1. Reference problem#
1.1. Material properties#
The material properties and the characteristics specific to the RCC -M calculation are as follows:
Young’s modulus: \(E\mathrm{=}2.E+05\mathit{MPa}\);
material constants for the calculation of \(\mathrm{Ke}\): \(n=0.2\), \(m=\mathrm{2 }\);
Young’s modulus of reference: \({E}_{\mathit{REFE}}\mathrm{=}2.E+05\mathit{MPa}\);
allowable stress: \(\mathit{Sm}=2000\mathit{MPa}\).
The Wöhler curve is defined analytically: \({N}_{\mathrm{adm}}=\frac{{5.10}^{5}}{{S}_{\mathrm{alt}}}\)
1.2. Evolution of constraints#
The constraints on the analysis segment are not calculated but read directly from a table. The only non-zero component of the stress tensor is \({\sigma }_{\mathrm{yy}}\). Two situations are considered. These situations do not aim to represent a specific real transient, but to cover all possible constraints (constant, linear or non-linear evolution of the stress in thickness).
Instant |
Thermal constraints |
Stress due to pressure |
**Thermal stresses+pressure |
||||||
Abscissor |
Abscissor |
Abscissor |
|||||||
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
|
1, 5 |
90 |
100 |
110 |
90 |
100 |
110 |
180 |
200 |
220 |
2, 5 |
0 |
100 |
0 |
0 |
100 |
0 |
0 |
200 |
0 |
3, 5 |
100 |
-50 |
-100 |
100 |
-50 |
-100 |
200 |
-100 |
-200 |
4, 5 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Table 1.2-1 : Definition of constraints \({\mathrm{\sigma }}_{\mathit{yy}}\) (in \(\mathit{MPa}\)) for the moments of situation 1 as a function of the curvilinear abscissa
Instant |
Thermal constraints |
Stress due to pressure |
**Thermal stresses+pressure |
||||||
Abscissor |
Abscissor |
Abscissor |
|||||||
0 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
2 |
|
1 |
90 |
100 |
90 |
0 |
0 |
0 |
90 |
100 |
90 |
2 |
0 |
100 |
0 |
0 |
0 |
0 |
0 |
100 |
0 |
3 |
100 |
-50 |
-100 |
0 |
0 |
0 |
100 |
-50 |
-100 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Table 1.2-2: Definition of the constraints \({\mathrm{\sigma }}_{\mathit{yy}}\) (in \(\mathit{MPa}\)) for the moments of situation 2 as a function of the curvilinear abscissa
In ZE200, the moments are defined according to two twists (in ze200a, the pressure also)
\({P}_{A}\) |
|
|
|
|
|
|
|
|||
Situation 1 |
201 |
1 |
21 |
21 |
0 |
0 |
1 |
0 |
0 |
|
Situation 2 |
0 |
0 |
0 |
1 |
0 |
0 |
61 |
0 |
0 |
Table 1.2-3: Definition of torsors on moments (in N.mm) and pressure (in MPa) for situations 1 and 2
In ZE200, the characteristics of the pipe (thickness, radius, moment of inertia) are necessary to calculate the quantities, as are the stress indices. In this example, we select*arbitrarily select*
\(e=1\mathit{mm}\)
\(R=\mathrm{0,5}\mathit{mm}\)
\(I=1{m}^{4}\)
\({K}_{1}=1\) and \({C}_{1}=1\)
\({K}_{2}=1\) and \({C}_{2}=2\)
\({K}_{3}=1\) and \({C}_{3}=1\)
\({M}_{\mathit{xS}}\) |
|
|
21 |
0 |
0 |
Table 1.2-4: Definition of torsors on moments (in N.mm) for the earthquake