A.2.3: Tips for Designing Statically Feasible Structures

Karamba3D can be used to analyze structures of any scale. When using the "Analyze" component to assess structural behavior, two important assumptions are made:

1. Small Deflections: The deflections are small compared to the size of the structure.

2. Linear Elastic Behavior: Materials behave in a linear elastic manner, meaning that an increase in deformation corresponds proportionally to an increase in load.

In reality, materials deviate from this ideal behavior, weakening and eventually failing.

For structures experiencing large deflections - where the change of axial forces due to transverse displacements needs to be taken into account, you must increment the load in steps and update the geometry after each step. This can be done using the "Large Deformation Analysis" component (see section 3.5.4) or the "AnalyzeNonlin WIP" component for geometrically non-linear analysis (see section 3.5.3).

Fig. A.4.3.1: Simply supported beam

For typical engineering structures, these initial assumptions are sufficient for a preliminary design. To determine meaningful cross-section dimensions, limit the maximum deflection of the structure. Figure A.4.3.1 shows a simply supported beam with maximum deflection δ under a single midspan load. As a general guideline, deflection should be limited so that it does not cause discomfort to building occupants. A rough rule of thumb is to limit deflection to L/250, where L is the span length. For cantilever structures, L/125 is often acceptable. Increasing cross-section size, particularly its height, is an efficient way to reduce deflection, especially when bending dominates (see section 3.1.10).

When checking deflection, ensure that all significant loads (e.g., dead weight, live load, wind) are considered. For a preliminary design, it is often sufficient to apply a multiple of the dead weight (e.g., by using a factor of 1.5). In Karamba3D, this can be done by setting the gravity vector length to 1.5.

In structures dominated by bending, large deflections typically precede collapse, as seen in the famous Tacoma-Narrows bridge collapse. Thus, limiting deflection can lead to a safer design, especially for slender structures. However, if failure is driven by compressive forces, collapse may occur suddenly without significant prior deformation, a phenomenon known as buckling.

For buckling analysis, use the "AnalyzeThII" component, which accounts for the destabilizing effects of compressive axial forces. The "Buckling Modes" component can be used to calculate the first buckling load factor, which indicates the factor by which external loads must be multiplied to trigger linear buckling.