NON-LINEAR ANALYSIS OF RC FRAMES WITH MASONRY INFILLS SUBJECTED TO COLUMN FAILURE

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1 Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal July 2016 Editors J.F. Silva Gomes and S.A. Meguid Publ. INEGI/FEUP (2016) PAPER REF: 6369 NON-LINEAR ANALYSIS OF RC FRAMES WITH MASONRY INFILLS SUBJECTED TO COLUMN FAILURE André Almeida 1(*), Eduardo Cavaco 2, Luís Neves 3, Eduardo Júlio 4 1 Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal 2 CEris, ICIST, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal 3 Centre for Risk and Reliability Engineering, University of Nottingham, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal 4 CEris, ICIST, Instituto Superior Técnico, Universidade de Lisboa, Portugal (*) andre.almeida@fct.unl.pt ABSTRACT This paper presents a non-linear FEM analysis of reinforced concrete (RC) frames, with and without masonry infills, subjected to a column loss as a result of an extreme unforeseen event. The objective is to assess the importance of non-resistant masonry walls and their contribution to the overall resistance and stiffness of RC buildings, as well as understand the failure modes associated with eccentric loading. The present analysis was performed using the Atena3D, a software directed to model RC and masonry elements. A RC frame without masonry model served as reference followed by a RC frame with a double leaf traditional brick wall. The numerical models presented a faithful simulation of the experimental tests capturing the evolution of cracking and the correct failure modes. Keywords: Reinforced concrete frame; masonry walls; robustness, non-linear FEM analysis. INTRODUCTION In different occasions RC buildings are subjected to unexpected loads that result from extreme events such as natural disasters, terrorist attacks, accidental explosions or vehicle impacts. Examples like the Ronan Point building (Cynthia Pearson and Norbert Delatte 2005) or the Bad Reinchnhall Ice-Arena (Munch-Andersen and Dietsch 2011) illustrate severe structural failures that were disproportionate to the loads and/or initial structural damage. However, literature also shows the opposite, buildings that are able to withstand damages beyond their theoretical capability, such as the case study presented by Tiago and Júlio (2010). A thirty year old RC building located in Coimbra, which a landslide caused the collapse of three exterior columns at the basement level, and yet, the building did not collapse. Usually, the resistant capacity of non-structural masonry walls is neglected during the design stage. However, it may be important to prevent the progressive collapse of a RC building when severely damaged. This study aimed at evaluating the masonry wall contribution in the global resistant capacity and stiffness of a RC frame, using non-linear FEM analysis. EXPERIMENTAL PROGRAM Experimental tests were performed to assess the influence of brick masonry in a reinforced concrete structure, both on the bare RC frame (Figure 1), and on the same frame infilled with

2 Symposium_23: Structural Robustness a double leaf masonry wall. As shown, the frame was pre-stressed against the strong floor and the shear wall on the left side and an ascending vertical displacement was imposed by a hydraulic jack on the right side. The frame reinforcement was overdesigned in order to allow a single frame to be tested with and without the masonry infill. Thus the infilled frame was firstly tested up to the masonry failure and without attaining plastic strains on the reinforcement. Then, the masonry infill was removed and the bare frame was tested up to the failure @100 mm 10@100 mm Hydraulic jack 5000 Fig. 1 - Experimental frame and test setup summary. FEM ANALYSIS FEM models A non-linear FEM analysis was performed, using the Atena3D software (Cervenka et al. 2005), to simulate the experimental tests previously referred to, aiming at understanding the failure mechanism, as well as the stress path and the materials influence in the overall stiffness and resistance. The first model to be assembled was the RC frame without masonry wall. Discrete elements were adopted to model each of the frame parts. For the RC frame, seven prismatic macro elements were used, considering a monolithically perfect connection in the elements interfaces. Three rigid elements were used, along with two pre-stressed external cables to replicate the experimental boundary conditions at the left side column. All other contacts with the shear wall and shear floor were assumed as fixed connections, as depicted in Figure

3 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Fig. 2 - Concrete frame macro elements and boundary conditions. The reinforcement bars, shown in Figure 3 were discretely placed according to the actual experimental frame detailed in Figure 1. At the right side edges of the concrete frame, transversal displacements were restrained to ensure lateral stability, mimicking what happened in the experimental frame. The second model consisted in adding a two pane ceramic brick wall, with 150x200x300mm Bricks and 110mmx200x300mm Bricks, respectively. Material Properties The material properties of steel, concrete and masonry considered in the FEM model correspond to the mean values obtained in the experimental tests. For the concrete frame, the Atena3D internal algorithm was used to generate a concrete with the mean compressive resistance of 35.5 MPa. For the steel reinforcement, a bilinear model, with hardening, was used with a yield stress of 540 MPa and a Young s modulus of 200 GPa. The ceramic brick material was defined as a cementitious material (3D Nonlinear Cementitious 2) with a mean compressive strength of 2.5 MPa, a tensile strength of 0.27 MPa and a Young s modulus of 6.55 GPa. These characteristics took into account the mortar contribution to the global stiffness and strength. The (post failure) residual strength was also increased to reckon the confinement given by the mortar. Following the observations of the experimental tests, the failure was assumed to start at the ceramic elements, thus the interfaces between bricks were considered with perfect connection. Test setup rigid elements such as spreader steel plates for load application, the top and bottom pre-stress anchorages and the pre-stress external cables were modeled as linear elastic steel

