2. Benchmark solution#

2.1. Calculation method#

The densities of longitudinal steels are calculated according to the Capra and Maury method, for the directions \(\text{X}\) and \(\text{Y}\) of each element and according to the 2 faces, \(\text{I}\) (Lower) and \(\text{S}\) (Upper), defined by their position according to the elementary \(\text{Z}\) normal. The transverse steel density is also calculated as described in the article entitled « Automatic calculation of the optimal reinforcement of reinforced concrete plates or shells » by Alain CAPRA and Jean-Francis MAURY.

2.2. Benchmark results#

The various results are published in the article by Capra and Maury in the form of graphs (for a quarter of a model only) are:

  • the deformation of the tank,

  • the iso-moments \(\text{Mxx}\) and \(\text{Myy}\),

  • reinforcement densities in the directions \(\text{X}\) and \(\text{Y}\) at the top and bottom.

Below is the excerpt from the article for the deformed and the moments \(\text{Mx}\), \(\text{My}\).

_images/10000000000003050000024FD8FBE987F962191D.png _images/10000000000003300000026F010E5D45883478DB.png _images/100000000000031A00000258D593EFF1DB9EC2EA.png

Below is the excerpt from the article for reinforcement densities. For better readability, colors have been associated with the various reinforcement density values.

_images/1000000000000346000002664A9CB343054D4218.png _images/10000000000003300000026834DC93C18C0CDE03.png _images/100000000000031F00000268EC12B01009F5563D.png _images/1000000000000329000002684BB849F21B2CA0F2.png

2.3. Bibliographical references#

[1] Annals of the Technical Institute of Building and Public Works N° 367 December 1978 - Series: INFORMATIQUE APPLIQUEE - Article entitled « Automatic calculation of the optimal reinforcement of reinforced concrete plates or shells » by Alain CAPRA and Jean-Francis MAURY.