Finite Element Modeling

The finite element method is a powerful tool to assess a wide range of engineering problems numerically in determining the deformation and stress analysis of building and bridge structures. With the development in computer technology and CAD systems, complex problems can now be modelled easily and, hence, several alternative configurations can be tested on a computer. Several FE packages are available to facilitate the process of constructing and solving a model, such as Vector2, DIANA and ABAQUS. In this section, a summary of research conducted on RC beam-column joints using FE software ABAQUS is described.

Danesh et al. (2008)

Danesh et al. (2008) carried out a finite element investigation using ABAQUS to study the effectiveness of GFRP layers for strengthening shear deficient of exterior RC beam-column joint tests conducted by El-Amoury and Ghobarah (2002). The FE study covered the unstrengthened and strengthened beam-column joint specimens.

The concrete damage plasticity (CDP) was employed to model the concrete behaviour in the plastic range where the failure of concrete was characterized with the tensile cracking and compressive crushing mechanism. Inelastic concrete stress-strain response under uniaxial compression was defined in forms of stress-inelastic strain response, while the concrete under uniaxial tension was assumed to be linear until the initial macroscopic cracks at failure was formed. Longitudinal and transverse steel reinforcement behaviour was modelled as an elastic-plastic material using bilinear curve. In addition, the GFRP was assumed to be an orthotropic material, where the failure criterion was generally defined in the stresses space

based on the shear strength and the maximum compressive and tensile strength in orthogonal directions. The concrete elements were discretised using an 8-node solid element (C3D8R) while T3D2 and four-node shell elements (S4R) were used to model the reinforcement and GFRP elements, respectively.

(a) (b)

Figure 2.37. Comparison of damage propagation in the joint between the experiment and the FE model: (a) Experiment conducted by T. El-Amoury and Ghobarah (2002); (b) FE model

by Danesh et al. (2008)

The crack propagations in the experiment were compared to those of the FE analysis in Figure 2.37. In the experiment, the joint failure was observed before the yielding of the main beam longitudinal bars. To recognize the crushed element in the FE study, the minimum strain at the crushing concrete was assumed at a value of 0.0025. The comparison of the crack pattern between the experiment and the FE study showed a good accuracy; both results showed cracks initiated at the upper side of the beam-column interface and the diagonal crack propagated towards the joint and reached the back of the column face at failure.

Abbas et al. (2014)

Abbas et al. (2014) conducted FE simulations to investigate the behaviour of steel-fibre RC (SFRC) beam-column joints tested by Bayasi and Gebman (2002) subjected to combination of reversed cyclic and constant column axial load. The 8-node brick elements were used to discretize the concrete element. Sensitivity analysis was conducted to determine the optimum mesh element size. Based on the validation to the experiment, the 50 mm element size was chosen, as it showed the best results to reproduce the experiment data. The reinforcement bars were modelled using the two-node truss element and were precisely located to match the reinforcement details in the experiment. In addition, the pre-mature localized cracking at the loading point and supports was avoided by utilizing a rigid element to distribute the stresses developed during the analysis.

! 2Ø15.9 mm COLUMN SECTION I - I 254 254 2Ø15.9 mm 9.5 mm @ 152 mm c/c 200 305 2 Ø15.9 mm and 1 Ø12.7 mm BEAM SECTION II - II 254 3 Ø12.7mm 9.5 mm @ 152 mm c/c 483 254 I I 610 II II

Figure 2.38. Geometry and reinforcement details of exterior beam-column joint tested by Bayasi and Gebman (2002)

From the experiment, steel-fibres enhanced the tensile post-cracking and exhibited concrete more ductile compared to the plain concrete (Kotsovos and Pavlović, 1995). However, the improvement was not observed in the case of uniaxial compression. This concluded that the

introduction of steel-fibres improved concrete in tension, preventing the formation of crack, whilst in compression their effect on concrete in compression could be neglected. Hence, the brittle cracking model in ABAQUS was used to model the concrete. This model was used for concrete in which the material behaviour is dictated by tensile cracking. Elastic-plastic material using bilinear curve (See Figure 2.39.(a)) was adopted to model the conventional steel reinforcement bars.

(a) (b)

Figure 2.39. FE analysis of Abbas et al. (2014): (a) Conventional steel reinforcement bars model; (b) Load-displacement hysteresis for the FE and experiment results

The analysis was carried out using explicit dynamic procedure available in ABAQUS/Explicit with a low rate of loading. The results comparison between the experiment and FE analysis showed a good agreement as depicted in Figure 2.39.(b). The failure in the FE analysis was associated with the increase in the kinetic energy, indicating the extensive cracks propagated within the joint region. However, the maximum ductility achieved in the FE was 50% lower than that of in the experiment.

Kam (2014)

Kam (2014) developed FE models using ABAQUS to study the effects of beam widths and beam depths on the performance of RC wide beam-column joints subjected to cyclic load. A

linear 8-node solid element (C3D8R) was used to model the concrete elements. The first order fully integrated element will experience locking behaviour under bending and resulted in false shear strain; hence the stiffness under bending will be over predicted. This issue can be solved by using reduced integration method, but this will bring another problem, “hourglassing” (Kam, 2014). C3D8R element has one integration point; all the developed strains will be evaluated as zero and cause an uncontrolled distortion. In order to achieve accurate results, enhanced hourglass control should be implemented. The beam and column longitudinal reinforcements were modelled using 2-node 3D truss element (T3D2) and were perfectly bonded to the concrete element. The CDP model was employed to model the concrete behaviour under cyclic load in which the compressive crushing and the tensile cracking are the main failure mechanisms. Two constitutive models were used to model the steel reinforcement bar: the fixed angle softened truss to model the behaviour of mild steel and elastic perfectly plastic relationship to model the behaviour of high yield steel.

In order to capture the pinching effect, cohesive crack was employed to model the diagonal cracks at the joint and cracks at the beam. In cohesive crack, the cracks are defined as surface- to-surface contact that is applied by a small sliding formulation. In his study, Kam (2014) utilized five contact pairs as depicted in Figure 2.40.

The results showed that the beam width had significant contribution in controlling the seismic performance at a joint by affecting the load transfer path in wide beams and the corresponding joint core. On the other hand, the beam depth was found insignificant effect in altering the load path, but it affected the seismic performance of the joint. The result also showed that joint shear stress in wide beam-column joint is higher than that of conventional joint.

2.8. CURRENT CODE OF PRACTICES IN DESIGNING REINFORCED