A.2.3: Tips for Designing Statically Feasible Structures

Karamba3D can be used to analyze the response of structures of any scale. When using the “Analyze”- component for assessing the structural behavior be aware of two preconditions: First, deflections are small as compared to the size of the structure. Second, materials do behave in a linear elastic manner – i.e. a certain increase of deformation is always coupled to the same increase of load. Real materials behave differently: they weaken at some point and break eventually.

Table A.2.3.1: Specific weights of some building materials

Table A.2.3.2: Loads for typical scenarios

If you want to calculate structures with large deflections you have to increase the load in several steps and update the deflected geometry. This can be done with the “Large Deformation Analysis”- component (see section 3.5.4) or the component for geometrically non-linear analysis “AnalyzeNonlin WIP” (see section 3.5.3).

For typical engineering structures the assumptions mentioned above suffice for an initial design. In order to get meaningful cross section dimensions limit the maximum deflection of the structure. Fig. A.4.3.1 shows a simply supported beam of length L with maximum deflection $∆$ under a single force at midspan. The maximum deflection of a building should be such that people using it do not start to feel uneasy. As a rough rule of thumb try to limit it to $∆ \leq L/300$ . If your structure is more like a cantilever $∆ \leq L/150$ will do. This can normally be achieved by increasing the size of the cross-sections. If deflection is dominated by bending (like in fig. A.4.3.1) it is much more efficient to increase the height of the cross-section than its area (see section 3.1.10). Make sure to include all significant loads (dead weight, live load, wind, . . . ) when checking the allowable maximum deflection. For a first design however it will be sufficient to take a multiple of the dead-weight (e.g. with a factor of 1.5). This can be done in Karamba3D by giving the vector of gravity a length of 1.5.

In case of structures dominated by bending, collapse is normally preceded by large deflections (see for example the video of the collapse of the Tacoma-Narrows bridge). So limiting deflection automatically leads to a safe design in case of slender structures. If however compressive forces initiate failure, collapse may occur without prior warning. The phenomenon is called buckling. When using the “Analyze”-component it makes no difference whether an axially loaded beam resists compressive or tensile loads: it either gets longer or shorter and the absolute value of its change of length is the same. In real structures the more slender a beam the less compressive force it takes to buckle it. An extreme example would be a rope. In case buckling might occur, use the “AnalyzeThII”-component which takes into account the destabilizing effect of compressive axial forces. The “Buckling Modes”-component lets you compute the first buckling load-factor. This is the factor with which the external loads need to be multiplied for initiating linear buckling.

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Table A.2.3.2: Loads for typical scenarios

∆

under a single force at midspan. The maximum deflection of a building should be such that people using it do not start to feel uneasy. As a rough rule of thumb try to limit it to

∆ \leq L/300

. If your structure is more like a cantilever

∆ \leq L/150

will do. This can normally be achieved by increasing the size of the cross-sections. If deflection is dominated by bending (like in fig. A.4.3.1) it is much more efficient to increase the height of the cross-section than its area (see section 3.1.10). Make sure to include all significant loads (dead weight, live load, wind, . . . ) when checking the allowable maximum deflection. For a first design however it will be sufficient to take a multiple of the dead-weight (e.g. with a factor of 1.5). This can be done in Karamba3D by giving the vector of gravity a length of 1.5.