Filip C. Filippou

FIBRE BEAM–COLUMN MODEL FOR NON-LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION

A companion paper presents the formulation of a fibre beam-column element for the non-linear static and dynamic analysis of R/C frames. This paper illustrates the application of the proposed element in the simulation of the hysteretic behaviour of several R/C beam and column specimens. The specimens are subjected to uniaxial and biaxial loading histories with varying axial load. The proposed element shows computationally stable and robust numerical behaviour, while being able to describe very well the hysteretic behaviour of the reinforced concrete members under the imposed complex loading histories.

Mixed formulation of nonlinear beam finite element

Recent studies show that beam finite elements that enforce equilibrium rather than compatibility along the element are better suited for the description of the nonlinear behavior of frame elements. This is particularly true for elements that exhibit loss of strength and stiffness under monotonic and cyclic loads. Existing formulations, however, fail to define a consistent way of implementing the force method in the context of imposed kinematic, rather than static, boundary conditions, as is the case for element models in a standard finite element program. This paper derives the general formulation of a beam finite element from a mixed approach which points the way to the consistent numerical implementation of the element state determination in the context of a standard finite element program. The element state determination centers on a new iterative solution algorithm that is based on residual deformations rather than residual forces at the section and element level. Equilibrium is enforced in a strict sense along the element, while the section constitutive relation is satisfied within a specified tolerance when the algorithm converges. The proposed algorithm is general and can be used with any section constitutive relation.

Non-linear spatial Timoshenko beam element with curvature interpolation

The paper presents a spatial Timoshenko beam element with a total Lagrangian formulation. The element is based on curvature interpolation that is independent of the rigid-body motion of the beam element and simplifies the formulation. The section response is derived from plane section kinematics. A two-node beam element with constant curvature is relatively simple to formulate and exhibits excellent numerical convergence. The formulation is extended to N-node elements with polynomial curvature interpolation. Models with moderate discretization yield results of sufficient accuracy with a small number of iterations at each load step. Generalized second-order stress resultants are identified and the section response takes into account non-linear material behaviour. Green–Lagrange strains are expressed in terms of section curvature and shear distortion, whose first and second variations are functions of node displacements and rotations. A symmetric tangent stiffness matrix is derived by consistent linearization and an iterative acceleration method is used to improve numerical convergence for hyperelastic materials. The comparison of analytical results with numerical simulations in the literature demonstrates the consistency, accuracy and superior numerical performance of the proposed element. Copyright

Nonlinear FE analysis of RC structures under monotonic loads

Abstract This paper deals with the finite element analysis of the monotonic behavior of reinforced concrete ( R C ) beams and beam-column subassemblages. It is assumed that the behavior of these members can be described by a plane stress field. Concrete and reinforcing bars are represented by separate material models which are combined together with a model of the interaction between reinforcing bar and concrete through bond-slip to describe the behavior of the composite reinforced concrete material. Using the rotating crack model among the smeared crack model, the structural behavior is simulated and a relation which can consider the tension stiffening effect in finite element analysis is proposed based on an improved cracking criterion derived from fracture mechanics principles. A new reinforcing steel model which is embedded inside a concrete element is developed to cope with the difficulty in modeling of complex geometry. Correlation studies between analytical and experimental results show the validity of the proposed models and identify the significance of various effects on the local and global response of reinforced concrete members.

Section Discretization of Fiber Beam-Column Elements for Cyclic Inelastic Response

AbstractThe paper presents studies of the effect of the number of material integration points at the monitored sections of fiber beam-column elements on the local response of typical structural cross sections under an extensive set of cyclic biaxial load conditions with constant and variable axial load. The study covers wide-flange steel sections and rectangular reinforced concrete sections. The integration over the section uses the midpoint rule and shows that a standard section discretization with relatively few fibers is a good compromise between accuracy and economy of means. The proposed coarse section discretization schemes are computationally efficient while ensuring the accurate representation of important aspects of the three-dimensional response of structural members, such as interaction of axial force with biaxial bending moment, effect of residual stress in steel members, and effect of cracking in reinforced concrete members. The local strain response is also represented with good accuracy by ...

