# 3.3.3: Spring Cross Sections

Springs allow you to directly define the stiffness relation between two nodes via spring constants. Each node has six degrees of freedom (DOFs): three translations and three rotations. Using the **“Cross Sections”** multi-component with **“Cross Section”** set to **“Spring”** lets one couple these DOFs by means of six spring-constants. A relative movement $$u\_{i,rel}$$ between two nodes thus leads to a spring force $$F\_i = c\_i \cdot u\_{i,rel}$$. In this equation $$u\_{i,rel}$$ stands for a relative translation or rotation in any of the three possible directions x, y, z, $$c\_i$$ is the spring stiffness. In Karamba3D the latter has the meaning of kilo Newton per meter $$kN/m$$ in case of translations and kilo Newton meter per radiant $$kNm/rad$$ in case of rotations. The input-plugs **“Ct”** and **“Cr”** expect to receive vectors with translational and rotational stiffness constants respectively. Their orientation corresponds to the local beam coordinate system to which they apply. In case of zero-length springs this defaults to the global coordinate system but can be changed with the **“OrientateBeam”**-component.

In case one wants to realize a rigid connection between two nodes the question arises as to which spring stiffness should be selected. A value too high makes the global stiffness matrix badly conditioned and can lead to a numerically singular stiffness matrix. A value too low results in unwanted relative displacements. So you have to find out by trial and error which value gives acceptable results.

![Figure 3.3.3.1: Spring fixed at one end and loaded by a point load on the other](https://1646753513-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M9XteyGDAU3Odla53cC%2Fsync%2Fb0d9bf317b1daf09ea1ed2d99f840d2be2d387be.png?generation=1591871199076581\&alt=media)

Fig. 3.3.3.1 shows a peculiarity one has to take into account when using springs: They are unaware of the relative position of their endpoints. This is why the load on the right end of the spring does not evoke a moment at the left, fixed end of the spring.