Investigation on the strength of spandrels in masonry façades
Earthquake is probably the most dangerous natural phenomenon that can threat the integrity of Unreinforced Masonry structures, putting in danger human lives and economical value. During the observation of past earthquakes the out of plane collapse mechanisms have been identified as the most dangerous. The observation and categorization of those mechanisms have been proved valuable for the implementation of interventions that aim to the improvement of the connection between orthogonal walls and floor diaphragms, which will result to a desired box behavior of the masonry structure. Once the out of plane mechanisms have been prevented the in plane behavior of the masonry façades is the critical factor that defines the overall capacity of the masonry structure.
Although the in plane behavior of piers in masonry façades has been studied and identified by several experimental, numerical and analytical campaigns, limited knowledge exists about the strength of masonry spandrels. The evaluation of their strength is based so far on available formulations derived for pier panels and provided by existing codes like Eurocode 8 (CEN) 1998). Those codes allow the spandrel panels to be included in the evaluation of the masonry capacity only in the presence of tie-rods, or reinforced concrete ring floor beams, at the top and lintels well-bonded to the adjoining piers at the bottom. Other codes like FEMA 356 ((ATC-43 Project) 1998) and New Zealand guidelines (NZSEE 2006) allow the calculation of the spandrel strength based on the strong spandrel-weak pier assumption. This case is not suitable for existing masonry buildings, due to the presence of just wooden or steel lintels without adequate anchorage length to support gravity loads. The assumption of weak spandrel-strong pier is also unsuitable, since it leads to full uncoupling between piers and spandrel.
The last years several experimental campaigns have been executed in order to investigate the strength of masonry spandrels and its contribution to the behavior and capacity of masonry façades. In addition several numerical approaches have been implemented to these cases, as well as known and new analytical expressions to validate their accuracy. These studies revealed that the strength of masonry spandrels cannot be neglected and has an important role in the in plane resistance of unreinforced masonry façades.
In this thesis, the author Myronas Drygiannakis aims to assess the strength of spandrels in masonry façades against horizontal loads, by means of different numerical methods adequately calibrated using experimental reference results.
Masonry façades: Type of elements and Seismic behavior
In most unreinforced masonry buildings, façades constitute the main vertical structural member. Therefore their behavior during seismic action is critical for the overall performance of the whole structure. In order to evaluate the seismic capacity of unreinforced masonry buildings the strength of façades is an important factor.
Masonry façades can be divided in two different categories of structural elements – piers and spandrels:
- Piers are the vertical structural elements that are responsible for the bearing of the vertical loads of a structure.
- Spandrel is the portion of the masonry that exists between the openings of two adjacent floors and couples two adjacent piers together. In existing structures there are several types of spandrels. Their categorization is made by the different geometry (Figure 1), types of lintels in the lower part of the spandrel, as well as the type of the floor slab between two adjacent floors and its relative position with the spandrel.
As regards the lintel type, this can be a linear element made of bricks, stones, wood or concrete, or consist of masonry or stone arch (Figure 2).
The behavior of masonry façades due to seismic action can be divided in two main categories according to the direction of the seismic action: out of plane and in plane failure modes.
- Out of plane failure modes
Out of plane collapse mechanisms take place in masonry buildings, where there is not adequate connection between orthogonal walls. Also the presence of non-rigid floor diaphragms, increase the probability of such failure modes. Typical collapse mechanisms have been identified by researchers, from observation of damages in masonry buildings during strong earthquakes. Some of the most characteristic collapse mechanisms are illustrated in Figure 3, Figure 4 and Figure 5.
- In plane failure modes
In case of strong connection between orthogonal walls and stiff rigid floor diaphragm, the out of plane failure is prevented and the damage is concentrated in the shear walls parallel to the direction of the seismic action. The damage is often observed to be concentrated in the piers, the spandrels or both types of elements.
(Tomaževič 1999), indicates that in the plane of the walls, bending and shear cause horizontal and diagonal cracks, respectively. In-plane mechanisms induce the typical shear damage, which often is not sufficient to lead to structure collapse. The limited damage in Figure 6 is due to the effective strong connection among the structural components and the presence of floors able to transmit the horizontal forces to shear walls, both characterizing the favorable ―box‖ behavior of buildings under seismic actions. Unfortunately the layout of historic buildings, their discontinuities, the changing in time, lack of maintenance etc., led frequently to different behavior.
Structural analysis of masonry façades
The research that was performed regarding the state of the art led the author to some valuable conclusions about the selection of the appropriate strategy for this thesis.
First of all the evaluation of the spandrel strength in masonry façades is a very interesting and important topic concerning the estimation of the in plane capacity of masonry façades. Several experiments have been performed the last years about this topic, the amount of different material type and patterns though, is not yet allowing the adequate understanding of this problem. Further investigation should be performed with the assistance of structural analysis techniques. Taking into account the review about the different structural analysis approaches that are available, the FE macromodelling approach proved to be the most appropriate in terms of accuracy and computational cost.
Another modeling approach worth investigated is the micromodelling approach, since it has proved to obtain more explicit results. Due to the complexity of these techniques and the requirement of several material properties as an input, their calibration based on appropriate benchmark problems is considered necessary.
