Numerical modelling of the seismic behavior of timber-framed structures
The main aim of this thesis, by the author Sonia Guerra Pinto is to obtain a better understanding of the mechanical behavior of Pombalino structures based on finite element modeling on the OpenSees program.
Numerical modelling of the seismic behavior of timber-framed structures
Timber Structures have been built worldwide having antiquity that dates 14.500 BP and it is being used until nowadays. Timber Structures have proven to have excellent seismic performance, as testified by the fact that in seismic regions houses and other structures are built in timber. It is interesting to see the diversity of constructive processes throughout the globe, every country adapts the timber structures according to their knowledge and construction types of materials available, and this also includes different infill types which are mostly composed of masonry or earth.
Although there is a large amount of information regarding timber structures throughout history, the present literature review will focus on historic timber framed structures which are dated since the 17th Century in Europe (Spain) and since the 16th Century in South America, specifically in Peru.
This type of framing is assigned different names which are associated to a specific constructive system that varies according to the region in which it has been built, for example:
- In territories from Southern Central Anatolia to the Ottoman Balkans including Black Sea Coasts of Romania, Crimea, Bulgaria, FYR Macedonia, and Bosnia Herzegovina to Greece in the West we can find 'hımıs';
- In Spain the timber framed construction system was called 'entramado o telar';
- 'Borbone' Constructive system is found in the Calabrian region of Italy;
- 'Dahjji Construction' in Pakistan;
- 'Pombalino' Constructions in Lisbon, Portugal;
- In South America we can find 'Quincha' Buildings in the coastal area of Perú;
- 'Adobillo' Structures in the Central Zone of Chile;
- ´Gingerbread Houses´ and 'Kay Peyi' in Haiti.
Connections and Infill of Timber Framed Structures
General Disposition and Components of Timber Framed Structures
Pombalino Case Study
Pombalino construction was standardized to be used for the reconstruction of Lisbon after the 1755 earthquake, but its use was not limited to Lisbon. Mass production of building components, a basic principle of Pombaline architecture in Portugal was also used in Vila Real de Santo Antonio, and in many other Portuguese cities. The form construction of these buildings was very similar to that of Lisbon, the party and exterior walls being in stone, while inside there were timber framed partition walls with St. Andrew crosses incorporated to them. Arches in bricks were used to tie the foundations together and for some walls.
The plan of Santo Antonio, as in Lisbon, consisted of a rectangle, with one of the long sides facing the river, to the east. The rectangle was cut by 5 streets in a North-South direction and orthogonally in an East–West direction. All the streets were the same width and they contained 43 blocks; 32 of which were identical in size, being 240 palms by 100. In Vila Real, there are four quite distinct architectural types: the river front buildings (Figure 13), the buildings in the square (Figure 14), the single storey houses with towers, and the single storey houses without towers. The walls of the residential floor had an anti-seismic wooden structure incorporated into them, similar to that seen in the Pombalino quarter in Lisbon. The roof structure was very simple and repetitive, covered by wooden boards on which the tiles were laid.
Behavior of Timber framed Structures under Seismic Loads
Studies show that timber structures behave very well under seismic loads, as following:
- 2010 the Haiti earthquake has revealed that traditional construction techniques have value in resisting earthquakes;
- Ambraseys & Jackson state that after the 1509 Istanbul Earthquake, the Ottoman authorities prohibited masonry and enforced the construction of timber-frame houses, claiming that masonry was responsible for most of the casualties produced by the earthquake. By the end of the century the city was almost entirely built-in wood;
- For a set of earthquakes between the beginning of the 20th century and 1980 in Turkey and Greece, it is stated that that 'the number of people killed per 100 houses destroyed by earthquakes of magnitude equal to or greater than 5,0 is only around 1 for timber constructions;
- In Peru the Quincha technique reached its peak after the 1687 earthquake when a law was passed ruling that quincha must be used for the upper storeys of any building greater than a single storey in height. Today a number of these buildings survive, most dating from the 18th and 19th centuries, with quincha in the upper storeys, and the first storey in adobe or fired brick;
- In the Calabrian region of Italy after the 1783 earthquake the government ruled by Borbone dynasty enacted what is considered the first European anti-seismic code; called 'Sistema costruttivo borbonico' that amongst other measures enforced the presence in the new constructions or repair of damaged buildings, of a timber skeleton as an essential requirement to ensure safety;
- In Portugal, the Pombalino buildings were introduced after the 1755 catastrophic earthquake as a structural solution that would provide the required seismic resistance. These were built in quarters, each block comprising an average of 10 buildings, it was arguably the first case in history of an entire town built to provide seismic resistance to its buildings.
