Evaluation of the wooden structural elements in the Behavior of Traditional masonry buildings Mohammad Reza Chenaghlou Sahand University of Technology Mohammad Kheirollahi Sahand University of Technology Yaser Shahbazi (  [email protected] ) Islamic Art university Mohammad bagher Kabirsaber University of Tehran Research Article Keywords: unreinforced masonry walls, seismic vulnerability, nonlinear static analysis, performance level, behavior coe cient Posted Date: September 9th, 2022 DOI: https://doi.org/10.21203/rs.3.rs-2034921/v1 License:   This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Evaluation of the wooden structural elements in the Behavior of Traditional masonry buildings Mohammad Reza Chenaghlou1, Mohammad Kheirollahi 2, Yaser Shahbazi3*, Mohammad bagher Kabirsaber4 1 Professor of structural engineering, Faculty of civil engineering, Sahand University of Technology, Tabriz, Iran, [email protected] 2 PhD of structural engineering, Faculty of civil engineering, Sahand University of Technology, Tabriz, Iran, [email protected] 3 Associated professor of smart structures and architectural technology, Faculty of architecture and urbanism, Islamic Art university, Tabriz, Iran [email protected] 4 Assistant professor of architectural engineering, Department of Architecture, School of Architecture, University of Tehran, Tehran, Iran [email protected] Abstract Most residential buildings in Iran are constructed from unreinforced masonry walls (URM) which are often characterized by high seismic vulnerability. The majority of these structures were designed only for the gravity loads; therefore, they don’t have adequate resistance and ductility against horizontally-applied loads such as those induced by earthquakes. When these structures are subjected to lateral loads applied by moderate and strong earthquakes, they collapse completely, causing massive death tolls and extensive losses. Iranian seismic history has shown that the majority of masonry buildings were completely destroyed under severe earthquakes, with a number of buildings with timber laces remaining safe and stable. In the past, timber framed masonry structures were built with no design guidelines and were solely based on the experience of traditional Iranian architects. Also, in the construction of these buildings, a form of wooden bracing system is used as the load carrying system. As a result, the buildings often show suitable seismic performance under severe earthquakes. Therefore, the main goal of this study is assessing the effects of timber ties on the seismic behavior of URMs. For this purpose, the plans of Iranian traditional buildings were reviewed and two groups of masonry models were selected to evaluate their seismic vulnerability. Nonlinear static analyses were performed on the models. The results demonstrated that confining masonry walls with timber increases the stiffness and capacity of the studied models. In addition, the performance level of the studied models can be modified from Collapse Prevention (CP) to Life Safety (LS). Also, the results showed that adding timber laces significantly increases the behavior coefficient of the masonry walls. It can therefore be concluded that timber laces significantly influence the performance of masonry structures. Keywords: unreinforced masonry walls, seismic vulnerability, nonlinear static analysis, performance level, behavior coefficient. 1. Introduction Masonry structures are often known for their high seismic vulnerability. The majority of these structures were designed for gravity loads, meaning that they do not have adequate resistance and ductility against horizontally-applied loads such as earthquake loads. When these structures come under the influence of lateral loads induced by moderate and strong earthquakes, they can go through complete collapse, which can be the cause of massive death tolls and extensive losses. Recent earthquakes, such as those in Bam, Varzghan, and Kermanshah (in Iran), have highlighted the high vulnerability of these structures against seismic loads. There are several instances of traditional structures with timbers and masonry infills that remained relatively undamaged and are *Corresponding Author still standing. During the Varzghan earthquake, which occurred on the 11th of August, 2012), most masonry, reinforced concrete, and steel structures collapsed, whereas the buildings in the Ushtubin village (located in Jolfa, East Azerbaijan province) maintained their structural integrity. Field observations showed that the buildings in the village, even though simple, are generally wellconstructed and intelligently-designed. The timber elements were used in the external masonry walls of these buildings as horizontal