Suppose we have a rigid jointed, statically indeterminate frame with bracing as shown below:

Example Of Braced Frame

Note: there would also be a distributed lateral load along at least one side of the structure and all reaction supports can be considered rigid/fixed.

In order to analyse this by hand (find bending moments, axial and shear forces), which method would I use? The main reason for the lack of clarity is due to various textbooks not demonstrating examples of analysing braced frames for statically indeterminate structures.

On a regular unbraced system, I would use moment distribution or slope deflection. However, for frames with bracing, I am unsure how to approach the problem. Any guidance would be appreciated.

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    $\begingroup$ Are you looking for a strictly analytical, exact solution or can we throw a bunch of assumption in to make this easier? Doing a five-story, five-span structure with bracing with exact methods by hand will be a nightmare. $\endgroup$ – Wasabi Jul 9 '20 at 18:29
  • $\begingroup$ Thanks for the reply. I would prefer the exact solution since I will only be using it for smaller structures (i.e. two-storey, double-span) but I would also like it to extend to larger systems such that I can write up excel sheets to complete this. $\endgroup$ – Amit Jul 9 '20 at 23:43
  • $\begingroup$ Any particular reason why you want to do this by hand/Excel instead of using software that's, well, made for this? $\endgroup$ – Wasabi Jul 10 '20 at 0:48
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    $\begingroup$ It's not missing. It's called the direct stiffness method. Problem is that for massive structures like this, it involves ridiculous matrix multiplications. $\endgroup$ – Wasabi Jul 10 '20 at 1:11
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    $\begingroup$ In the region, where I live, the standard method before the advent of computers was to apply the lower bound theorem of plasticity theory, which can make the calculation of the braces very simple, and not bother with exact solutions. Obviously, this requires appropriate choices of brace and frame members. $\endgroup$ – ingenørd Jul 10 '20 at 9:12

Many of the solution techniques are only now used because we have computers.

Trial and error was used - many buildings failed both during and after construction. Look at how churches had to have buttresses to keep the walls in place as they got bigger - did they have the maths to calculate those? Or even the theory? They did come up with empirical formulae - and stonemasons learnt the craft with those formulae - it was not information freely given.

So you have the theory and simple structures are possible by hand.

Complicated structures tend to be solved, well, preliminary estimates are calculated using simplified structures just to check the final results.

  • $\begingroup$ Thanks for the reply. Consider structures such as the empire state building or various other high-rise structures designed before 1960 (prior to when structural analysis programs became available). Some method should have been present to analyse the braced frames before construction. I am curious to see which method it is. $\endgroup$ – Amit Jul 10 '20 at 4:23
  • $\begingroup$ @Amit how did victorian engineers or designers achieve what they did? Over-engineer. $\endgroup$ – Solar Mike Jul 10 '20 at 4:50

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