How reliable are the results of this General Matrix?
Becuase is a math model derived from the general integration method the results should be exact. To demonstrate this I decided run a model on AutoCAD Mechanical and compare it's results with the ones obtained from the General Matrix. I decided to use AutoCAD Mechanical because it's solution algorithm is based on a matrixial method for solving structures, which by the way is a highly trusted method employed extensively by civil engineers.
I desided to evaluate a short "I" beam of 1 meter of length, using 10 supports equally spaced, loaded with a equally distributed load of 75 N/mm [75 kN/m] all over its length as shown in the screen-cap below. (you can also download a copy of this CAD file here).
The results of maximum stress and deflections are shown in the big blue box in the left. But right now we are interested only in the reactions. Each one appear below its respective support, as you can see in the figure below.
Now, loading the same specifications of the beam modeled in the General Matrix (download file here), as you see in the next screen-cap:
The Answer would be obtained in the page n10, because we are modeling 10 supports equally spaced.
In the last picture you can notice two matrices. The upper matrix is the General Matrix formulation that represents the geometry, next to it there is a vector which are the elements that represents the load. The matrix below is the inverse of the general Matrix and next to it we have the results computed. They are amplified in the picture below:
By comparing this results with the ones obtained in AutoCAD it is possible to notice that there is no difference in the results withing the first 8 digits.
As a conclusion:
The General Matrix is a reliable method for solving Indeterminate beams reactions.
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