and vertical ties and fastened the walls together. As a result of this, buildings were able to resist against the earthquake. This system can efficiently reduce the seismic vulnerability of masonry walls. Similar approaches have been used in other villages of Tabriz in low-cost buildings that are composed of timbers, various materials such as bricks, stones, and mud. The desirable seismic behavior of these systems has attracted the interest of researchers to investigate the structural performance of timber-masonry walls. Also, this system can be introduced as a method to retrofit different types of masonry walls. Doudoumis, 2010 [1] proposed an approach for modeling timber-masonry walls with sufficient accuracy. Analysis results showed that the contact boundary conditions at the timber-masonry interfaces, the arrangement and orientation of the timber diagonal bracings, as well as the construction details at the joint connections, can considerably affect the overall response of the structure. Dutu A. et al., 2016 [2] studied the interaction between timber elements and masonry walls via experimental investigations. The results showed the significant influence of timber elements on the seismic behavior of masonry walls. Kouris and Kappos, 2012 [3] performed non-linear numerical analyses on traditional timber-framed walls. Also, experimental works have been carried out to evaluate the strengthening techniques used to retrofit timber-framed walls. Aktas et al. [4], in 2017, studied the in-plane cyclic performance of traditional Turkish timber-framed walls considering different infill types. In 2014, Vieux-Champagne et al. [5] performed tests on Haitian timber-framed walls. Moreira et al. [6] studied the seismic retrofit of wall-to-floor connections of masonry buildings with wooden diaphragms. The results demonstrated that the retrofitting approach increases the capacity, displacement, and energy dissipation of the masonry structures. Poletti El., 2015 [7] assessed the seismic behavior of framed walls with different types of infill. Static cyclic tests were performed on unreinforced timber-framed walls in order to study their seismic capacity in terms of strength, stiffness, ductility, and energy dissipation. The experimental results obtained showed that the infill increases the seismic capacity parameters. In 2015, Steiger et al. [8] carried out research on the connections and the strengthening of timber structural members with glued-in rods (GIR). In that study, existing design recommendations and a theoretical approach were applied to estimate the load-carrying capacity of the studied structures. Anil et al. [9], in 2018, presented a model with a fictive diagonal for exact and quick estimation of the stiffness of timber-framed wall elements. Bedon et al., 2015 [10] investigated the nonlinear behavior and cyclic response of timber walls under in-plane loads. The results showed that the proposed modeling method is capable of predicting the load–carrying capacity and vulnerability of shear walls. Dutu A. [2], in 2016, studied the seismic behavior of timber frames with rectangular masonry infill panels. For this purpose, experimental tests were carried out to determine the parameters affecting the performance of the frames. The interaction between masonry and timber elements were also investigated. In addition, a numerical modeling approach was developed and validated using the experimental results. In 2017, Sheheryar et al. [11] proposed a numerical modeling technique for timber-braced rubble stone masonry, and described its application for evaluating the in-plane force-deformation capacity of panels with different bracing configurations. Bagbanci et al., 2018 [12] studied six historic two-story timber-framed masonry structures using laboratory data and in-situ structural health monitoring tests. Various masonry infill materials are used inside timber frames. The dynamic and mechanical parameters of the building were investigated and comparatively studied. The results depicted that the materials of the infill have important roles in the dynamic behavior of these structures. Guíñez et al., 2019 [13] studied the seismic response of timber walls and applied code-specified equations to shear walls with strong end-studs in mid-height timber buildings. Vijay P. et al. [14], in 2019, evaluated several school buildings that were primarily built using masonry and timber. These buildings, which were old and had historical value, had to be evaluated for their structural condition using visual and nondestructive load-testing techniques. The results demonstrated that most of the building elements had the required design strength and provided the serviceability criteria. Estrella el al., 2021 [15] presented a nonlinear modeling method to better understand the response of timber-framed walls. The results demonstrated that redesigning the nailing pattern leads to an increase in the capacity of wood-framed walls. Carrero et al. [16], in 2020, investigated the static and dynamic responses of laminated timber with reinforced concrete. In 2018, Jayamon et al. [17] studied ways of improving rational damping models and developed procedures for analyzing timber-framed shear walls. Mohammadi et al. [18], in 2020, investigated the behavior of masonry walls with timber elements. It was shown that the timber elements enhance the ductility and shear capacity of the walls. Cassol et al., 2021 [19] investigated the out-of-plane behavior of un-retrofitted and retrofitted masonry walls under cyclic loading. The retrofitting technique of masonry walls consisted of connecting vertical timber elements to the interior surface of the wall. Also, the experimental results were compared with those of numerical models. In this study, the behavior of these systems has been investigated in terms of their in-plane behavior. For this purpose, two groups of masonry walls were selected and the behavior coefficients of the models were determined in two states, i.e. with and without timber bonds. The models were analyzed in the SAP2000 software [20] and the effects of timber elements in the behavior of the masonry walls were investigated. Also, the behavior coefficient of each model was obtained using nonlinear static analyses. 2. History of Tabriz earthquake The city of Tabriz, located to the immediate south of the North Tabriz Fault (NTF) in the northwest Iran, is a highly-seismic region and has witnessed the tragic demolition of many historical monuments and buildings by several large-magnitude earthquakes. Figure 1 reveals the recorded seismicity of Tabriz with respect to its population. Figure 1. Seismicity of Tabriz with population. The 1779 Tabriz earthquake had a large number of casualties and the destruction of buildings was so that ZOKA, a renowned architect, remarked that it was the most severe and frightening earthquake in the history of Tabriz. Also, he stated that a few buildings were still standing after the earthquake. After this event, architects attempted to reach some sort of a plan to reduce earthquake risk by constructing low-rise, light and symmetrical buildings such as the historical buildings of Behnam, Ganje zade, Kalantar and Gadaki. Ambersiz and Melovil expressed that Tabriz was "gradually rebuilt on the same site". The houses were built with one story, without an upper extension. These houses, and even the palaces, were built with timber bracing and a new system of construction, the Takht-E-Push, become widely used. A similar account cab be seen in the James-Motier itinerary. He wrote that the fear of earthquake prompted people to build the low-rise buildings using wooden elements instead of the bricks and gypsum. Therefore, most bazaars are equipped with a wooden roof. Also, the results showed that the dome-like buildings remained stable under earthquake loads, while the other structures went through complete collapse. 3. Wooden confinements in traditional architecture Stability improvement of structures using engineered wooden grids was an efficient approach used by architects of Tabriz after the 1779 earthquake for retrofitting structures under seismic loads. It should be noted that the answers to why and how wooden frames should be used in masonry structures, as well as the evaluation of their performance, was largely based on the available documents. In the past, traditional masons applied the evaluations and analyses of surviving earthquakestricken structures and concluded that the ones with wooden bonds showed higher resilience against seismic loads. Therefore, wooden confining elements were chosen as the suitable technology for enhancing the stability of structures under earthquake loads. This approach was the result of the creativity of local architects for rehabilitating the structures. The samples of wooden bonds had been applied in the buildings of some villages including KRINGHAN and ASTEMAL. Figure 2 shows some of these buildings. (a) (b) (c) Figure 2. The application of wooden bods in the Tabriz village; (a) Oshtobin, (b) Astemal, (c) Kringan. These buildings are considered as “compound” structure due to the materials used in their construction. In these buildings, the basement and the ground-level floor were constructed from rock, lime and gypsum mortars, while the second story was a wooden skeleton. It should be noted that these compound structures comprise most of the buildings including residential architecture, Timche, etc. (see Figure 3). Wooden