Development of Seismic Demand and Capacity Assessment Methodology for Rectangular Concrete-filled Steel Tube (rcft) Members and Frames

Accurate assessment of demand and capacity of structures is critical in developing performance-based design methodologies. In this research, new methods are presented towards quantifying demand and capacity of RCFT frames and members. An experimental database was compiled documenting local damage levels of RCFT members. The quantified information collected from the experiments was utilized in calculating the available capacity of RCFT members at multiple performance levels. To assess seismic demand, a 3D corotational mixed fiber-based finite element formulation was derived allowing both geometrically and materially nonlinear analysis of frames made up of RCFT columns and steel girders. This finite element formulation has several unique features designed to capture the main characteristics of RCFT members observed in experimental tests, including slip between the steel tube and concrete core, local buckling of steel tube, and confinement of the concrete. It was implemented in a general purpose finite element program and verified by comparing to the cyclic and monotonic beam-column tests. Introduction Rectangular concrete-filled steel tube (RCFT) frames are known for their excellent seismic performance with high ductility and large energy absorption capacity (Hajjar 2002). This is often attributed to the interaction of the steel tube and concrete core. Confinement of concrete provided by the steel tube alleviates the abrupt failure of concrete and also local buckling of the steel tube is delayed due to the restraining action of the concrete media. Therefore, it is important to account for the interaction between steel and concrete in modeling RCFT members. In addition, RCFT members exhibit distinct local damage levels of concrete cracking, concrete cracking, steel tube yielding etc. as reported in (Tort and Hajjar 2004). Prediction of these local damage levels is only possible with accurate modeling of composite nature of RCFT members. In this research, an experimental database was constructed consolidating worldwide literature on RCFT members and frames. The experimental results documented in the database were later used in quantifying the available local capacity of RCFT members. To conduct studies for the assessment of seismic demand, a new 3D corotational mixed finite element formulation was derived following the past work by (Hajjar et al. 1998) and (White and Nukala 1 Graduate Research Assistant, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55455 2 Professor, Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL 61801 2003). This finite element formulation has the capability to simulate slip between the steel tube and concrete core. Uniaxial cyclic constitutive models of the steel tube and concrete core were derived to simulate the materially nonlinear response of RCFTs. The finite element formulation was implemented in (OpenSEES 1999) and verified with respect to monotonic and cyclic experimental tests from the literature. Developing a comprehensive computational formulation to analyze RCFT frames both allows researchers to develop, test, and verify new analysis and design methods (e.g., intensity measures, demand measures) for performance-based design and also it helps practitioners use advanced analysis methods (e.g., nonlinear push-over, nonlinear time history) in design to evaluate a wide range of performance objectives with reduced uncertainty. Development of Experimental Database Worldwide experimental literature on RCFT members was examined and the specimens of well reported tests were included in the database. The specimens were classified as columns, beam-columns, pinned-connections, panel zones, and frames depending on the test setup and loading conditions. The database contained information about the geometric dimensions and material properties of the specimens. In addition, experimental results of the specimens were reported covering information about load and deformation capacities, failure modes, and occurrence of local damage levels in terms of their load and deformation values. Using experimental results in the database, damage function equations were derived to estimate the available capacity of the specimens at multiple performance levels (Tort and Hajjar 2004). Finite Element Formulation In performance-based design, capacity and demand of frame structures are often quantified through conducting a series of nonlinear time history analyses. However, the prerequisite of this stage is to develop a finite element model that is capable of representing the key features of RCFT members under static loading applied either monotonically or cyclically. An 18 DOF beam-column finite element was formulated to model RCFT members based on the past work by (Hajjar et al.1998). In this model, the translational degree of freedoms of steel tube and concrete core are defined separately creating 3 additional degrees of freedom at each joint. This approach allows differential movement of steel tube and concrete core. Since concrete core is placed inside steel tube, shear deformation compatibility is ensured through utilizing penalty functions between shear translational DOFs of steel tube and concrete core. This results in differential movement between steel tube and concrete core only in the axial direction. The DOFs of the RCFT beam-column finite element are numbered in a manner that allowed automated assembly of 12 DOF steel beam elements into 18 DOF RCFT beam-column elements in a composite frame. When a steel girder frames into an RCFT column, the DOFs of the steel girder are assembled into the first 6 DOFs of the RCFT joint, which corresponds to the steel tube DOFs. The last 3 DOFs of the RCFT joints are defined for concrete translations, and the nodal forces from steel girder are transferred to the concrete core through the slip interface between the steel tube and concrete core. The slip response of RCFT beam-column elements was calibrated with respect to push-out tests and connections tests available in the literature by (Hajjar et al. 1998). A bond strength of 0.087 ksi was assumed and a bilinear slip vs. bond strength response was adopted with an initial stiffness ( ksc ) of 1450 ksi defined around the perimeter of the steel tube. In this research, the RCFT beam-column finite element by (Hajjar et al. 1998) was augmented by implementing a new mixed finite element-based state determination scheme following the work by (Nukala and White 2003). The mixed finite element formulations are known to have better accuracy with a coarse mesh as compared to equivalent displacementbased formulations due to the fact that in mixed formulations curvature distribution along the element length can be estimated more accurately (Nukala and White 2003). In addition, in mixed formulation, equilibrium along the element length is strictly enforced while it is satisfied only in the variational sense in displacement-based formulations. Equilibrium of element forces alleviates numerical difficulties arising from concrete cracking (Hajjar et al. 1998). The proposed state determination methodology follows the Hellinger-Reissner two-field variational principle, where displacement fields and forces fields are interpolated independently. The element internal forces ( Q ) are calculated by satisfying the element equilibrium, displacement compatibility, and cross-section equilibrium given in Eqs. 1, 2 and 3, respectively (symbols not defined in the text are defined in the Appendix; the left superscript in the symbols below identifies the configuration in which a quantity is measured while left subscript identifies the reference state; “1” denotes the last converged configuration (C1) and “2” denotes the current configuration (C2); L is the element length; “δ” identifies the variation): δ δ δ 12 12 0 1 2 1 2