4 Symposium_23: Structural Robustness Fig. 3 - Discrete steel reinforcement bar elements. Analysis description To accurately replicate the initial test conditions, the boundary conditions were not applied at the same time. In order to apply the pre-stress force to the external cables, the vertical restrictions at the frame s side surfaces were applied after the pre-stress application. Once the pre-stress reached the desired value, the fixed supports were implemented and the vertical displacement imposition was initiated. The pre-stress load was 300kN, applied in 10 steps. An 8 node element Brick FE mesh, was used for both concrete and brick elements, while a 4 node element Tetra mesh was used for the rigid steel plates. Concrete frame s mesh size was chosen so that at least eight mesh elements were present in the beam and column s thickness. Several iterations showed that this is a good comprise between result accuracy and computation resources. For the bricks, larger mesh elements were used, in a total of twenty four by each whole brick. For the solution convergence, Newton-Raphson method was used with an allowed number of iterations per step of 200. RESULTS The load-deflection comparison of the FEM and the experimental bare RC frame is depicted in Figure 4, where a good approximation can be seen for both the stiffness and load capacity. The failure mode was also accurately modelled and consisted on the development of four plastic hinges at the frame joints on the beams side. Figure 5 shows that the cracking pattern is according to the one obtained experimentally. The absence of cracks in the left side column is due to the fixed connections to the shear wall and strong floor and the pre-stress applied at the top of the column

5 Proceedings of the 5th International Conference on Integrity-Reliability-Failure 350,00 300,00 250,00 Load [kn] 200,00 150,00 100,00 50,00 Experimenta l ,00 20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 Vertical displacement [mm] Fig. 4 - Load-displacement comparison chart for the frame only models. Fig. 5 - Cracking pattern near failure. The load-deflection comparison of the FEM and the experimental masonry infilled RC frame is depicted in Figure 6. The comparison of the two results show that this is a significantly more complex structure, and the brittle behaviour of the masonry elements is extremely difficult to replicate numerically. Nevertheless, a good agreement is obtained in the elastic range, and the ultimate load of the frame is well approximated. It is also visible for both cases, the cracking of the first masonry strut

6 Symposium_23: Structural Robustness Load [kn] Experimental FEM Vertical displacement [mm] Fig. 6 - Load-displacement comparison chart for the frame and masonry models. Figure 7 shows Von Mises stresses and cracking pattern for increasing load steps. For all steps, a compressive strut is visible. Throughout the test, cracking occurs and provides local stress relief, changing the stress path to a different compressive strut. Failure occurs when no available paths were to be found. Figure 8 shows a parametric FEM study that shows the performance predictions when the interface characteristics between brick elements and the brick compressive resistance are reduced. Results show that if an efficient connection by the mortar is not granted, the frame behaves as there is no masonry wall. Also, as expected, if the masonry compressive strength is reduced, cracking and masonry failure occurs for lower loads and consequently, lower displacements. It s important to note that when masonry failure occurs, the RC frame resistance persists. CONCLUSIONS From the developed work, the following conclusions can be drawn: - The presence of non-resistant masonry walls did not increase the ultimate frame resistance, although increasing stiffness and energy dissipation. However it must be highlighted that in this case reinforcement was significantly overdesigned in order to allow the frame to be tested twice, with and without the masonry wall without attaining plastic strains between tests. It is believed that for lower reinforcement ratios the masonry walls may increase also the frame strength; - A strut is formed within the wall, increasing resistance for smaller displacements. When the main stress path fails, stresses redistribute in order to find a new path. This phenomenon is repeated until failure due to the lack of available flow paths; - The interface efficiency is crucial to the masonry contribution to the overall performance; - Masonry s compressive strength influences the global structural resistance;

7 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Displacement: 12mm Displacement: 15mm Displacement: 18mm Displacement: 22mm Displacement: 24mm Displacement: 30mm Fig. 7 - RC frame and masonry Von Mises stresses and cracking pattern for several load steps (Red: 0 MPa; Dark Blue: 4MPa)

8 Symposium_23: Structural Robustness Load [kn] FEM Weak interface connection FEM FEM Fc = 0,7MPa 0 0,00 10,00 20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 Vertical displacement [mm] Fig. 8 - Influence of a reduced brick compressive strenght (Fc) and interface resistance compared with the original model (FEM) ACKNOWLEDGMENTS The authors gratefully acknowledge the funding by Ministério da Ciência, Tecnologia e Ensino Superior, FCT, Portugal, under grants of PTDC/ECM-COM/2911/2012. REFERENCES [1]- Cervenka, V., Jendele, L., and Cervenka, J. (2005). ATENA Program Documentation, Part 1: Theory. Praha, Czech Republic. [2]-Cynthia Pearson, and Norbert Delatte Ronan Point Apartment Tower Collapse and Its Effect on Building Codes. Journal of Performance of Constructed Facilities 19 (2): doi: /(asce) (2005)19:2( ). [3]-Munch-Andersen, Jørgen, and Philipp Dietsch Robustness of Large-Span Timber Roof Structures - Two Examples. Engineering Structures, Modelling the Performance of Timber Structures, 33 (11): doi: /j.engstruct [4]-Tiago, P., and E. Júlio Case Study: Damage of an RC Building after a Landslideinspection, Analysis and Retrofitting. Engineering Structures, Learning from Structural Failures, 32 (7): doi: /j.engstruct