitly messed up (i.e. in both models you forgot that that one beam there is actually hinged to the column, not fixed... a mistake you likely would've made even if doing the verification fully by hand). Getting someone else to take a look at your 2D model should further reduce the odds of that happening. And the odds of you having made different mistakes in each model that cancel out to give similar wrong results are infinitesimal.

If they're different, it's far easier to double-check that you didn't mess up your 2D model, and then compare the results to see what's similar and what's different, helping you identify your mistake (while doing it by hand risks a screw up in one element of the stiffness matrix leading you to get everything wrong).

This offers an efficient verification which is quite close to "by hand" -- you are still the one defining the structure's loads, supports and dimensions, in a format (2D) where it's much harder to accidentally mess up the model -- while still being efficient and honestly less error-prone than literally doing it by hand.

• Would you recommend approximate methods such as portal frame method to verify computer programs?
– Amit
Apr 8, 2020 at 2:13
• @Amit I don't have much experience with the portal frame method, but a quick glance at Google tells me it makes some pretty significant assumptions, which are only valid for very simple, standardized frames (i.e. all columns must be identical, as must the beams). If your structure can be reasonably considered to satisfy those conditions, then sure, go for it (again, I have no experience with that method, but I'm sure it works when appropriate, it wouldn't exist in the literature if it were useless). I still think it's more work and more error-prone than using a 2D modelling software, though.
– Wasabi
Apr 8, 2020 at 12:16