Beschreibung
A structure consists of I-profile simply supported beam. The axial rotation φx is restricted on the both ends but the cross-section is free to warp (fork support). The beam has an initial imperfection in Y-direction defined as a parabolic curve with maximum displacement 30 mm in the middle. Uniform loading is applied in the middle of the top flange of I-profile. Das Problem wird durch folgenden Parametersatz beschrieben. The verification example is based on the example introduced by Gensichen and Lumpe see the reference.
| Material | Steel S235 | Elastizitätsmodul | E | 210000.000 | MPa |
| Schubmodul | G | 81000.000 | MPa | ||
| Geometrie | Struktur | Länge | L | 6.000 | m |
| Imperfection | Maximum Imperfection | imax | 30.000 | mm | |
| I-Profil | Höhe | h | 400.000 | mm | |
| Breite | b | 180.000 | mm | ||
| Stegdicke | s | 10.000 | mm | ||
| Flanschdicke | t1 | 14.000 | mm | ||
| Last | Continuous Load | q | 30.000 | kN/m | |
| Exzentrizität | ez | -200.000 | mm | ||
Analytische Lösung
Eine analytische Lösung ist nicht verfügbar. Die Ergebnisse aus der Software S3D werden als Referenz herangezogen.
RFEM- und RSTAB-Einstellungen
- Modeled in RFEM 6.06 and RSTAB 9.06
- The element size is lFE= 0.010 m
- Es wird ein isotropes linear-elastisches Materialmodell vorausgesetzt.
- Die Anzahl der Inkremente beträgt 10
- Second-Order and Large Deformation Analysis are used
- Torsional Warping (7DOF) Add-on is used
- Das Problem wird sowohl durch Stäbe als auch durch eine Kombination von Stäben und Flächenelementen modelliert
- Stiffness is reduced by means of Partial Safety Factor γM=1.1
Ergebnisse
In RFEM 6 werden zwei Modellierungstechniken verwendet. At first, the I-section is modeled as a beam with given imperfection (parabolic shape). Next, the I-profile is modeled by means of surface elements (plates). In this case the boundary conditions are modeled as close as possible to the beam case, but the results can be influenced by the differencies in the modeling style. In RSTAB 9 the imperfection is modeled by means of the set of short beams with given imperfection in nodes.
RSTAB 9 results:
| Anzahl | S3D | RSTAB 9 - Second-Order Analysys | Verhältnis | RSTAB 9 - Large Deformation Analysys | Verhältnis |
| uy(x=3 m) [mm] | 24.2 | 31.041 | 1.283 | 30.182 | 1.247 |
| uz(x=3 m) [mm] | 18.8 | 16.772 | 0.892 | 22.644 | 1.204 |
| φx(x=3 m) [mrad] | 152 | 186.528 | 1.227 | 194.596 | 1.280 |
| My(x=3 m) [kNm] | 134 | 134.738 | 1.006 | 135.550 | 1.012 |
| Mz(x=3 m) [kNm] | -20.5 | -24.875 | 1.213 | -26.716 | 1.303 |
| Mω(x=3 m) [kNm2] | 4.02 | 5.053 | 1.257 | 5.276 | 1.312 |
| MTpri(x=0 m) [kNm] | 2.91 | 3.165 | 1.088 | 3.301 | 1.134 |
| MTsec(x=3 m) [kNm] | 1.78 | 2.307 | 1.296 | 2.410 | 1.354 |
RFEM 6 results:
| Anzahl | S3D | RFEM 6 - Second-Order Analysys | Verhältnis | RFEM 6 - Large Deformation Analysys | Verhältnis | RFEM 6 - Plates - Large Deformation Analysys | Verhältnis |
| uy(x=3 m) [mm] | 24.2 | 14.476 | 0.598 | 26.962 | 1.114 | 26.339 | 1.088 |
| uz(x=3 m) [mm] | 18.8 | 14.022 | 0.746 | 20.213 | 1.075 | 20.159 | 1.072 |
| φx(x=3 m) [mrad] | 152 | 86.937 | 0.572 | 175.234 | 1.153 | 172.512 | 1.135 |
| My(x=3 m) [kNm] | 134 | 133.477 | 0.996 | 132.992 | 0.992 | - | - |
| Mz(x=3 m) [kNm] | -20.5 | -17.476 | 0.852 | -23.546 | 1.149 | - | - |
| Mω(x=3 m) [kNm2] | 4.02 | 2.335 | 0.581 | 4.716 | 1.173 | - | - |
| MTpri(x=0 m) [kNm] | 2.91 | 1.490 | 0.512 | 3.002 | 1.032 | - | - |
| MTsec(x=3 m) [kNm] | 1.78 | 1.160 | 0.652 | 2.300 | 1.292 | - | - |