CORRELATION STUDIES ON AN RC FRAME SHAKING-TABLE SPECIMEN

SUMMARY This paper presents the correlation of the results of a new model for the dynamic analysis of reinforced concrete (RC) frames with the experimental time history of a two storey RC frame shaking-table specimen. The frame member model consists of separate subelements that describe the deformations due to flexure, shear and bond slip in RC structural elements. The subelements are combined by superposition of flexibility matrices to form the frame element. A non-linear solution method which accounts for the unbalance of internal forces between di⁄erent subelements during a given load increment is used with the model. The ability of the proposed model to describe the dynamic response of frame structures under earthquake excitations is evaluated by comparing the analytical results with experimental evidence from a twostorey, one bay reinforced concrete frame tested on the shaking-table. The model parameters for the shaking-table specimen are derived from available experimental evidence and first principles of reinforced concrete. The e⁄ect of reinforcing bar slip on the local and global dynamic response of the test structure is assessed. ( 1997 John Wiley & Sons, Ltd.

Analysis of Hysteretic Behavior of Anchored Reinforcing Bars

This paper presents the analysis of the hysteretic behavior of anchored reinforcing bars with a new finite element model. The finite element is based on the interpretation of the steel stress distribution and, thus, is flexibility-based. It is characterized by robust and stable numerical behavior even in the presence of significant strength loss and softening as might be the case with reinforcing bars of insufficient anchorage length. After a brief description of the salient features of the model, the paper establishes the validity of the model by correlation of analytical with experimental results on anchored reinforcing bars under severe load reversals. Several parametric studies are presented in order to study analytical features of the model, such as sensitivity to mesh reinforcement and number of integration points. A second objective of the parametric studies is to investigate the effect of key material on the hysteretic behavior of anchored reinforcing bars.

Finite-Element Model for Pretensioned Prestressed Concrete Girders

This paper presents a nonlinear model for pretensioned prestressed concrete girders. The model consists of three main components: a beam-column element that describes the behavior of concrete, a truss element that describes the behavior of prestressing tendons, and a bond element that describes the transfer of stresses between the prestressing tendons and the concrete. The model is based on a two-field mixed formulation, where forces and deformations are both approximated within the element. The nonlinear response of the concrete and tendon components is based on the section discretization into fibers with uniaxial hysteretic material models. The stress transfer mechanism is modeled with a distributed interface element with special bond stress-slip relation. A method for accurately simulating the prestressing operation is presented. Accordingly, a complete nonlinear analysis is performed at the different stages of prestressing. Correlation studies of the proposed model with experimental results of pretensioned specimens are conducted. These studies confirmed the accuracy and efficiency of the model.

Efficient Beam-Column Element with Variable Inelastic End Zones

The paper presents a new beam-column element that combines computational efficiency with accuracy. The element uses only one monitoring section in each end inelastic zone of the structural member, but accounts for the spread of inelastic deformations under strain hardening response. It is, therefore, a variable inelastic zone model that combines the benefit of integrating the section moment-curvature response with the computational efficiency of concentrated hinge models for beams and columns. The element is more accurate than current distributed inelasticity models in simulating the monotonic and cyclic inelastic response of beams and columns under typical curvature distributions, while being much more cost effective. The element is also suitable for softening response, as long as a relation is available between the length of the softening zone and element response parameters.

Frame Element for Metallic Shear-Yielding Members under Cyclic Loading

Modeling the energy dissipation capacity of shear-yielding members is important in the evaluation of the seismic response of earthquake resistant structural systems. This paper presents the model of a frame element for the hysteretic behavior of these members. The model is based on a three-field variational formulation with independent displacement, stress, and strain fields. The displacement field is based on the Timoshenko beam theory. The nonlinear response of the element is derived from the section integration of the multiaxial material stress-strain relation at several control points along the element, thus accounting for the interaction between normal and shear stress and the spread of inelastic deformations in the member. With the derivation of the axial force-shear-flexure interaction of short members from the material response the proposed model is general, in contrast to existing concentrated plasticity models that require parameter calibration for different loading and support conditions. Furthermore, the model does not suffer from shear locking and does not require mesh refinement for the accurate representation of inelastic member deformations. Correlation studies of analytical results with available experimental data of the hysteretic behavior of shear-yielding members confirm the capabilities of the proposed model. Its computational efficiency makes it suitable for large scale simulations of the earthquake response of structures with shear-yielding members.