How to calculate bending moment for continuous beam?
Answers
If the spans are equal and the loading is symmetric, use any Structural Steel Manual or Civil Engineering Handbook which lists formulas for the support moments and mid span moments for standard loads like UDL and point loads. First find the loads for UDL and then for each point load and superpose the results.
If the spans are unequal, and the loads are non symmetrical, you have to do an analysis.
We used Moment Distribution and slope deflections and the Clapyeron’s three moment theorems to find them whichever was convenient. Nowadays you can simply call up a spreadsheet or some beam analysis package and plug in your data and get your results instantly. Probably there may even be a mobile phone app for this. Please inquire.
Many times in my career, I needed a quick approximate answer just to decide if a particular beam size would be okay or not without needing to actually know the value of the moment.
I would make an intelligent guess.
I know WL/8 (mid span moment in a simply supported beam) is too high.
I know that WL/12(fixed end moments) would be too low.
So consider WL/10 and proceed. You won’t be too far off from the correct value.
(W=total load on one span, L= the particular span being considered)
Hope this is useful.