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Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016
Editors J.F. Silva Gomes and S.A. Meguid
Publ. INEGI/FEUP (2016)
-1367-
PAPER REF: 6369
NON-LINEAR ANALYSIS OF RC FRAMES WITH MASONRY INFILLS
SUBJECTED TO COLUMN FAILURE
André Almeida1(*)
, Eduardo Cavaco2, Luís Neves
3, Eduardo Júlio
4
1Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal 2CEris, ICIST, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal 3Centre for Risk and Reliability Engineering, University of Nottingham, Faculdade de Ciências e Tecnologia,
Universidade Nova de Lisboa, Portugal 4CEris, ICIST, Instituto Superior Técnico, Universidade de Lisboa, Portugal (*)Email:[email protected]
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
Symposium_23: Structural Robustness
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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.
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 2.
2012
10@100 mm
10@100 mm
203 16 2 162 20 3
Hydraulic jack
2550
500
705000
5000
780
Proceedings of the 5th International Conference on Integrity-Reliability-Failure
-1369-
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.
Symposium_23: Structural Robustness
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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.
Proceedings of the 5th International Conference on Integrity-Reliability-Failure
-1371-
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.
-
50,00
100,00
150,00
200,00
250,00
300,00
350,00
- 10,00 20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00
Loa
d [
kN
]
Vertical displacement [mm]
Experimenta
l
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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;
0
50
100
150
200
250
300
350
0 5 10 15 20 25 30 35 40
Loa
d [
kN
]
Vertical displacement [mm]
Experimental
FEM
Proceedings of the 5th International Conference on Integrity-Reliability-Failure
-1373-
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).
Symposium_23: Structural Robustness
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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. 2005. ‘Ronan Point Apartment Tower Collapse and
Its Effect on Building Codes’. Journal of Performance of Constructed Facilities 19 (2): 172-
177. doi:10.1061/(ASCE)0887-3828(2005)19:2(172-177).
[3]-Munch-Andersen, Jørgen, and Philipp Dietsch. 2011. ‘Robustness of Large-Span Timber
Roof Structures - Two Examples’. Engineering Structures, Modelling the Performance of
Timber Structures, 33 (11): 3113-3117. doi:10.1016/j.engstruct.2011.03.015.
[4]-Tiago, P., and E. Júlio. 2010. ‘Case Study: Damage of an RC Building after a Landslide-
inspection, Analysis and Retrofitting’. Engineering Structures, Learning from Structural
Failures, 32 (7): 1814-1820. doi:10.1016/j.engstruct.2010.02.018.
0
50
100
150
200
250
300
350
0,00 10,00 20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00
Loa
d [
kN
]
Vertical displacement [mm]
FEM Weak interface connection
FEM
FEM Fc = 0,7MPa