In the serviceability limit state, deformations are primarily analyzed and compared with allowable limit deformations. To comply with the allowable limit deformations, the member cross-sections must be dimensioned accordingly. For this purpose, RFEM 6 and RSTAB 9 offer an automated function for cross-section optimization, which is explained in this article.
Areas of application
The cross-section optimization in the serviceability limit state is available as a function for the following add-ons:
- Steel design
- Timber design
- Aluminum design
All design standards available in the program are supported.
Input in the program
In the table, switch to the Input Data → Cross-sections tab of the respective design add-on. In the "Use other cross-section for optimization" column, select the "Optimize" option for all cross-sections you want to optimize.
You can now start the design. The most economical cross-section is automatically determined. After completing the design, you can check the optimized cross-sections and, if necessary, import them directly into the model.
Functionality
The cross-section optimization in the serviceability limit state is performed iteratively, as is also the case for the ultimate limit state. With the existing internal forces and deformations from the structural analysis, the design checks are performed. If checks are exceeded, the cross-section is enlarged. If, instead, all checks are not fully utilized, the cross-section is reduced. The internal forces and deformations are not recalculated, so this method provides an approximate solution, especially for nonlinear systems. However, this is generally sufficient for pre-dimensioning. In the serviceability limit state, there is the particularity that the cross-section properties are not directly included in the design formulas, since only existing deformations are compared with allowable deformations. To solve this problem, a factor alpha is introduced into the design formulas, which represents the ratio of the moment of inertia of the optimized cross-section to the moment of inertia of the original cross-section. The design check utilization is ultimately multiplied by this factor.
The factor alpha is calculated for the general case (deformation analysis in the resulting axis) as follows.
For the deformation analysis in the local axis direction, the expression is simplified to:
Special features
The cross-section optimization in the serviceability limit state is linked to two conditions. If one of these conditions is not met, no optimization is performed for the relevant members or checks. The conditions are as follows:
- Displacement reference "Deformed segment ends" selected
The displacement reference "Undeformed system" is not accepted for a cross-section optimization. The reason for this is that, for example, in multi-story buildings, the total deformation of a member is primarily determined by the global building inclination. Enlarging a single cross-section has a subordinate influence on this deformation, which is why optimization in this case would often lead to nonsensical results.
- No cross-section camber
Members with defined camber are excluded from the cross-section optimization.
