I am currently performing nonlinear analysis of a transmission tower subjected to wind loading using Abaqus. The objective of my study is to obtain capacity curves and fragility curves from multiple simulations.
The tower height in my model is 39.1 m, and for fragility analysis I adopted the displacement limit recommended in ASCE-74, defined as:
DS=0.015H
which corresponds to 0.5865 m displacement.
To capture instability and post-peak structural behavior, I used the Riks (arc-length) method with geometric nonlinearity enabled. From the Abaqus history output, I extracted top displacement and corresponding wind speed and generated capacity curves.
During post-processing, I observed that several capacity curves exhibit snap-back behavior near the peak load. After the peak, the equilibrium path folds backward and then continues along a descending branch. A representative curve is attached for reference.
What confuses me is the following observation. Around the snap-back region, it appears that multiple equilibrium states exist at nearly the same displacement value. In other words, for a single displacement (for example around 0.85–0.9 m), the capacity curve shows more than one possible wind speed.
This raises a question about the interpretation of the equilibrium path:
If three different load values correspond to nearly the same displacement value, does this mean that three equilibrium solutions exist simultaneously for that displacement? Physically, it seems difficult to interpret how the structure could satisfy equilibrium at multiple load levels for the same displacement.
Therefore, I would like to ask:
- How does Abaqus solve this situation using the Riks (arc-length) method when multiple equilibrium points appear in the capacity curve?
- Does this behavior represent physically meaningful unstable equilibrium states, or could it be related to numerical issues in the analysis?
- In practice, when interpreting capacity curves for structural collapse analysis, should these snap-back segments be considered part of the physical response, or should the curve be truncated at the first peak load?
I would greatly appreciate any guidance you could provide regarding the correct interpretation of this behavior.
Thank you very much for your time and assistance.
