pycba.nonlinear#
PyCBA Nonlinear Module — Generalized Clough Model#
Incremental nonlinear analysis of continuous beams using the Generalized Clough model for material nonlinearity (concentrated plasticity).
The Generalized Clough model tracks a stiffness-reduction parameter R at each element end. R = 1 is fully elastic and R = q (the strain- hardening ratio) indicates a fully plastic hinge. Between yield (M_y) and the plastic moment (M_p), R degrades linearly, producing a bilinear moment–rotation response at the section level.
Each plastic hinge is owned by a single element end so that the adjacent element retains rotational stiffness at the shared node. This keeps the global stiffness matrix non-singular during load redistribution and allows the analysis to continue past first-hinge formation. True collapse is detected by a separate rank test that zeros both element ends at every hinged node and checks for global singularity.
References
Clough, R.W. & Johnston, S.B. (1966). “Effect of stiffness degradation on earthquake ductility requirements.” Proc. Japan Earthquake Engineering Symposium, Tokyo, pp. 227–232.
Li, G.Q. & Li, J.J. (2007). Advanced Analysis and Design of Steel Frames. John Wiley & Sons, Chapter 4.
McCarthy, L.A. (2012). Probabilistic Analysis of Indeterminate Highway Bridges Considering Material Nonlinearity. MPhil Thesis, Dublin Institute of Technology.
Caprani, C.C. (2006). “Probabilistic Analysis of Highway Bridge Traffic Loading.” PhD Thesis, University College Dublin.
Classes
Record of a yield or plastic-hinge formation event. |
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Nonlinear continuous beam analysis using the Generalized Clough model. |
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Results container for a nonlinear beam analysis. |