Description
A thin-walled cantilever of QRO-profile is fully fixed on the left end (x=0), and the warping is free. The cantilever is subjected to a torque M at x=L1. The problem is described by the following set of parameters. Small deformations are considered and the self-weight is neglected. Determine the maximum rotation φx,max and control the values of the primary torsional moment MTpri, secondary torsional moment MTsec and warping moment Mω at the point x=L1. The verification example is based on the example introduced by Gensichen and Lumpe (see the reference).
| Material | Steel | Modulus of Elasticity | E | 210000.000 | MPa |
| Shear Modulus | G | 81000.000 | MPa | ||
| Geometry | QRO Cantilever | Length | L | 4.000 | m |
| Width and Height | b | 200.000 | mm | ||
| Wall Thickness | t | 6.000 | mm | ||
| Load | Torque | M | 80.000 | kNm | |
| Position | L1 | 2.800 | m | ||
Analytical Solution
The maximum rotation about the x-axis φx,max occurs at the point x=L1 and it has the same value to the free end.
For this thin-walled profile (radii in the corners are neglected) is the warping constant Cω=0. Thus the moments MTsec and Mω should be zero on the full length of the profile. The primary torsional moment MTpri should be coincident with the total torsional moment MT=M.
RFEM and RSTAB Settings
- Modeled in RFEM 5.05, RSTAB 8.05 and RFEM 6.01, RSTAB 9.01
- The element size is lFE= 0.200 m
- The number of increments is 5
- Isotropic linear elastic material model is used
- The structure is modeled using members
- Second-Order Analysis is used
- RF-FE-LTB and FE-LTB module is used in RFEM 5 and RSTAB 8
- Torsional Warping and Steel Design add-on is used in RFEM 6 and
Results
| Analytical Solution | RFEM 6 | Ratio | RSTAB 9 | Ratio | |
| φx,max [rad] | 0.063 | 0.063 | 1.000 | 0.063 | 1.000 |
| Analytical Solution | RFEM 5 - RF-FE-LTB | Ratio | RSTAB 8 - FE-LTB | Ratio | |
| φx,max [rad] | 0.063 | 0.063 | 1.000 | 0.063 | 1.000 |
In the following graphs there is demonstrated the behaviour of all the moments on the given cantilever calculated in RF-FE-LTB or FE-LTB module. The primary torsional moment MTpri should be coincident with the total torsional moment MT. The moments MTsec and Mω should be zero on the full length of the profile. It can be seen there is the affected area in the nearby of the loading point x=L1, when the warping is considered. Note that the above mentioned effect is getting smaller with the smoother mesh.
The same task is also solved in RFEM 6 and RSTAB 9 with Torsional Warping Add-on. The results are shown in following graphs. It can be seen in RFEM 6 and RSTAB 9 results, there is no computational error due to the discretization.
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