Review of Coarse Softening Analysis of Framed Concrete Structures

Abstract

“Coarse” softening analysis of concrete structures relies on the primary assumptions that softening occurs over a finite hinge length and that the moment curvature or torque-twist relationship for any section may be closely described by a multi-linear curve. Results from several series of tests demonstrate that these are good approximations. A hinge length of 0.75d is recommended for first draft computations for flexural softening.Singularity difficulties with stiffness coefficients may be eliminated by ensuring that equilibrium states (eigenvectors) of the stiffness matrix for members with softening hinges are consistent with the presumed stiffnesses. The direction dependency of hinge stiffness must be taken into account. Resolution of the computational problems implies a reduced equivalent hinge length ratio for small values of the softening or hardening parameter a (ie in situations near perfect plasticity). There is also a problem of path dependency in deformations involving the softening state. The critical softening parameter may be determined for a hinge at any location in a framed structure.In elastic-plastic softening frames a steeper softening slope reduces both the number of hinges formed before collapse and the collapse load. When axial load (stability) effects are included, the absolute values of critical softening parameters are reduced. Shakedown loads may be severely reduced by the presence of significant residual moments and only very slight softening. For unidirectional dynamic loads there is a critical softening value for the resistance function of the structure which depends on the nature of the dynamic load. For reversible loads the softening hysteretic behavior of each hinge is reflected in the overall response and a critical ground excitation frequency may be identified for a given softening slope and peak load/yield load.KeywordsStiffness CoefficientReinforce Concrete BeamCollapse LoadSoftening ParameterRotation CapacityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.