For each segment, we have to find the weight of the filling between the top of the vaulting and a plane, which is parallel to the ground and whose distance from the top of the vaulting is 0.15e. In our R2 projection we will find the area between k2 and a line y = 7.8525 (7.7025 + 0.15), and multiply it by one ell and the filling density (since we divided the whole vaulting into segments of 1e width, the third parameter of the volume is area times one ell). The equation of k2 could be written as:
So the general formula for the specified area is:
where x1 and x2 are the borders of the particular segment.
If we then multiply it by one ell and the density of the filling (500 kg/e3) we obtain the weight.