# Aval, Saadeghvaziri, and Golafshani 2002

The paper presents the formulation of an inelastic fiber element for cyclic analysis of CFT beam-columns. The element is planar and consists of three components, the steel tube, the concrete core, and a distributed bond interface element. Results from the new element were compared to experimental results.

## Analytical Study

The authors identified a need for more advanced modeling of CFT members which includes bond between the steel tube and concrete core. To fill this need they developed a practical nonlinear distributed plasticity element for monotonic and cyclic loads with distributed bond between the steel tube and concrete core. Several assumptions were made in the derivation of the model. 1) Plane sections remain plane for both the steel and concrete but the angles of rotation are independent. 2) Shear deformations due to the size of the section are negligible. 3) The steel tube will not experience local buckling. 4) Multiaxial effects in the materials are accounted for in the uniaxial models. 5) Creep and shrinkage are negligible. 6) Residual stresses are negligible.

The proposed element was comprised of three components: one to model the steel tube, one to model the concrete core, and one to model the relative slip between the steel and concrete. In order to better model the curvature distribution of CFT members, quartic shape functions were used for transverse displacements (rather than the typical cubic shape function). Quadratic shape functions were used for axial deformation. The tangent stiffness matrix was given in terms of equivalent section stiffness values to be evaluated during the loading history by the fiber method. This requires that the steel and concrete sections as well as the slip boundary be divided into small areas for numerical integration.

Three material models were necessary for this formulation. The concrete model used in the study was taken from Mohd Yassin. In order to evaluate the maximum compressive strength of the concrete, taking into consideration different shaped and sized steel tubes, the following equation was used:

where α is a shape factor and A and B are empirical parameters expressed in terms of f'c. The steel model used was a modified version of the one proposed by Menegotto and Pinto. An equation similar to the one above is used to determine the reduction in yield stress due to biaxial effects. The bond is modeled as elastic perfectly plastic, with yield point and elastic stiffness determined from experimental results.

## Comparison of Results

The new element was implemented in the finite element analysis program FEAP and two examples were reported, one of monotonic load and one of cyclic load. The experimental results were compared to the results of the three analyses, each with a different bond (without, partial, and perfect). The results clearly demonstrated the effect of bond and the partial bond is shown to fit the experimental data the best.