*Practitioners' Guide to Finite Element Modelling of Reinforced Concrete Structures*contains a design example of a deep concrete beam with opening. The example is used in that report to demonstrate the "Strut-and-Tie" method that Thomas and Bernd discussed in an earlier post (https://forum.freecadweb.org/viewtopic. ... 35#p232799). I will use it here to compare/validate the method I coded in FreeCAD (https://forum.freecadweb.org/viewtopic.php?f=18&t=28821).

For reasons of copyright I cannot cut and past information from the aforementioned report, but will discuss the problem using the FreeCAD model:

The beam dimensions are 11x4x0.6m and it is loaded at the top by a distributed load of 120kN/m and a load of 5000kN introduced by a 1m wide column.

The factored compressive strength of the concrete is 0.75 x 0.6 x fc = 0.45 * 35 = 15.8MPa and the factored yield strength of the reinforcement steel is 315MPa.

The reinforcement ratios and principal concrete stresses (compression only) derived with FreeCAD are shown below:

The required horizontal reinforcement (below in red) is determined by integration of the horizontal reinforcement ratio over the vertical cuts of interest (below in black). This is done using a Paraview integration filter.

The insert to the above figure shows a comparison of reinforcement requirements (in mm^2 of steel) determined with FreeCAD to those in the FIB report.

In general the two sets of result are in good agreement, except at the corners of the opening, where FreeCAD requires double the amount of reinforcement. As theoretical stresses at sharp corners are infinite, the result will be sensitive to modelling assumptions. Interestingly, this is not discussed or considered in the FIB report. Rounding of the corners in the model would stabilise the result.

Anyway, the FreeCAD approach holds promise and I will work on making it available in my Github repository

I will compare the vertical reinforcement ratio in a future post