Several studies were done to study the following:
- Timber Elements Behavior
- Infill Behavior
- Multi-Scale Behavior
Damages by Biological Decay
Güchan indicates that some damages in timber structures produced by earthquakes are due to biological degradation. Most of the significant earthquake damage to these structures was often related to pre–existing damage caused by termites, and in some instances other forms of wood rot. It is determined that that the natural timber degradation causes damping ratios to increase and secant stiffness to decrease, leading to higher periods when submitted to seismic loads. The roof and the ground floor are identified as the main susceptible deterioration focuses, due to the water infiltrations.
- OPENSEES PROGRAM and general element considerations for the preparation of the model, such:
- Model Builder:
- Non-Linear Beam Column Elements: The model builder constructs as in any finite element analysis, the analyst's first step is to establish the nodes and its coordinates, afterward the column, beam, diagonal, and girders are established as displacement beam column, truss element, linear beam column, plastic hinge, among others
- Shell Element: This command is used to construct a plane 2D mesh object which can be represented as a Quadrilateral Element, Shell Element, Bbar Plane Strain Quadrilateral Element, or Enhanced Strain Quadrilateral Element
- Section Command: The elements of the studied model will be considered as an Elastic section
- Linear Co-Ordinate Transformation: The linear co-ordinate transformation object command performs a linear geometric transformation of beam stiffness and resisting force from the basic local system to the global coordinate system
- SAWS Uniaxial Material: SAWS provides the implementation of a one-dimensional hysteretic model developed as part of the CUREE Caltech wood frame project
- Domain, Recorder, and Analysis
- EXPERIMENTAL SURVEY
The thesis elaborated by Goncalves aimed at evaluating the seismic vulnerability of the Pombalino buildings throughout an extensive experimental campaign consisting of a series of cyclic and dynamic tests. The experimental program consisted in developing a prototype, representative of the current characteristic Frontal wall, which was subsequently used for the construction of full-scale experimental models. From the results obtained from this survey, the material characteristics and general geometry of the model will be taken and analyzed.
- NUMERICAL MODEL CONSIDERATIONS
The current model was elaborated based on numerical model performed by Lukic and modified according to the experimental survey completed by Goncalves in OpenSees Program.
- SENSITIVITY ANALYSIS
The current model will consider the beam, gird, column, and diagonal elements as trusses because we want the nonlinearities and model dynamics concentrated on the central element. The model properties will be modified, and iterations will be done in order to obtain a similar envelope curve for the Cyclic Analysis. The masses will be concentrated on the nodes, so this may lead to important differences in the calibration results. The load pattern will be represented on nodes 6 and 9.
- Final Numerical Model calibration
The analysis will focus on obtaining similarities in the cyclic envelope curve.
It is possible to calibrate a model based on experimental survey, although certain issues still have to be worked on, such as the calibration of the envelope curve and frequencies simultaneously. The application of a distributed mass along the beams could resolve this issue, but this would have to be proven in a new numerical model. Also, in the final model the beam, columns, and girders were considered with large areas so they could work as trusses and concentrate the non-linear behavior in the central element, this factor will also influence the original behavior of the structure. Overall, it is important to highlight that a numerical model can be done and calibrated from an experimental survey. These properties will be used later on to elaborate a real scale building and analyze its dynamic properties.
REAL CASE STUDY
The properties of the macromodel calibrated were used as a basis to elaborate a numerical model of a global pombalino building.
– Case Study – Lots 210 to 220 of Rua (Street) da Prata
The plan that created the downtown Pombalino was defined by a regular scheme of streets and squares. Each square was divided into lots of buildings with different front widths, but maintaining the same depth and height as shown in Figure 57, which also shows the studies building. The total area of the square was 2.000 m2, varying the areas of the lots between one hundred and three hundred square meters.
The studied lots have a very wide façade, In terms of the initial plan, the width of seventeen meters corresponds to six modules of the facade, each having 2.8 meters. In the Floor Plan (Figure 58) there are two shops and the entrance of the building. The upper floors (2nd to 4th) are composed of a floor-plan type, in which we can find: on the first floor, a row of rods and a commercial store; In the second, an office; In the third, housing; In the fourth, a house with a balcony; The fifth floor is composed of two attics.
