UC Berkeley

This dissertation presents a family of new beam-column element models which are based on damage-plasticity and are suitable for the damage assessment and the collapse simulation of structures.

First, a new 1d hysteretic damage model based on damage mechanics is developed that relates any two work-conjugate response variables such as force-displacement, moment-rotation or stress-strain. The strength and stiffness deterioration is described by a damage variable with continuous evolution. The formulation uses a criterion based on the hysteretic energy and the maximum absolute deformation value for the damage initiation with a cumulative probability distribution function for the damage evolution.

The damage evolution function is extended to accommodate the sudden strength and stiffness degradation of the force-deformation relation due to brittle fracture. The model shows excellent agreement with the hysteretic response of an extensive set of reinforced concrete, steel, plywood, and masonry specimens. In this context, it is possible to relate the model's damage variable to the Park-Ang damage index so as to benefit from the extensive calibration of the latter against experimental evidence.

The 1d damage model is then extended to the development of beam-column elements based on damage-plasticity. In these models, the non-degrading force-deformation relation in the effective space is described by a linear elastic element in series with two rigid-plastic springs with linear kinematic and isotropic hardening behavior. The first model, the series beam element, assumes that the axial response is linear elastic and uncoupled from the flexural response. The second model, the NMYS column element, uses an axial-flexure interaction surface for the springs to account for the inelastic axial response and capture the effect of a variable axial load on the flexural response. A novel aspect of the beam-column formulation is that the inelastic response is monitored at two locations that are offset from the element ends to account for the spread of inelasticity for hardening response and the size of the damage zones for softening response. The plastic hinge offsets account for the response coupling between the two element ends.

The implementation of the damage-plasticity elements with the return-mapping algorithm ensures excellent convergence characteristics for the state determination. The proposed elements compare favorably in terms of computational efficiency with more sophisticated models with fiber discretization of the cross section while achieving excellent agreement in the response description for homogeneous metallic structural components. The excellent accuracy is also confirmed by the agreement with experimental results from more than 50 steel specimens under monotonic and cyclic loading. The models are able to describe accurately the main characteristics of steel members, including the accumulation of plastic deformations, the cyclic strength hardening in early cycles, the low-cycle fatigue behavior, and the different deterioration rates in primary and follower half cycles. With the plastic axial energy dissipation accounted for in the damage loading function, the damage-plasticity column model captures the effect of a variable axial force on the strength and stiffness deterioration in flexure, the severe deterioration under high axial compression, the nonsymmetric response under a variable axial force, and the very large plastic axial and flexural deformations before column failure. The validation studies point out the dependence of the strength and stiffness deterioration on the section compactness, the element slenderness, the axial force history, and the axial shortening of the columns. A regression analysis is then used to establish guidelines for the damage parameter selection in relation to the geometry and the boundary conditions of the structural member.

The proposed damage-plasticity frame elements are deployed in an analysis framework for the large-scale simulation and collapse assessment of structural systems. The capabilities of the modeling approach are demonstrated with the

case study of an 8-story 3-bay special moment-resisting steel frame that investigates various aspects of the structural collapse behavior, including the global and local response under strength and stiffness deterioration, the magnitude and distribution of the local damage variables, and the different types of collapse mechanism. The study proposes new local and global damage indices, which are better suited for the collapse assessment of structures than existing engineering demand parameters like the maximum story drift. The incremental dynamic analysis of the 8-story moment frame under a suite of earthquake ground motions confirms the benefits of the proposed damage indices for the collapse assessment of structures. The study shows that an aftershock as strong as the main shock increases the collapse margin ratio by as much as 30\% and requires more stringent design criteria for protecting the building from collapse that currently specified.

The study compares different modeling aspects for the archetype building to assess the benefits of the proposed beam-column elements, such as the ability to account for the member damage, the offset location of the plastic hinges, the inelastic axial response, the axial-flexure interaction, and the sudden strength and stiffness deterioration due to brittle fracture of the structural member.

The study concludes that the proposed family of beam-column elements holds great promise for the large scale seismic response simulation of structural systems with strength and stiffness deterioration, because of their computational efficiency and excellent accuracy. Consequently, the proposed models should prove very useful for the damage assessment and the collapse simulation of structures under extreme loading conditions.