Understanding Geometric Stiffness in Tensioned Beam Models

Analysis, Guides

This video shows a support case involving beam tipping in a prestressed concrete beam. It explains why a stable model with cable elements can become unstable when cable elements are replaced with couplings.

The workflow starts with self-weight and prestress, followed by a skew introduced via a pre-bending load case scaled to a maximum Y-deformation of 10 cm. Nonlinear material analysis and an extreme check with three times the self-weight and only 40% prestress confirm that the beam remains stable during transport, supported by compressive stresses in the top flange and an inclined neutral axis. Nonlinear results may even show slightly reduced deformation because slack reinforcement contributes to stiffness.

The critical issue arises when couplings are used instead of cable elements: couplings do not provide geometric stiffness from normal force, which is essential for stabilising the system and enabling meaningful eigenvalue calculations. Without this contribution, negative stiffness and instability can occur. A future solution aims to reintroduce this effect by modelling couplings as fictitious rods.

  • Build the skew via a pre-bend load case and scale it to 10 cm maximum Y-deformation
  • Combine 1.35× self-weight with reduced prestress for creep and shrinkage effects.
  • Nonlinear results may show less deformation because slack reinforcement increases stiffness.
  • Middle node-line placement improves accuracy, especially under eccentric flange loading.
  • Couplings add no geometric stiffness; a “fictitious rod” approach can restore stability.