Description of Structure
A specific construction type with a wooden structure (gaiola) was used in the Lisbon reconstruction, its origin is unknown (though similar construction was already present in
Portugal and in Lisbon in particular and it behaved well during the earthquake), but considered at the time as being the most appropriate to resist earthquakes. Gaiola can be described as a structure constituted by a skeleton of timber with infill of traditional masonry; in case of a seismic hazard and with the probable disintegration and collapse of the masonry, the wooden structure would remain standing.
For the development of the real model:
- Shell Elements we considered for the external walls, due to the great amount of masonry walls on the ground floor and the perimeters of the building;
- Rigid Diaphragms were considered on the first-floor level, due to the important stiffness of the masonry volts on the ground storey, and the macro-model to introduce the frontal wall.
- First macro shells were considered in the façade and lateral sides of the building and afterward smaller shells of maximum 50×50 cm were designed in the lateral shell elements of the buildings.
The coordinates, elements, and nodes of the shell elements were elaborated by a simplified model in GID program which was later imported to OpenSees.
It is possible to elaborate a simplified numerical model based on experimental results in OpenSees Program, but we must previously do a rigorous calibration process for the results to be accurate. The original dimensions and properties of the structure can be modified to obtain the same results as in experimental surveys, considering an error not larger than 10%.
The modification of the materials' properties can be done throughout a sensitivity analysis, in which parameters are changed and an iteration process is performed to understand the variation and the effect of each parameter on the envelope curve of frequency as appropriate.
The macro-modelling of elements is a useful tool that allows the user to obtain results of the dynamic behaviors of building in a reduced amount of time, due to the small amount of computational resources that it needs in order to perform the analysis.
When elaborating a model (shell, beam-column, or combined) it is recommended to elaborate it from the beginning as such, node superposition is an important issue in the change of one model typology to another and leads to important mistakes that are reflected in iteration problems in OpenSees called 'Lackpack' which is traduced as a connectivity issue, the major issue of this is that it is not possible to localize the error and this can become a complicated matter in large scale models that have large amounts of nodes and elements. It is recommended to combine programs to obtain easier node/shell modelling of a large structure. Albeit OpenSees has visualizers, the coordinates have to be set manually, which is a very time-consuming process. In this case, GID was used to model the shells, which simplified this process, obtaining automatically the elements, nodes and their coordinates.
Macro-modelling is a viable option for representing the overall response of timber and mixed timber framed structures. It is possible to elaborate a real scale macro-model of an existing building taking information from previously calibrated numerical models of similar characteristics and materials. This information can be used afterward in seismic assessment of real scale buildings. The change of materials in a structure will vary significantly the dynamic response of it. In the studied case the rigidity of the masonry walls consequently increases the major stress concentration on timber frame (non-braced) elements. Although it is shown that gaiola (mixed timber masonry) structure has an important contribution in absorbing the stresses.
Overall, the studied pombalino building has good seismic behavior in which the high stresses are concentrated on the top section of the building. This is a good indication because the structure will not fail from the middle floors, although it is important to consider the large stress concentrations on the 3rd floor. Seismic assessment can be performed from the obtained results to reduce the stress in this section (it could be recommended to include some longitudinal gaiola bracing element).
It is recommended that the calibration process of the experimental survey should improve, in what respects the calibration of the frequencies and cyclic envelope curve simultaneously. In order to do this, masses can be evaluated as distributed loads across the beams. It is important to evaluate the timber structure behavior in the pinching stage, to do this the connections of timber frame must be considered. The partition walls of the studied pombalino building may have a structural function that is not mentioned in the literature of Mascarenhas (2005), further investigation should be done to obtain more detailed information regarding this matter.
A calibration process of the shell elements before applying them to a real scale model is necessary in order to verify the concordance of the applied materials, and also to apply properly a pushover analysis. It can be useful to have certain parameters of the dynamic response (modal shape, frequencies) of similar real scale structures to prove that the elaborated model has a realistic dynamic behavior.
The real scale structure can be submitted to multiple simulations of various earthquakes. It is recommended to perform a cyclic test analysis to obtain more parameters for a more adequate seismic assessment.