Cable Forces: FCAB, FX0, or LX0, and Cable sagging

For elements type Cable there are also different considerations for the cable behaviors: linear, CabSag, or Stay Cable Nonlinear. Depending on the type of analysis performed, each one could be more advantageous:

• Cable element: Normal only forces, tension only.
• CabSag: is the non-linear behavior simplification that is modeled with just an equivalent E-modulus taking into account the sag;
• Non-linear stay cables: is the exact non-linear calculation and requires the elements Cable to be subdivided either internally or at their development to consider the deformations.

RM Bridge CONNECT Edition offers different forms of cable force load definitions for stressing the cables: FCAB, FX0, and LX0.

• FCAB: is the jacking force, the prestressing or installation force at the cable, and it has limited utilization for linear calculations, while;
• FX0/LX0: is the cable shortening defined by equivalent force (FX0) or the length change defined by the stress-free fitting element length (LX0) where any non-linearity and unit forces can be applied for optimization, construction simulation, or erection control.

The big difference is the consideration of cable sagging for FX0 or LX0. This is required for longer cable elements and, as the cable is external to the structure, the cable sag is a complex calculation that is different from prestressing. For medium structures, the cable curvature due to gravity has to be taken into account and this is relative to the level of tension.

• FX0 (kN) is the normal force being equivalent to the desired length change:   FX0 = E A ε0 = [ ( E A ) / L0 ] × ΔL
• LX0 (m) is the theoretical stress-free length of the element:   LX0 = LX / [ 1 + Fx / ( E × A ) ] 
  • Considering the length change:   ΔL  = L * Fx / ( E A )  
  • Then, the elongation is:   ε0 = ΔL / L0 = ( LX0 - LX ) / LX0

There is a long iterative process to calculate the full bridge that includes not only the calculation of the final structure but also the construction stage calculation. So, one of the most important non-linearities in this type of analysis is the continuous change of the structural system caused by the evolution of the construction schedule. There are two options: Accumulate Loads or Accumulate Stiffness (more usual); and, if the analysis and design include construction control, there is the additional option Erection Control with or without construction kink.

AddCon: Additional Constraints technique can be used to perform structure optimization allowing the user to specify boundary conditions to be achieved and follow the variable forces factors convergence process to achieve a solution.

More information can be found at the links below and our Help (F1), Manuals, Training Examples, and FAQ Documents.