1. Reference problem#

1.1. Geometry#

1.1.1. A to G models#

We consider a semi-ring of concrete, with a square cross section, with a cable in the center of the section. The half ring has a radius \(r\mathrm{=}5m\), from the center to the origin, in a \((\mathit{xy})\) plane and the half of the ring in question is \(y\) positive. A section of the ring in plane \(y\mathrm{=}0\) is given by the following two points on the diagonal \((4.5;\mathrm{0 };\mathrm{-}0.5)\) and \((5.5;\mathrm{0 };\mathrm{0,5})\) (i.e. an area of \(1m\) by \(1m\)). The cable cross section is \(\mathrm{2,5}\mathrm{\times }{10}^{\mathrm{-}3}m\).

For models A to E, the concrete modeling is solid, for models F and G, the modeling is flat.

_images/1000000000000394000001F857B568B5FD478AC2.png

Figure 1-1: view of the concrete mesh used (models A to E)

_images/1000000000000396000001F57B357D2520C0AD5B.png

Figure 1-2: view of the concrete mesh used (F and G models)

_images/100000000000031A0000015A9C4D31592E6F7161.png

Figure 1-3: view of the prestressing cable embedded in concrete

1.1.2. H modeling#

We consider a concrete beam with a length \(10m\), a square cross section of \(1m\) on a side with a cable in the center of the section. The cable cross section is \(\mathrm{2,5}\times {10}^{-3}{m}^{2}\).

_images/10000201000004020000023C2006FCC64EE967C4.png

Figure 1-4: View of the concrete mesh from the H model

1.2. Material properties#

Concrete is isotropic elastic, its properties are:

  • \(E=45000\mathit{MPa}\)

  • \(\nu =0\)

Steel is isotropic elastic, its properties are:

  • \(E=185000\mathit{MPa}\)

  • \(\nu =0\)

1.3. Boundary conditions and loads#

1.3.1. A to G models#

The section at \(y\mathrm{=}0\) and \(x<0\) of the ring is embedded (side containing ANCR2).

1.3.2. H modeling#

The face in plane \(x\mathrm{=}0\) is embedded and a pressure is exerted distributed on the lower face of the beam (\(z\mathrm{=}\mathrm{-}\mathrm{0,5}\)) with a value of \({10}^{5}\mathit{Pa}\). There is no pretension in this test.

1.4. Initial conditions#

Nil.