# 3.5.8: Optimize Cross Section 🔷

Use the **“Optimize Cross Section”**-component for the automatic selection of the most appropriate cross sections for beams and shells. It takes into account the cross sections load bearing capacity and optionally limits the maximum deflection of the structure.

First the **“OptiCroSec”**-component determines the cross section of each element in such a way that their load-bearing capacity is sufficient for all load-cases. In order to achieve this, Karamba3D uses the following procedure:

Determination of section forces at

**“nSamples”**points along all beams using the initial cross section.For each element or given set of elements: selection of the first sufficient entry from the family to which each cross section belongs.

If no changes were necessary in step two or the maximum number of design iterations is reached, the algorithm stops. Otherwise it returns to step one using the cross sections selected in step two.

In statically indeterminate structures the section forces depend on the stiffness (i.e. cross section and materials) of the members. This necessitates the iterative procedure described above.

In fig. 3.5.8.1 one can see the example of a cantilever idealized with shell elements: The optimization results in thicker shell elements at the top and bottom edge of the built-in side. The **“CroSecs”**-input of the **“OptiCroSec”**-component consists of a family of constant shell cross sections.

For shells the mechanical utilization is calculated as the maximum Von Mises stress in a point divided by the material strength. For cross section optimization of shells the same procedure applies as for beams. Starting with the first item of a cross section family the algorithm tests all members and stops when a cross section is encountered for which the utilization is less than a pre-set value which is 1 by default. This corresponds to 100 %.

After ensuring safety against structural failure a second, optional step follows where Karamba3D tries to reach a user supplied maximum deflection. Behind the scenes Karamba3D iteratively adapts temporarily the strength of the materials. This may lead to uneconomic results in case of structures where the maximum displacement occurs in a small region, whereas the rest of the structure shows a much smaller deformation. In order that the iterative adaption for the maximum displacement works, the number of design iterations should be chosen appropriately – five is normally sufficient.

When the given loads surpass the load bearing capacity of the biggest cross section available in a cross section family, Karamba3D issues a warning via the **“Info”** output-plug (see fig. 3.5.8.2).

There is no guarantee, that the iteration procedure for finding the optimal cross sections eventually converges. One can check the results via the **“Utilization of Elements”**-component. It applies the same procedure as the **“OptiCroSec”**-component for assessing elements according to Eurocode 3 [5] and considers the load-bearing capacity of the whole cross section. The utilization-output of the **“ModelView”**-component only shows the ratio between the stress in a point of a cross section and the material strength there. Effects like buckling under compression are not considered. This is why the utilization as displayed by the **“ModelView”**-component may deviate from the results of the **“Utilization of Elements”**-component.

Due to the lower-bound theorem of plasticity, the structure will be sufficient for the given loads at any iteration step – although some elements may show over-utilization – provided that the material is sufficiently plastic (like e.g. steel). With increasing number of iterations the structural system tends to become more and more statically determinate.

The profile selection procedure assumes that the cross sections of a family are ordered: starting with your most favorite and descending to the least desired cross section. In the cross section table “CrossSectionValues.bin” that comes with Karamba3D all family members are ranked according to their height. The cross section with the smallest height comes first, the one with the largest height last. When using the cross section area as sorting criteria, structures of minimum weight (and thus approximately cost) result. See section 3.3.12 for how to switch between minimum height and minimum weight design. Ordering the profiles by area may lead to structures where the cross section heights vary significantly from one beam to the next.

The design procedure applied in Karamba3D takes lateral torsional buckling into account. An element's lateral torsional buckling length is calculated in the same way as for conventional buckling. The buckling length for lateral torsional buckling can be set manually via the property **“BklLenLT”** of the **“Modify Beam”**-component.

In the course of cross section optimization Karamba3D checks the cross sections for local buckling and issues a warning if necessary. The check for local buckling uses the classification of cross sections into classes 1 to 4 according to EN 1993-1-1. Class 4 cross sections are susceptible to local buckling.

The **"OptiCroSec"**-component provides the following set of input-plugs:

In order to see all input-plugs click on the **“Settings”**-button to unfold the rest of the component:

On the output side the **“Model”**-plug renders the structure with optimized cross sections. Check the **“Info”**-plug in order to see whether any problems occurred during optimization. The **“Mass”**-output informs you about the overall mass of the optimized structure. **“Disp”**- and **“Energy”**-plugs return the maximum displacement and internal energy of the structure after the last cross section design iteration.

The aim of the design procedure applied in Karamba3D is to render plausible cross section choices. Be aware that it builds upon assumptions like the correct determination of buckling lengths.

Last updated