Form Finding and Cable Tension Optimization

LARSA 4D Bridge Plus provides two solutions for form finding, the problem of finding the correct initial unloaded geometry so that the structure takes on the design shape under loading. The first method determines cable tension forces in a model in which the structure is constructed in a single step. The second is based on the unit-load method and is used for models with a construction sequence.

A common problem in the analysis of cable-supported structures is the determination of initial cable tension forces that in combination with other loading, the construction sequence, and time-dependent material effects gives the structure its desired final geometry and internal forces.

We call these procedures model optimization. Optimization is the term from mathematics of finding a minimum of a function. These procedures are used in LARSA 4D to minimize deflection or other model results.

Cable Tension Optimization

The first method for form finding is called cable tension optimization. This procedure, shown in the diagram at the left, is an iterative method that adjusts cable pretension forces until the model has zero deformation under loading.

General Model Optimization

The "unit load method" can also solve this problem. In this method, we apply a unit-tug --- i.e. one extra unit of jacking force --- to each cable and observe its effect on each of the joints at the bases of the cables. Then we solve for a factor to apply to the tugs to zero-out the displacements at the joints simultaneously.

We have found this to be a useful method for cable-stayed bridges with a complex construction sequence.