3.3.7: Eccentricity on Beam and Cross Section 🔷

Fig. 3.3.7.1: Beam positioned eccentrically with respect to the connection line of its two end-nodes

Cross section forces of beam and truss elements relate to the line that connects the cross section centroids. When a cross section changes, chances are high that also the position of its centroid shifts. In case of elements predominantly loaded by bending moments, such a shift can normally be neglected. In the presence of normal forces however – e.g. when considering columns – changes in the centroid position lead to additional bending moments that may be decisive for a members cross section design.

In Karamba3D there exist two components that can be used to take care of eccentricities (see fig. 3.3.7.1): One works on beams, the other on cross sections. When both variants of definition coincide for an element, then the eccentricities get combined. This enables one to define families of cross sections of different size with e.g. the position of their upper sides at one level.

The definition of a local eccentricity for cross sections with a “Eccent-CroSec”-component is straight forward: The “EcceLoc”-input plug expects a vector that defines the offset with respect to the local beam axes. Values are in centimeters. “x” represents the longitudinal beam axis, “y” is horizontal or parallel to the global Y-axis, “z” points vertically upwards (see section 3.1.14). Cross sections with eccentricities can be stored in cross section tables using the “Generate Cross Section Table”-component and thus be made reusable in other projects.

The “Eccent-Beam”-component has one additional input-plug as compared to the cross section variant: “EcceGlo” lets one define beam eccentricities ($cm$) with respect to the global coordinate system.