TR.37.3 Nonlinear Cable Analysis
General Format
For basic cable analysis:
PERFORM CABLE ANALYSIS BASIC (STEPS f1) (EQITERATIONS f2) (EQTOLERANCE f3) (SAGMINIMUM f4) (STABILITY f5 f6) (KSMALL f7) (PRINT print-options)
For advanced cable analysis:
PERFORM CABLE ANALYSIS ( ADVANCED ) (STEPS f8) (EQITERATIONS f9) (EQTOLERANCE f10) (REFORM f11) (KGEOM f12) (PRINT print-options)
Where:
print-options = { LOAD DATA | STATICS CHECK | STATICS LOAD | BOTH | ALL }
See TR.37.1 Linear Elastic Analysis for details.
See TR.42 Print Specifications for details on including the cable sag in the output.
This command may be continued to the next line by ending with a hyphen.
| Parameter | Default Value | Description |
|---|---|---|
| STEPS f1 | 145 | The number of load steps for basic cable analysis. The applied loads will be applied gradually in this many steps. Each step will be iterated to convergence. If entered, the value should be in the range 5 to 145. |
| EQITERATIONS f2 | 300 | Maximum number of iterations permitted in each load step. Should be in the range of 10 to 500. |
| EQTOLERANCE f3 | 0.0001 | The convergence tolerance for the above iterations. |
| SAGMINIMUM f4 | 0.0 |
Cables (not trusses) may sag when tension is low. This is accounted for by reducing the E value. Sag minimum may be between 1.0 (no sag E reduction) and 0.0 (full sag E reduction). As soon as SAGMIN becomes less than 0.95, the possibility exists that a converged solution will not be achieved without increasing the steps to 145 or the pretension loads. The Eq iterations may need to be 300 or more. The Eq tolerance may need to be greater or smaller. |
| STABILITY f5 | 1.0 | A stiffness matrix value (f5) that is added to the global matrix at each translational direction for joints connected to cables and nonlinear trusses for the first f6 load steps. The amount added linearly decreases with each of the f6 load steps. If f5 is entered, use 0.0 to 1000.0. This parameter alters the stiffness of the structure. |
| f6 | 1 | The number of load steps over which f5 is gradually applied. The default is one step. |
| KSMALL f7 | 0.0 | A stiffness matrix value that is added to the global matrix at each translational direction for joints connected to cables and nonlinear trusses for every load step. The range for f7 is between 0.0 and 1.0. This parameter alters the stiffness of the structure. |
| Parameter | Default Value | Description |
|---|---|---|
| STEPS f8 | 1 | Used to divide the loading into small increments. Any positive integer is valid. Generally, a value larger than one (1) may be beneficial for solution convergence, because the loading is applied gradually. However, with cable elements having fixed prestressing, a single step typical converges faster. |
| EQITERATIONS f9 | 300 | Maximum number of iterations permitted in each load step. During each loading increment, the analysis will iterate to find the converging solution. Once the iteration number reaches the maximum value, the analysis will be stopped even though converged solution is not achieved. Any positive integer is valid. Values too small may prevent the solution to achieve convergence. However, excessively large values may cost unnecessary running time when the problem diverges. |
| EQTOLERANCE f10 | 1.0E-6 | The convergence tolerance for
the iterations specified in
EQITERATIONS. The residual force norm is used
for this convergence. This error threshold indicates when the nonlinear solver
will stop iterating and consider the ongoing step as converged once the
computed error is equal or smaller than this value. A value that is too small
may prevent the solution to be considered as converged. However, value that is
too larger may result in inaccurate results.
The tolerance printed in the output file is the norm of the current out-of-balance forces, divided by the norm of all the externally applied forces. This calculated tolerance must be less than f10 for the current iteration to converge. |
| REFORM f11 | 1 | Used to specify if full Newton-Raphson method or modified Newton- Raphson method will be used. Theoretically, the full Newton-Raphson method can approach converge with less iterations but may require more computation effort than modified Newton-Raphson method. |
| KGEOM f12 | 0 | Used to specify whether or not geometric stiffness will be used. |
Notes
-
STAAD.Pro allows multiple analysis in the same run (see the General Comments in TR.37.1 Linear Elastic Analysis).
-
Multiple analyses may require use of additional commands like the SET NL command and the CHANGE command.
-
When using a basic cable analysis, only one primary load case should be defined before the analysis command which then should be followed by a CHANGE command. This is not required if using the advanced cable analysis where multiple load cases can be defined.
- A cable element cannot be loaded with either a non-uniformly distributed load or a concentrated load (using a MEMBER LOAD command).