# Non-linear springs, gaps (esas.09)

esas.09

Analysis of the structure with the possibility to define non-linear springs in supports or internal nodes (e.g. semi-rigid connections) and gap elements (e.g. members resisting forces only as of a certain elongation). For each degree of freedom (X, Y, Z, Rx, Ry, Rz) a nonlinear function can be inputted. The function can signify the relation between moment and rotation or force and displacement.

### Non-linear springs for supports and internal hinges

Parameters of a non-linear support can be divided into two groups:

• Stiffness - This basic stiffness is used for the initial linear calculation.
• Function - The function defines non-linear behaviour of the support. This function is taken into account during the non-linear calculation.

#### Non-linear function manager

Non-linear function that specifies the behaviour of a non-linear support can be defined in a standard SCIA Engineer database manager. The function itself consists of a positive and negative branch. The function must always pass the zero point, i.e. the zero displacement must correspond to zero force. Any "switchbacks" in the diagram are not allowed.

This means that e.g. the positive branch may rise or keep a constant force value but it is not possible to let the force go down with increasing displacement. In addition to the function itself, there is a special parameter for the positive and negative axis. Possible values of this parameter are:

• Rigid - If ON, the support is considered infinitely rigid once the limit displacement (the last input displacement value defined in the diagram) is reached.
• Free - If ON, the support is considered free once the limit displacement (the last input displacement value defined in the diagram) is reached.
• Flexible - If ON, the stiffness of the support is considered constant once the limit displacement (the last input displacement value defined in the diagram) is reached. The force value specified for the last input displacement is used.

Example of use of non-linear springs in pallet racking

### Gap elements

(e.g. elements taking normal force after an elongation of 10 mm)

There are various connection and support conditions used in a real structure. It may happen that a 1D member is not attached rigidly to the structure but "starts its action" only after some initial change of its length. The behaviour of such a beam is defined by the absolute value of the initial "slip". The beam then member starts to bear the load only after its elongation or shortening reaches the input value. There are three options available:

no tension - Modelling e.g. the instant when a 1D member bears against a support.

no compression - Modelling e.g. a free rope

free in both directions - E.g. a scaffold pipe.

The algorithm applied has been designed for large structures. All 1D members are tested and processed simultaneously in every iteration step. The procedure is iterative and converges to the accurate solution. 1D members inserted into the model may be again eliminated in a next step if their deformation gets under the input value if initial displacement ("slip"). The convergence speed is high and does not depend on the number of 1D members. Eight to ten iteration steps should be sufficient for an arbitrary structure.

When inserted into the model, a 1D member with this type of nonlinearity is marked by the following symbol (remember that in order to see the symbol, view parameters must be adjusted to show model data).

28/01/2015