Vaulting A
l = 10.2e (one ell equals 0,71m)
Rise of the central line = 2e
We will now need equations of the important curves. Let's mark the circle where b1 and c1 lie as k1, similarly circle with b, c as k, and circle with b2, c2 as k2 and put the center of the coordinate system to the point C. Then the equations are:
From now on we can consider only the right half of the vaulting, as mentioned before.
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We will divide the vaulting into five segments, each 1.02e wide. Then the equations of the border lines are: x = 0, x = 1.02, x = 2.04, x = 3.06, x = 4.08, x = 5.1. To evaluate the force acting on the vaulting, we will evaluate five basic forces, each of them acting in the middle of the segment (Fig.5). Before we proceed further, I can say that, based on preliminary calculations, the most suitable material capable to withstand the pressure of the cathedral is granite. The density of the fill is 500kg/e3 and the density of granite is approximately 960 kg/e3. The reduced superimposed load shall be minimal: let's set it at 50 kg for each segment.
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Segment |
1 |
2 |
3 |
4 |
5 |
|
88 |
156 |
296 |
516 |
832 | |
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Super. load |
50 |
50 |
50 |
50 |
50 |
|
394 |
409 |
441 |
497 |
596 | |
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Total load |
532 |
615 |
786 |
1063 |
1479 |
* All weights in all the tables are in kg and all data are rounded to nearest one, because, with regards to practice, it could not be built that accurate.
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The resultant force RP is in balance with the horizontal force H1 acting at the upper 1/3 point of the crown joint (d) and with the reactive force Ra acting at the lower 1/3 point of the impost joint (b) (see Fig. 6). |
