Description
The structure consists of a simply supported I-profile beam. The axial rotation φx is restricted on both ends, but the cross-section is free to warp (fork support). The beam has an initial imperfection in the 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 the I-profile. The problem is described by the following set of parameters. The verification example is based on the example introduced by Gensichen and Lumpe (see the reference).
| Material | Steel S235 | Modulus of Elasticity | E | 210000.000 | MPa |
| Shear Modulus | G | 81000.000 | MPa | ||
| Geometry | Structure | Length | L | 6.000 | m |
| Imperfection | Maximum Imperfection | imax | 30.000 | mm | |
| I-profile | Height | h | 400.000 | mm | |
| Width | b | 180.000 | mm | ||
| Web Thickness | s | 10.000 | mm | ||
| Flange Thickness | t1 | 14.000 | mm | ||
| Load | Continuous Load | q | 30.000 | kN/m | |
| Eccentricity | ez | -200.000 | mm | ||
Analytical Solution
An analytical solution is not available. The results from the S3D software are taken as reference.
RFEM and RSTAB Settings
- Modeled in RFEM 6.06 and RSTAB 9.06
- The element size is lFE= 0.010 m
- Isotropic linear elastic material model is used
- The number of increments is 10
- Second-Order and Large Deformation Analysis are used
- Torsional Warping (7DOF) add-on is used
- The problem is modeled both by members and by a combination of members and surface elements
- Stiffness is reduced by means of the Partial Safety Factor γM=1.1
Results
Two modeling techniques are used in RFEM 6. First, the I-section is modeled as a beam with the 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 closely as possible to the beam case, but the results can be influenced by the differences in the modeling style. In RSTAB 9 the imperfection is modeled by means of the set of short beams with the given node imperfections.
RSTAB 9 results:
| Quantity | S3D | RSTAB 9 - Second-Order Analysis | Ratio | RSTAB 9 - Large Deformation Analysis | Ratio |
| 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=0 m) [kNm] | 1.78 | 2.307 | 1.296 | 2.410 | 1.354 |
RFEM 6 results:
| Quantity | S3D | RFEM 6 - Second-Order Analysis | Ratio | RFEM 6 - Large Deformation Analysis | Ratio | RFEM 6 - Plates - Large Deformation Analysis | Ratio |
| 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=0 m) [kNm] | 1.78 | 1.160 | 0.652 | 2.300 | 1.292 | - | - |