roof Wooden column Masonry wall Stone fondation Figure 3. the combined structural system in the Haj Mohammad Goli Timche. The main idea of wooden skeleton is the use of the properties of wooden elements as bracing elements to increase the stability of the structure (see Figure 4). Also, the reduction in the buildings’ weight in the upper stories and increased integrity and ductility of the buildings are other properties of wooden systems (see Figure 5). Figure 4. position of wooden bonds in Gajariye houses. Figure 5. integrity and ductility of the buildings using the wooden systems. To evaluate the effect of the wooden elements on the behavior of masonry structures, several historical houses in the RASTE and the MAGSODIYE districts, which are in the historicalcultural zone of Tabriz, were studied. These buildings are constructed from different materials, with the ground floor having been made from brick and stone, and the first floor from a wooden structure. The studied buildings are shown in Figure 6. (a) (b) (c) Figure 6. Wooden bonds of a GAJARIYE house in (a) HESAR alley, Tabriz; (b) MAGSODIYE alley, Tabriz; (c) TURKIHA valley, Tabriz. 4. Modeling of Masonry Structure Masonry structures are one of the oldest structural systems which have been in use for a long time; a variety of experimental studies have been carried out to investigate the behavior of these structures. In recent decades, numerical modeling of masonry structures has been a widelyresearched topic. The existence of masonry structures and valuable historical buildings with complex architecture has prompted engineers and researchers to investigate the seismic behavior of these structures using numerical methods. A number of methods for the modeling of URM buildings have been introduced by researchers, such as finite element models and equivalent frame methods. 4.1. Finite Element Method The brick wall is a composite material made of three main components, brick, mortar and unit-brick interface. In the micro-modeling approach, the components of a brick wall are all modeled separately. Although micro modeling is significantly accurate, this approach is not suited for modeling large structural walls due to its high computational cost and complexity. The micro-modeling approach is carried out in two ways: Detailed Micro-Modeling: In this case, units and mortar in the joints are represented by continuum elements, while the unit-mortar interface is represented by discontinuous elements. The Young's modulus, Poisson's ratio, and inelastic properties of both unit and mortar are taken into account. Simplified Micro-Modeling: In this case, expanded units are represented by continuum elements, while the behaviors of the mortar joints and the unit-mortar interface are taken into account as lumped masses in discontinuous elements. Masonry is considered as a set of elastic blocks bonded by potential fracture / slip lines at the joints. The Young's modulus and Poisson's ratio of the mortar are not included. In macro modeling, the mechanical properties of the homogenous wall must represent the overall wall. This method has been widely accepted as a suitable technique due to its simplicity and low computational cost, as well as being a user-friendly approach for modeling large scales models. In recent years, there has been an interest to study the mechanics of unreinforced masonry structures, with the aim of providing efficient tools for a better understanding of their complex behavior. Many researchers proposed some methods for modeling brick walls using different techniques. There are some limitations due to the complexity of modeling masonry, which means that designers use the existing methods according to their requirements. A.W.Page (1997) [21] studied micro modeling of brick walls subjected to in-plane loads. In this method, an elastic model is used to represent the behavior of the brick wall, and a nonlinear model was used to represent mortar joints. In this model, the Mohr-Coulomb criterion is considered for the failure of the mortar joint. Shing and lotfi (1994)[22] proposed an interface element using plasticity and fracture mechanics. The mentioned model uses the Mohr-Coulomb criterion with maximum tensile strength and a compression cap. 4.2. Modeling using Equivalent Frame Method (EFM) Another approach is based on the adoption of “equivalent frames”, a model which is very appealing to structural engineers. In this method, the structure is idealized as an assemblage of vertical and horizontal elements: the first elements (piers) are the vertical elements resisting both gravity loads and seismic forces ;the horizontal elements (spandrels) are secondary elements which couple the piers in case of the application