Comparison of performance of partial prestressed beam-column subassemblages made of reactive powder concrete and normal concrete materials using finite element models

Research on concrete material continues in several countries and had produced a concrete type of Ultra High Performance Concrete (UHPC) which has a better compressive strength, tensile strength, flexural strength, modulus of elasticity, and durability than normal concrete (NC) namely Reactive Powder Concrete (RPC). Researches on structures using RPC material showed that the RPC structures had a better performance than the NC structures in resisting gravity and lateral cyclic loads. In this study, an experiment was conducted to apply combination of constant axial and lateral cyclic loads to a prototype of RPC interior partial prestressed beam-column subassemblage (prototype of BCS-RPC) with a value of Partial Prestressed Ratio (PPR) of 31.72% on the beam. The test results were compared with finite element model of beam-column subassemblage made of RPC by PPR of 31.72% (BCS-RPC-31.72). Furthermore, there was BCS-RPC modeling with PPR of 21.39% (BCS-RPC-21.39) and beam-column subassemblages made of NC materials modeling with a value of PPR at 21.09% (BCS-NC-21.09) and 32.02% (BCS-NC-32.02). The purpose of this study was to determine the performance of the BCS-RPC models compared to the performance of the BCS-NC models with PPR values below and above 25%, which is the maximum limit of permitted PPR. The results showed that all models of BCS-RPC had a better performance than all models of BCS-NC and the BCS-RPC model with PPR above 25% still behaved ductile and was able to dissipate energy well.


Introduction
Research on Ultra High Performance Concrete (UHPC) has produced a high-performance concrete in compressive strength, tensile strength, flexural strength, modulus of elasticity, and durability namely Reactive Powder Concrete (RPC). RPC consists of micro-sized material composed of silica sand, silica flour, silica fume, and superplasticizer, that leads it has a compact behavior better than Normal Concrete (NC). To increase the compressive strength since early age and accelerate the hydration process, RPC was treated in a steamed room or placed in hot water under temperature of 90° Celsius for three days.
In an ideal condition of laboratory, the compressive strength of 120-230 MPa was achieved by RPC cylinders, while the RPC cylinders restrained by steel sleeves achieved the compressive strength of 490-680 MPa [1].

Literature Review
The use of open frame structures reinforced by partial prestressed strands are commonly used to reduce the dimensions of the structural elements and expand the space. The partial prestressed structures are The beam-column subassemblage structures were analyzed using discrete element models of threedimensional finite element. Finite element modeling of reinforced concrete was done by setting concrete, mild steels and prestressed strands as separate discrete elements. Finite element analysis performed by ANSYS program. Concrete elements were modeled as SOLID65 elements which are three dimensional elements and has eight nodals. Each node has three translational degrees of freedom in the direction of X, Y, and Z axes as shown in figure 1. SOLID65 was modeled as element that fractured by tensile stress, crushing due to compressive stress, plastic deformation, and creep. Modeling of longitudinal mild steels, transversal mild steels, and longitudinal prestressed strands elements used LINK8 elements. The forces acting on the elements were axial forces on the ends of the elements as shown in figure 2.  In the structure field, the equilibrium equation for the linear system is expressed as:

: load vector
In the nonlinear case, equation (1) could not be directly used. The iteration process was required to obtain a solution of the equation. In the ANSYS program, there were several methods that can be used to obtain convergent solutions. One of them was the Newton-Raphson method. This method is an iterative process in solving nonlinear equations. In this study, the method chosen for the ANSYS program was Full Newton-Raphson method, where the stiffness matrix was updated in each iteration as expressed in equation (2) and equation (3).

Modeling of Beam Column Subassemblages by Finite Element Methods
The beam-column subassemblage models were created by a nonlinear finite element program with varied values of PPR below and above 25%, while the concrete material structure was RPC and NC. PPR by 25% is the maximum value allowed as it had been presented in section 2. In the area of plastic hinges, the prestressed strands were placed unbondedly. The program input were the dimensions and details of the structure, as well as the stress-strain curves of each material that were parts of the structural models. The average compressive strength of RPC at 28 days for the program input was based on material experiments which will be elaborated in section 5. before. At the age of 42 days, the compressive strength tests were conducted because there was a lateral cyclic loading experiment of the prototype BCS-RPC-31.72. The test results are displayed in the form of curves in figure 6. The figure shows that the compressive strength (fc) of concrete was relatively the same since the age (t) of 4 days up to 42 days. The RPC average compressive strength at the age of 28 and 42 days were 120.65 MPa and 117.84 MPa, respectively.

Comparison of BCS-RPC Prototype and Finite Element Model Hysteretic Curves
The results of the BCS-RPC-31.72 prototype experiment were compared with the BCS-RPC-31.72 model. Figure 7 shows that the hysteretic curve of BCS-RPC-31.72 model was relatively close to the hysteretic curve of BCS-RPC-31.72 prototype with almost the same deflections () and loads (F). Figure  8 shows that the gradient of the backbone curve of the BCS-RPC-31.72 model was close to one of the BCS-RPC-31.72 prototype.

Behavior of BCS-RPC and BCS-NC Models
Modeling of BCS-RPC and BCS-NC generated hysteretic curves (load-deflection relation) as shown in figure 9. The BCS-RPC-21.39 model achieved drift ratio of 5.00% under push loading (positive) and 3.50% under pull loading (negative). The BCS-RPC-31.72 model achieved drift ratio of 5.00% both under push and pull loadings. Under push loading, the BCS-NC-21.09 and BCS-NC-32.02 models achieved drift ratio of 3.50% and 5.00%, respectively. While under pull loading, the BCS-NC-21.09 and BCS-NC-32.02 models achieved the same drift ratio of 3.50%. All BCS-RPC models had higher initial stiffnesses than all BCS-NC models as shown in figure 10. This was because the RPC has a higher compressive strength than NC at the same strain. The values of maximum drift ratio, maximum deformation, and yield deformation are shown in table 2.       Table 3 shows the values of ductility () and energy dissipation (Ed) of all models. The achieved maximum drift ratio affected the ductility and energy dissipation of each model. Despite BCS-RPC-31.72 model had PPR over 25%, it developed the highest ductility than other models because it was able to achieve the drift ratio up to 5.00% under push and pull loadings. It indicates that the PPR of 31.72% still allows the model to behave ductile. Under push loading, the values of the next highest ductility achieved by the BCS-RPC-21.39, BCS-NC-32.02, and BCS-NC-21.09 models, respectively. While under pull loading, the values of the next highest ductility achieved by the BCS-RPC-21.39, BCS-NC-21.09, and BCS-NC-32.02 models, respectively.  The modeling of partial prestressed beam-column subassemblages made of Reactive Powder Concrete (RPC) material was able to provide information of performance of prestressed beamcolumn subassemblage prototypes as proven by the hysteretic curve shape of the model was relatively close to the hysteretic curve of prototype test results. Then the model can be used as a platform for modeling the beam-column subassemblages made of Normal Concrete (NC).  Analysis of all of beam-columns subassemblage models made of RPC and NC showed that all BCS-RPC models had better performance in terms of strength, stiffness, ductility, and energy dissipation than all BCS-NC models.  The BCS-RPC-31.72 model that had PPR over 25% exhibited ductile behavior up to drift ratio of 5.00% under push and pull loadings and dissipate energy better than BCS-RPC-21.39 model which had PPR less that 25%.