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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)

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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

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Proceedings of the 5th International Conference on Integrity-Reliability-Failure

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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.


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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.


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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.

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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;

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Displacement: 12mm Displacement: 15mm



Fig. 7 - RC frame and masonry Von Mises stresses and cracking pattern for several load steps

(Red: 0 MPa; Dark Blue: 4MPa).


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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.

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FEM Weak interface connection

FEM

FEM Fc = 0,7MPa

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