3.1.16: Support

Without supports a structure would have the potential to freely move around in space. This is not desirable in case of most buildings. Thus there should always be enough supports so that the structure to be calculated can not move without deforming i.e. exhibits no rigid body modes.

When defining the supports for a structure one has to bear in mind, that in three dimensional space a body has six degrees of freedom (DOFs): three translations and three rotations (see fig. 3.1.16.1). The structure must be supported in such a way that none of these is possible without invoking a reaction force at one of the supports. Otherwise Karamba3D either refuses to calculate the deflected state or renders very large displacements. Sometimes you get results from moveable structures although you should not: The reason for this lies in the limited accuracy of computer-calculations which leads to round-off errors. Sometimes one is tempted to think that if there act no forces in one direction – consider e.g. a plane truss – then there is no need for corresponding supports. That is wrong: What counts is the possibility of a displacement.

Fig. 3.1.16.1: Metaphor for the six degrees of freedom of a body in three-dimensional space

Errors in defining support conditions are easy to detect with Karamba3D: In section 3.5.6 it is shown how to calculate the eigenmodes of a structure. This kind of calculation works even in cases of moveable structures: rigid body modes – if present – correspond to the first few eigenmodes.

Fig. 3.1.16.2 shows a simply supported beam. The “Support”-component takes as input either the index or the coordinates of the point to which it applies.

Fig. 3.1.16.2: Define the position of supports by node-index or position

By default the coordinate system for defining support conditions is the global one. This can be changed by defining a plane and feeding it into the “Plane”-input plug of the “Support”-component.

Six small circles on the component indicate the type of fixation: The first three correspond to translations in global x, y and z-direction, the last stand for rotations about the global x, y and z-axis. Filled circles indicate fixation which means that the corresponding degree of freedom is zero. The state of each circle can be changed by clicking on it. The string output of the component lists node-index or nodal coordinate, an array of six binaries corresponding to its six degrees of freedom and the number of load-case to which it applies. Supports apply to all load cases by default.

Supports cause reaction forces. These can be visualized by activating “Reactions” in the “Display Scales” section of the “ModelView”-component (see section 3.6.1). They show as arrows with numbers in green – representing forces – and purple – representing moments. The numbers either mean$kN$in case of forces or $kNm$ when depicting moments. The orientation of the moment arrows corresponds to the screw-driver convention: They rotate about the axis of the arrow anti-clockwise when looked at in such a way that the arrow head points towards the observer. (See fig. 6.17 in [12] for an unforgettable way of remembering the right-hand rule of rotation.).

From the support-conditions in fig. 3.1.16.2 one can see that the structure is a simply supported beam: green arrows symbolize locked displacements in the corresponding direction. The translational movements of the left node are completely fixed. At the right side two supports in y- and z-direction block rotations about the global y- and z-axis. The only degree of freedom left is rotation of the beam about its longitudinal axis. Therefore it has to be blocked at one of the nodes. In this case it is the left node where a purple circle indicates the rotational support.

Fig. 3.1.16.3: Influence of support conditions – undeformed and deflected geometry

The displacement boundary conditions may influence the structural response significantly. Fig. 3.1.16.3 shows an example for this: Left: All translations fixed at supports, Right: One support moveable in horizontal direction. When calculating e.g. the deflection of a chair, support its legs in such a way that no excessive constraints exist in horizontal direction – otherwise you underestimate its deformation. The more supports one applies the stiffer the structure and the smaller the deflection under given loads. In order to arrive at realistic results introduce supports only when they reliably exist.

By default the size of the support symbols is set to approximately $1.5m$. The slider with the heading “Support” on the “ModelView”-component lets you scale the size of the support symbols. Double click on the knob of the slider in order to set the value range.