# 3.4.1: Beam-Joints π·

A structure usually consists of a large number of load bearing elements that need to be joined together. When rigidly connected, such a joint has to transfer three section forces (one axial force, two shear forces) and three moments (one torsional and two bending moments). Depending on the type of material such full connections are sometimes (e.g. for wood) hard to achieve, costly and bulky. A solution to this problem consists in introducing hinges.

Fig. 3.4.1.1 shows a beam under dead weight with fully fixed boundary conditions at both end-points. At the right end the joint (which is in fact no joint any more) completely dissociates the beam from the support there. The result is a cantilever.

The symbols for joints resemble that for supports: pink arrows represent translational joints, white circles symbolize moment hinges. In Karamba3D joints are realized by inserting a spring between the endpoint of a beam and the node to which it connects. This necessitates sufficient support conditions at the actual nodes to prevent them from freely moving around. See for example the right node in fig. 3.4.1.1 which has to be fully fixed β otherwise the system would be kinematic.

The βBeam-Jointβ-component allows to define hinges at a beamβs starting- and end-node. A list of beam-identifiers lets you select the beams where the joint definition shall apply. Filled circles mean that the corresponding degrees of freedom represent joints. βTβ stands for translation, βRβ for rotation. Feed the resulting cross-section into the βJointβ-plug of the βAssembleβ-component. The orientation of the axes of the joints corresponds to the local coordinate system of the beam they apply to.

Sometimes the stiffness of connections lies between fully fixed and zero. With the input-plugs βCt-startβ and βCr-startβ it is possible to set the stiffness of the hinge in translation $(kN/m)$ and rotation$(kNm/rad)$ respectively at the start of the element. βCt-endβ and βCr-endβ provide the same functionality for the end-point.

In order to make the definition of hinges accessible to optimization the input-plugs βDofs-startβ and βDofs-endβ can be used to set hinges at the beams endpoints with a list of numbers. Integers in the range from 0 to 5 signify degrees of freedom to be released in addition to those specified manually with the radio-buttons.

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