3.1.15: Support

Without supports, a structure would have the potential to move freely in space. This is undesirable for most buildings. Therefore, it is essential to have enough supports so that the structure cannot move without deforming, i.e., exhibits no rigid body modes.

When defining supports for a structure, remember that in three-dimensional space, a body has six degrees of freedom (DOFs): three translations and three rotations (see Fig. 3.1.15.1). The structure must be supported in such a way that none of these DOFs are 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, results are obtained from movable structures due to the limited accuracy of computer calculations, which leads to round-off errors. It is a misconception to think that if there are no forces in one direction (e.g., in a plane truss), there is no need for corresponding supports. The possibility of displacement is what matters.

Errors in defining support conditions are easy to detect with Karamba3D. Section 3.6.6 shows how to calculate the eigenmodes of a structure. This type of calculation works even for movable structures: rigid body modes, if present, correspond to the first few eigenmodes.

Fig. 3.1.15.2 shows a simply supported beam. The “Support”-component takes as input either the index or the coordinates of the point to which it applies.

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 the global x, y, and z directions, and the last three correspond to rotations about the global x, y, and z axes. Filled circles indicate fixation, meaning that the corresponding degree of freedom is zero. The state of each circle can be changed by clicking on it. In addition to the radio buttons, the supported degrees of freedom can also be specified parametrically using the “Dofs” input plug. It expects a list of integer values where the numbers '0' to '5' stand for Tx to Rx. Right-click on the component and select “Expand ValueLists” to get a ValueList component, as shown in Fig. 3.1.15.2.

The string output of the component lists the node index or nodal coordinate, an array of six binaries corresponding to its six degrees of freedom, and the number of load cases 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 3.7.1.1). They appear 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: The orientation of the moment arrows follows the screw-driver convention: they rotate about the axis of the arrow counterclockwise when viewed such that the arrowhead points toward the observer.

From the support conditions in Fig. 3.1.15.2, 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. On the right side, two supports in the y- and z-directions block rotations about the global y- and z-axes. The only degree of freedom left is the rotation of the beam about its longitudinal axis, which is blocked at one of the nodes. In this case, it is the left node where a purple circle indicates the rotational support.

The displacement boundary conditions can significantly influence the structural response. Fig. 3.1.15.3 shows an example of this: on the left, all translations are fixed at supports; on the right, one support is movable in the horizontal direction. When calculating the deflection of a chair, support its legs in such a way that no excessive constraints exist in the horizontal direction; otherwise, you underestimate its deformation. The more supports applied, the stiffer the structure and the smaller the deflection under given loads. To achieve 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.