Dear researchers
As you know, one of the challenges of using nonlinear procedures is to determine the behavior of plastic hinges of members with deformation controlled action that this behavior is assigned to the plastic hinge by a force-deformation curve and its relations using parameters modeling. various researches has shown that the uncertainties in these modeling parameters significantly affect the structural responses.
Also, the acceptance criteria of different performance levels relating to the mentioned force-deformation curve are needed for performance-based design of structures.
There are two questions now:
1- Are force-deformation curves presented in ASCE 41-13 suitable only for nonlinear static analysis (push over)? or also is applicable for nonlinear dynamic analysis?
2- Given that the acceptance criteria presented in ASCE 41-13 are derived based on the mentioned force-deformation relations in this code (a, b and c modeling parameters), what acceptance criteria can be used to evaluate the structure at the IO, LS and CP performance levels if the other force-deformation relations presented in the technical literature (such as Lignos and Hartloper relations for beams and columns of moment frames, respectively) are utilized for concentrated plasticity modeling?
The mentioned curves (Lignos and Hartloper relations) are mostly used in structural modeling to study the structural collapse, in which the collapse is determined by the criteria mentioned in FEMA p-695 and as a result, acceptance criteria in accordance with these behavior curves have not been researched.
1. Seismic codes suggest simplified force-deformation models in order to estimate the inelastic behavior both in monotonic and cyclic loading. The monotonic F-δ curve is considered as the envelope and the skeleton curve of F-δ loops under cyclic loading. The real inelastic behavior under cyclic loading depends on the material and the dynamic loading, e.g. reinforced concrete under seismic loading. So, stiffness and strength deterioration should be considered under cyclic loading in the concentrated plasticity modeling technique.
2. Uncertainties about deformation capacity are high beyond the point C of the F-δ curve. Even in the Collapse Prevention performance level (before point C), the ultimate deformations shows significant dispersion in experimental cyclic tests (e.g. reinforced concrete). Consequently, appropriate acceptance criteria for different performance levels and for different materials can be found in seismic codes (ASCE 41-13, FEMA, Eurocode, EN 1998-3, etc) or in other technical literature using model safety factors to scale down the proposed mean values to mean plus standard deviation ones.
Dear Al Mouayed Bellah Nafeh
About second question, I know what you say. But I mentioned that all acceptance criteria presented in ASCE 41-13 are derived based on the simplified force-deformation introduced in ASCE41-13 and it is clearly stated that the use of these acceptance criteria is applicable only if this simplified curve is used.
For examples, I can not use acceptance criteria for nonlinear analysis which presented in ASCE41-13 for steel moment frames when Hartloper relations are used for inelastic behavior of members.
Therefore, to perform performance-based design, either simple curves should be used for inelastic behavior or, if other force-deformation relations are used, specific criteria must be set for the acceptance criteria of performance levels according to its relations.
The suggested F-δ curves and the acceptance criteria of inelastic behavior is a unified package in various Seismic Codes. On one hand, F-δ curves differ slightly between various seismic codes. On the other hand, acceptance criteria for inelastic behavior show greater differences.
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