Eliza Guse has send me a pdf with information about this equation. In the next text I will try to tell how I interpret the formula
The equation of Émile Clapeyron.
This equation gives the moments that are introduced in the support points. In that case the load can be seen as just a load on a beam from point to point. Every part can in this way been seen as a loose part.
ln Line with a certain length
An Area under the line of moment
xn Distance from Point Pn on the line ln
Every beam length now has influence from a moment on every side and as well a load on the beam. This means the following for line ln:
Moment in point Pn
Moment in point Pn+1
Moment because of the q load
As I see it now I can calculate of give a formula for a prescription of the moment on the side points of a line. Then also the moment because of the q load can be calculated of prescribed. The total line of moment is the sum of all the graphs of the moments.
From the total moment graph it would be possible to calculate the total displacement per point. Further it would also be possible to use the same method as used in the bridge where the height and the width become variables.
For a simple situation, with equally divided load, the same EI everywhere, where a beam is supported in three places and where both the end points are supported this means the following:
(simplified because An = qln and because EI is the same everywhere.)
(in the middle point of the line and 3/4 Mln,max on the quarter parts of the line, because of the parabolic form)
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