of seismic loads. Piers and spandrels are connected by rigid offsets and each element is modeled by suitable constitutive laws. This approach clearly introduces strong simplifications, and thus its accuracy depends on the consistency between the adopted hypotheses and the actual structural problem. From these preliminary pictures, it is clear that the choice between accurate and simplified models should be obtained as a balanced compromise between accuracy and complexity of models, and in some cases (for instance in the vulnerability assessment of a large stock of existing buildings), the adoption of FEM models becomes unsustainable from the practical point of view and so the equivalent frame model can be an effective alternative, provided that the main hypotheses are carefully investigated. With some modifications, EFM models, which are used to model concrete shear walls, can also be used to model masonry walls. This approach has been presented in international codes such as FEMA356 [23], EUROCODE [24], etc. The advantages of EFM are as follows: 1234- Less time required for analysis; Application of EFM in software such as ETABS 2000 and SAP 2000; Application of this method in the seismic evaluation and retrofitting of masonry structures; Computational efficiency and simplicity in the modeling of masonry structures in comparison with finite element models. The following figure (Figure 7) illustrates a shear wall modeled using the equivalent-frame method. The most widely-used form of the equivalent-frame model is the use of horizontal and vertical members as elasto-plastic beam-column components and rigid connections. Among other models that are used are elasto-plastic columns and beams with brittle elastic behavior. There are also models in which only the beam-to-column connections are considered as rigid areas and other parts are modeled as beams and columns. However, these methods are not calibrated for modeling masonry walls. The yield criterion for each member is defined based on the Iranian 376 code [25]. Figure 7. Modeling the masonry shear walls using the equivalent frame method. 4.3. Modeling using shell elements This method was presented by Sweeny (2004)[26] for modeling a firehouse. Nonlinear static analyses were performed using SAP 2000 based on the FEMA 356 guideline. In this method, masonry walls are modeled using shell elements. Since the plastic hinges cannot be assigned to the shear elements, the frame elements were defined in the critical place of the masonry walls based on the dominant failure modes. Then, the nonlinear behavior of masonry piers was assigned to the frames using plastic hinges. Figure 8 demonstrates the numerical modeling of masonry walls using the shell element method. Figure 8. Modeling the masonry shear walls using the shell element method. To define the nonlinear behavior of the wall, the failure modes of masonry piers were first determined. The dominant failure mode was obtained for each masonry pier in the next step of the analysis. To do this, in the first step, the structure was analyzed using a force-based nonlinear static procedure under two gravity load combinations of 0.9 dead and 1.1 (dead + 0.25 live). The expected strength (QCE) and lower-bound (QCL) were estimated based on the existing force on each masonry pier. The expected lateral strength of the masonry bases, which were subjected to the shear slip of the mortar joints, is obtained via Eq. (1). If the obtained value was less than the resistance related of the tensile diagonal (Eq. 2), a displacement-control analysis would be used to obtain the dominant failure mode. Otherwise, a force-based analysis would be employed. Figure 9 displays the displacement-control behavior of the building. Also, the acceptance criteria of the masonry wall to the shear slip of the mortar joints has been presented in Table 1. (1) QCE = Vbjs = vme.An 𝑃𝐷 Vme = 0.56Vte+0.75( ) QCL = Vdt = f’dt.An.( 𝐴𝑛 𝐿 ℎ𝑒𝑓𝑓 ).√1 + 𝑓𝑎 𝑓′𝑑𝑡 (2) where: 𝐴𝑛 = Area of net mortared/grouted section ℎ𝑒𝑓𝑓 = Height to resultant of lateral force 𝐿 = Length of wall or pier 𝑃𝐸 = Expected axial compressive force due to gravity loads 𝑉𝑚𝑒 = Expected bed-joint sliding shear strength 𝑉𝑏𝑗𝑠 = Expected shear strength of wall or pier based on bed-joint sliding shear strength 𝑄𝑐𝑙 = Lower bound lateral strength 𝑓𝑎 = Axial compressive stress due to gravity loads ′ 𝑓𝑑𝑡 = Lower bound masonry tensile diagonal strength ′ 𝑓𝑚 = Lower bound masonry compressive strength 𝑉𝑑𝑡 = Lower bound shear strength based on diagonal tensile stress for the wall or pier 𝑄 𝑄𝑦 e=0.8% d=0.4% C B D E c=0.6% A ∆ ℎ𝑒𝑓𝑓 Figure 9. Displacement-control diagram of the masonry pier. Table 1. the acceptance criteria of deformation-controlled masonry walls based on code 