THE PRACTICAL APPLICATION OF CABLES IN ROBOT

Cable elements in ROBOT are members that can only carry tension and their sole stiffness comes from their axial rigidity. They differ from tension only members since tension members can also have flexural rigidity and can be pin ended.

Modelling with cable elements:

In ROBOT cable elements can be used with 2d frames, 3d frames and shell models. As soon as a cable member is input, a non-linear analysis type is chosen automatically, where the load is applied in increments (see later description). It is usually not necessary to input cables as a chain of elements, since ROBOT cables are “explicitly integrated” which means that cable forces and movements are calculated across an element and therefore give a precise solution.

Cable elements are, by their very nature, pin ended. This means that if a cable is supported it must be restrained in rotation as well as movement – this is analogous to a pin ended member support, where the supported node must be “clamped” to a support. Also, if cables are connected to each other, a rotational support must also be applied. However, if a cable end is connected to an unreleased bar, then a support is not necessary since the bar is “clamped” to the node.

Input parameters:

As discussed, a cable attains its stiffness solely from its axial rigidity, so material properties and area are all the data that is required. In terms of prestress there are 2 methods:

a)  Input of force or stress. When either of these are defined, the program attempts to find a solution under the assembly load case (usually the first case and usually self weight) so that the requested forces appear in the cables AFTER analysis. So, in this way, the program calculates a deformed geometry and necessary cables’ lengths to satisfy the required loading regime. It can easily be seen that the loads applied as prestress or force must be very close to equilibrium, or convergence cannot occur. This method is useful, however, if the forces in cables have been measured on site. The above mentioned procedure is used for assembly load case to find necessary cables’ lengths (“regulations”). After this step each cable length is fixed with its “regulation” and all consecutive load cases are calculated with these fixed lengths (although, of course, the cables are elastic and the cable lengths will change under the applied load).

b)  Input of length, dilatation or relative dilatation. The length input refers to the cable length before installation, the dilatation to increase in length compared to the length in the model (negative causes tension, positive in cables can also give tension due to tension occurring due to self weight). Relative dilatation refers to the increase in length divided by the total length, and is therefore equivalent to strain (negative is tension). If any of these values are input ROBOT will calculate the structure (the deformed geometry and cable forces) under the subsequent loads and assembly loads. It is often easy to achieve better convergence using this approach than in a). All consecutive load cases (after assembly load case) are calculated with the same cable lengths (defined with length, dilatation or relative dilatation) as the assembly load case.

As it can be seen from the description above the difference between 2 approaches occurs only for assembling load case:

·  in case b) user defines cable lengths and the structure assembling loads and the program calculates corresponding forces in cables and other results (displacements, forces in other bar or surface elements, etc.),

·  in case a) user defines demanded forces in cables and the structure assembling loads and the program calculates corresponding (fulfilling equilibrium conditions) cable lengths and other results

Loading:

Any bar load type may be applied except concentrated or distributed moment. All load combinations are input as loads, since superposition does not apply to non-linear solutions.

Solution:

There are several types of non-linear formulation.

(i)  only the non-linearity of non-linear elements (here cables but it can be also tension or compression only members, unidirectional supports – with uplift or unidirectional releases)

(ii)  Non Linear – this includes the stress stiffening effects (first order non-linear effects)

(iii)  Pdelta – includes large displacement effects (second order non-linear effects – updating structure stiffness according to structure’s deformation). It is not recommended to use Pdelta without non-linear, since it is meaningless.

As a default, ROBOT assumes non linear behaviour for the cables. Non linear for other members in the model and also Pdelta analysis may also be included to the Users requirements.

There are also options to set different types of non-linear solution. The 3 options are described:

1/ BFGS – where the stiffness matrix is updated after each load step and BFGS corrections are applied. This is a default method because of the optimum balance between speed and robustness for most of cases.

2/ Modified Newton Raphson – where the stiffness matrix is updated after each load step but BFGS corrections are not applied

3/ Full Newton Raphson - where the stiffness matrix is updated after each load step and after each iteration. This is a most robust but also a slowest method – it should be used if convergence problems occur.

The number of load steps, solution type and step halving parameters may be set for each load applied

Results Interpretation:

The assembly load case results are automatically included with all other load cases analysed. If a load combination is made then ROBOT adjusts the result so that only one participation of the assembly load (with the factor of unity) is included. The only exception to this is when a combination with factors other than unity for assembling load case are applied – in such case this user defined factor for assembling load case will overwrite the default factor of unity.

Errors often made with cable models:

1/ Incorrectly assigning supports so that cable ends are unrestrained rotationally (not necessary starting from v.14.0)

2/ Input of force or stress in cable definition that cannot physically occur.

3/ Not choosing enough load steps.

4/ Using BFGS instead of Newton Raphson.

5/ Choosing loads that may cause cables to attempt to go into compression, resulting in non convergence.

6/ Not recognising that results of load cases include the results of assembly case too.

7/ Not specifying P-Delta analysis for co-linear chains of cables or for planar cable nets – for such structures Pdelta analysis is necessary to produce the stiffness in the direction perpendicular to the chain or net