Finally, another important aspect is their application with both academic and commercial software in order to be reliable but also applicable in engineering practice.
The process of creating and calibrating the numerical model as well as the parametric study and the comparison with similar numerical approaches led to the adoption of several conclusions and recommendations regarding the structural analysis of masonry façades:
- The Finite Element macromodelling approach consists a reliable and explicit tool for the estimation of the in-plane behavior of masonry façades, requiring relatively low computational cost.
- The Finite Element method requires the estimation of several material properties from experimental tests as well as their influence through the execution of an analytical parametric study.
- The proper simulation of the timber lintel-masonry interface is significantly influencing the behavior of masonry spandrels.
- More explicit and accurate methodologies such as micromodelling, can lead to less accurate results if physical parameters such as the lintel influence are not defined properly.
- The smeared crack approach leads to diffused crack pattern, which consequently can lead to underestimation of the spandrels maximum capacity.
- Crack tracking techniques can enhance the possibilities of the macromodelling approach.
The attempt of a micromodel development in this thesis provided a series of valuable conclusions:
- The micromodelling approach is giving satisfying results regarding the damage pattern of portal frames. Nevertheless a diffused crack pattern is also obtained as in the macromodelling technique.
- The force-displacement diagram was not able to be defined properly, due to the shear failure of the masonry spandrel for a lower horizontal displacement than the experimental case. This drawback could not be overcome due to the limited number of parametric analysis, which did not allow to define properly the influence of all the material properties used for the model.
- The computational cost of the micromodelling approach as well as the need for definition of a large number of material properties is making its application extremely difficult and time demanding.
- Besides its drawbacks a calibrated micromodel can provide very accurate results for the behavior of masonry façades. Further investigation and research should be executed to overcome the difficulties of its application.
Application of the Macromodel to a new test
The macromodel that was created for the purposes of this study proved to be a reliable tool for the assessment and the evaluation of the behavior of masonry façades subjected to in-plane loading. Its application to the ongoing experimental campaign of the Technical University of Catalonia gave a first idea about the expected load capacity and damage pattern. Although it manage to estimate a horizontal capacity of maximum 173 kN, less than the actuator maximum capacity of 250 kN, nevertheless it did not gave a reliable estimation of whether or not the spandrel is going to fail in shear. The shear failure of the spandrel proved to be connected with the propagation of the horizontal crack in the left pier. The crack pattern proved to be influenced by the geometry, the vertical loading and the tensile strength of the masonry.
Since the tensile strength of the masonry as a composite material is not easy defined, the safest method for continuing this study would be the use of more analytical techniques or different geometry configurations in order to obtain a numerical model with shear failure of the spandrel. For those studies, the maximum tensile strength, resulted from the diagonal compression tests, is proposed to be used as an input, to get as conservative results as possible.
The present study managed to apply a variety of different methods for the evaluation of the strength of masonry spandrels. Valuable conclusions that were derived from this thesis are the following:
- The state of the art review regarding this topic was valuable to highlight the importance of spandrels in the structural performance of masonry buildings. Also the conclusions from the state of the art leaded to the appropriate selection of the modeling strategy that was followed.
- The macromodelling technique proved to be able to estimate the behavior of existing masonry façades. Some drawbacks of this method could be the obtaining of a diffused crack pattern as well as an underestimation of the maximum strength capacity of 6.8%. Nevertheless it provided a good approximation of the response of portal frames to in plane loads.
- The micromodelling technique that was applied proved to be accurate in terms of damage pattern but not in terms of load-displacement relation. The increased demand for input parameters and its higher computational cost made this approach much more difficult to handle.
- The comparison between the different methods applied showed that the macromodelling technique is the most suitable technique for investigating masonry spandrels and for that reason it was applied to the ongoing experimental campaign of UPC, with satisfying estimations.
- The modelling of the timber lintel as well as its connection with the spandrel is very influential for the nonlinear behavior of masonry spandrels. Therefore it should be executed with great caution.
- Some of the properties of the interface between timber lintel and masonry that the numerical model requires as an input (e.g. stiffness), are difficult to be estimated since it can be influenced by unpredictable factors as the construction process and its quality.
Due to the limitation of time and significant computational effort involved in running each analysis on this numerical model, several areas that need to be addressed by further research have been identified:
- An extensive parametric analysis should be executed in order to identify the different parameters required for the simplified micromodelling approach. Great caution should be given for the interface parameters, since they are a simplification of the joint mortar. Therefore defining a physical meaning for their properties would be a challenging task.
- Further investigation, experimental and numerical, should be performed about the interaction between timber lintel and masonry spandrel, which proved to be very influential for the total response of masonry portal frames.
- The reliability of the existing analytical expressions should be defined with their application on existing experimental campaigns.
- The application of an equivalent frame method for masonry spandrels, using the existing analytical equations as a failure criterion, and its comparison with a Finite Element model would be valuable for further research. With this method the reliability of analytical expressions proposed by codes and bibliography could be defined. Since this method is widely used in engineering practice it would be important to estimate how much the simulation of the spandrel component is affecting the in plane capacity of unreinforced masonry buildings.