376. Performance Level Modeling parameters primary secondary Limiting Behavioral Mode c d e IO LS CP LS% CP% Bed joint sliding 0.6% 0.4% 0.8% 0.1% 0.3% 0.4% 0.6% 0.8% 4.4 Validation of the Numerical modeling To evaluate the accuracy and validity of the numerical modeling, a study conducted by Akhaveisi et al. [27]. was employed. For this purpose, a masonry wall confined using the wooden elements was modeled in SAP2000.V20.2 using the shell element approach. The configuration and dimensions of the model are shown in Figure 10(a). Furthermore, the numerical model of masonry wall in SAP2000 is depicted in Figure 10(b). The behavior of the was obtained using the nonlinear static analysis. Figure 11 illustrates the analysis results. Also, a comparison of the results is presented in Table 2. According to the table, the ultimate load in the numerical model was 111.3 kN, which is close to 98.2 kN, i.e. the ultimate load of the original result. In addition, the initial stiffness of the numerical model obtained from the original study was equal to 113 kN/mm, and the corresponding numerical value is 128.475 kN/mm. The 13.6% difference demonstrates that the numerical model in comparison to Akhaveisi‘s study has a stiffer behavior. The absorbed energy of the study was 124.6 kN.mm, and the corresponding numerical value was 140.6 kN.mm. The absorbed energy in the analytical model is around 12.8% more than the value reported in the study. With regard to the disparity in energy absorption, the accuracy of the numerical model can be considered satisfactory. By comparing the results, the analytical model used in this study can be considered precise enough and can be extended to be used in numerical studies. (a) (b) Figure 10. (a) Configuration and geometrical dimensions of Akhaveisi model; (b) numerical model in SAP2000.V20.2. Table 2. comparison of numerical model with regard to the result of Akhaveisi et al. model Initial stiffness Ultimate load Absorbed energy (kN/mm) (kN) (kN.mm) Akhaveisi et al. model 113 98.2 124.6 Numerical model 128.47 111.3 140.6 120 Base shear(kN) 100 80 60 40 Akhaveisi et al. Numerical modeling 20 0 0 0.5 1 1.5 Displacement(mm) 2 Figure 11. comparison of the numerical result with Akhaveisi ‘s study. 5. Numerical results and discussion In this study, two groups of masonry walls have been modeled using shell elements in SAP2000. v. 20.2. The main difference of the two groups is in their number of bays and stories. The first group are masonry walls with a single bay and two stories, while the second group includes models with six bays and three stories. Each group has been retrofitted with timber laces. It is worth noting that the in-plane behavior of each model was evaluated and the out-of-plane bending of the masonry walls was not considered. After identifying the dominant failure mode, nonlinear behavior was assigned to each masonry pier. In the next phase, nonlinear static (pushover) analyses were performed on the structure using triangular and uniform lateral load patterns until the target displacement was reached. The vulnerable points of the structure were then identified based on the results. Based on the locations of these points, retrofitting schemes were recommended to seismically improve the walls. To define the behavior of the wooded elements, the experimental results obtained by Jung et al. 2016 were used. Based on the bilinear stress-strain curve and the orthotropic behavior of the wooden elements in three directions, (i.e., longitudinal (L), radial(R), and tangential (T)), the mechanical properties of the wooden elements were defined. The characteristics and mechanical properties of each model are given in Tables 3 and 4, respectively. The analysis results of the models can be described as: 1- In model-1, a two-story masonry wall has been evaluated. The results showed the collapse of the first story walls. In model-2, the masonry wall was retrofitted using wooden bonds in the second floor. The results showed that the first story walls were damaged and the plastic hinges indicate the collapse prevention performance level. The second story walls are safe and there is not any plasticity in the wooden elements and masonry walls. 2- In model-3, a two-story model has been considered, with the first story being a masonry pier and the second story having wooden bonds. Analysis results demonstrated that the plastic hinges of masonry pier are in the collapse prevention limit state. Also, the results indicated no plasticity in the wooden elements used in the model. 3- In model-4, the masonry wall has been retrofitted using wooden beams and columns. The results revealed that adding the wooden elements increase the stiffness and strength of the walls. In addition, the plastic hinges formed in the masonry walls are in the LS (life safety) limit state in the first story and the IO (Immediate occupancy) limit state in the second story. 4- In model-5, a three-story masonry wall has been evaluated using the shell elements. According to the analysis, the failure mode of the piers in the left and right sides of wall was diagonal tension, while the other piers had a bed joint sliding mode. The analysis results depicted the collapse of masonry walls in the first story and the plastic hinges formed were in the Collapse Prevention performance level. Then, the behavior of the masonry wall was assessed using the wooden bonds. The results of the pushover analysis showed the effectiveness of the wooden bonds in the behavior of wall (model-6). The status of the plastic hinges in the piers changed from Collapse Prevention (CP) to Immediate Occupancy (IO). Table 3. Material property in models. Material Compressive Strength )MPa( Poisson 's Ratio Young 's modulus )MPa( 5 21 𝜎𝐿 =44.3 𝜎𝑅 =4.5 0.15 0.2 𝜈𝑅𝐿 = 0.018 𝜈𝐿𝑇 = 0.37 2750 21882 𝐸𝐿 = 16900 𝐸𝑅 = 832 masonry concrete wood 𝜎𝑇 =4.5 Group Model Dimension 𝜈𝑅𝑇 = 0.38 2nd story: URM 2.5m×0.3m Table 4. Structural models. Geometry Feature First and second story is URM 1 1st story: URM 2.5m×0.3m Model-2 2nd story: URM 2.5m×0.3m And wooden bond 0.4m×0.3m 1800 2400 850 𝐸𝑇 =832 1st story: URM 2.5m×0.3m Model-1 𝛾(kg/m3) 1st story is URM,2nd story is a confined masonry wall using wooden bond Nonlinear static analysis results 1st story: URM 2.5m×0.3m Model-3 1st story is URM,2nd story has wooden bonds 2nd story: wooden bond 0.4m×0.3m 1st story: URM 2.5m×0.3m 2nd story: URM 2.5m×0.3m 1st& 2nd story have confined URM using concrete bonds Model-4 1st& 2nd story concrete bonds 0.3m×0.3m Model-5 1st story: URM 3m×0.3m 2nd story: URM 3m×0.3m Stories are URM 3rd story: URM 3m×0.3m 1st story: URM 3m×0.3m 2 Model-6 2nd story: URM 3m×0.3m The URM was retrofitted using wooden braces. 3rd story: URM 3m×0.3m The results of the nonlinear static analyses are shown in Figure 12. It should be noted that the capacity curves of the models have been presented up to the target displacement, which is defined as the displacement of the second story of the studied models. Based on the results, it can be concluded that the addition of wooden elements to the masonry wall improves such structural parameters as strength, stiffness, and ductility. In order to evaluate the effects of the wooden elements, the ratios of ultimate strength and stiffness of the two groups were calculated. The calculations, as shown in Table 5, demonstrate the increasing of these parameters in the models. The ductility ratios of the models were also determined. The ductility (𝜇) is calculated as the ratio of ultimate displacement 𝛿𝑢 to the yield displacement 𝛿𝑦 . 𝛿 𝜇 = 𝛿𝑢 𝑦 (3) The yield displacement is computed based on the first plastic hinge formed in the model. Furthermore, energy absorptions of the models were determined. According to the results obtained, the energy absorption in models 1 to 6 are, respectively, 0.228, 0.21, 0.215, 0.518 (group 1), 36.2, and 175.3 (group 2). Also, the ductility ratios in the studied models are 1, 2.35, 2.67, 5.71 in group 1 and 2.76 and 7.51 in group 2, respectively. Therefore, it can be concluded that the wooden elements used in the masonry walls have a significant effect on the absorbed energy and the increase in the ductility of the models. Table 5. Effects of wood element on the structural important parameters. Model 1 Model 2 Group 1 Model 3 Model 4 Model 5 Group 2 Model 6 Ultimate strength (kN) Stiffness (MPa) Ductility (𝜇) Energy absorption (kN.m) 37.1 22.3 22.6 79.3 232 828 3.2 4.9 6 9.5 25 28.9 1 2.35 2.67 5.71 3.76 7.51 0.228 0.21 0.215 0.518 36.2 175.3 800 700 Base shear(kN) 600 500 400 300 200 Model 1 Model 2 Model 3 Model 4 100 0 0 0.003 0.006 0.009 0.012 Displacement(m) (a) 9000 8000 Base shear(kN) 7000 6000 5000 4000 3000 2000 Model 6 1000 Model 5 0 0 0.01 0.02 0.03 0.04 Displacement(m) (b) Figure 12. Capacity curves of models without and with Wood elements; (a) Models 1 to 4 (b) Models 5 and 6. 6. Behavior Coefficient The applied seismic load to the structures is related to the structural characteristics. Based on the equivalent static seismic load, the base shear is calculated using the relationship V = Cs.W, in which the value of Cs is equal to - 𝐴𝐵𝐼 𝑅 [28] ,where: A is the design base acceleration ratio; - B is the building response factor, determined from the design response spectrum; in this study, the site class C was selected for soil parameters. Also, it was assumed that the location of the models is in Tabriz, Iran. The site spectral accelerations are S0=1, S=1.5, T0=0.1, Ts=0.5. - I is the importance factor; - The behavior factor (R) of the structures. In the past, the construction philosophy of masonry buildings was to decrease the weight of the structure to reduce the seismic load. Thus, wooden skeletons have been used in the buildings. For instance, in a two-story building, a wooden skeleton has been used on the second floor, and calculating the seismic load shows that the seismic load decreases by up to 50%. The behavior coefficient is a force reduction factor, R, in seismic design codes, which is used to reduce the elastic design response spectrum in force-based seismic design procedures. This factor is obtained by the multiplication of the ductility reduction factor (Rμ) and the over-strength factor (Rs)[29]. 𝑅 = 𝑅𝜇 × 𝑅𝑠𝑜 (4) In this research, the method proposed by Uang [30] is used to obtain the behavior factor. In this method, after obtaining the capacity curve, the curve is idealized by a bilinear diagram. Then, the constituent parameters of the behavior factor and the displacement amplification factor including the ductility factor, μ, the over-strength factor, Rso, and the ductility reduction factor, Rμ, are calculated. The strength of a structure, from the formation of the first plastic hinge, Vs, to the final yielding (or the actual mechanism) of the structure, Vy, is called the over-strength factor. The parameter is denoted by Rs0, and is calculated as follows [29]: 𝑅𝑠0 = 𝑉𝑦 𝑉𝑠 (5) The ductility factor is the ratio of the maximum displacement to the yield displacement of the structure (Eq.6): 𝛿 𝜇 = 𝛿𝑢 𝑦 (6) To determine the ductility reduction factor, several equations such as the Newmark-Hall [31], the Krawinkler-Nassar [32], and the Miranda-Bertero[33] have been formulated. These equations are related to the ductility, time period, soil type, and hardening factor. These equations are given in Table 6. Method Nemark-Hall KrawinklerNessar Miranda-Bertero Table 6. The equations of the ductility reduction factor[29]. Equation Description 𝑅𝜇 = 1 → 𝑇 < 0.05𝑠 𝑅𝜇 = √2𝜇 − 1 → 0.05𝑠 < 𝑇 < 0.12𝑠 𝑅𝜇 = 𝜇 → 𝑇 > 1𝑠 1 𝑅𝜇 = [𝐶(𝜇 − 1) + 1]𝐶 𝑏 𝑇𝑎 𝐶(𝑇, 𝛼) = + 𝑎 1+𝑇 𝑇 𝑅𝜇 = 𝜇−1 𝜑 +1 Interpolation is used for intermediate values. a b 𝛼 0 1 0.42 0.02 1.01 0.37 0.1 0.8 0.29 1 1 𝜑 = 1+ − exp(−1.5(𝑙𝑛(𝑇) − 0.6)2 ) 𝑅𝑜𝑐𝑘 𝑠𝑖𝑡𝑒𝑠 10𝑇 − 𝜇𝑇 𝑇 1 2 𝜑 = 1+ − exp(−2(𝑙𝑛(𝑇) − 0.2)2 ) 𝐴𝑙𝑙𝑢𝑣𝑖𝑢𝑚 𝑠𝑖𝑡𝑒𝑠 12𝑇 − 𝜇𝑇 5𝑇 2 𝑇𝑔 3𝑇𝑔 𝑇 − exp (−3 (𝑙𝑛 ( ) − 0.25) ) 𝑆𝑜𝑓𝑡 𝑠𝑜𝑖𝑙 𝑠𝑖𝑡𝑒𝑠 𝜑 = 1+ 𝑇𝑔 3𝑇 4𝑇 The ductility factor, ductility reduction factor, and behavior factor have been obtained for the studied models. The results are given in Tables 7 and 8. The results demonstrate that the behavior coefficient of the masonry wall (model 1) is equal to 1.155 according to the Newmark-Hall, Krawinkler-Nessar, and Miranda-Bertero methods, which is indicative that the bare masonry walls have low ductility. In comparison with models 2 and 3, the wooden elements (model 4) significantly increase the behavior coefficient of the masonry wall. Also, the results obtained from models 5 and 6 show that the wooden elements have increased the ductility, the ductility reduction factor, and behavior coefficient of the masonry wall. Table 7. The maximum displacement, yield displacement and ductility factor for the studied models Model ∆𝑦 ∆𝑚𝑎𝑥 𝜇 (m) (m) 1 0.012 0.012 1 2 0.012 0.0051 2.35 3 0.012 0.0045 2.67 4 0.012 0.0021 5.71 5 0.02 0.00532 3.76 6 0.04 0.00532 7.51 Table 8. The ductility reduction factor, over-strength factor, behavior factor for the studied models. 𝑅𝜇 R Model Newmark- Krawinkler- Miranda𝑅𝑠𝑜 Newmark Krawinkler MirandaHall Nessar Bertero -Hall -Nessar Bertero 1 1 1.155 1.155 1.155 1.155 1 1 2 1.92 1.691 3.246 2.58 2.68 1.53 1.588 3 2.08 1.559 3.24 2.26 2.45 1.45 1.568 4 3.45 1.899 6.55 6.09 6.889 3.21 3.628 5 2.55 2.52 2.7 1.316 3.356 3.316 3.55 6 3.74 1.155 4.319 3.99 4.527 3.46 3.92 In addition, the effect of the wooden elements on the stiffness and base shear of the models has been studied. The results showed that the wooden elements increase the base shear and stiffness of the masonry walls due to the confinement they provide for the wall (Table 9). Based on the analysis results, it can be deduced that the masonry wall with wood frames is an efficient system for bearing seismic loads. If the new structure were to be designed with this system, the base shear of the structure would be less than that of the wall without wooden frames. Table 10 and Figure 13 show the effects of adding the wooden frame on the masonry wall’s base shear. The results demonstrated that in comparison with the bare masonry wall, the reduction percentage of the base shear in models 2 to 4 is, respectively, 64%, 81%, and 79.7% (model 1). Similar to the results of group 1, the reduction percentage of the base shear in group 2 is 22.3%. Table 9. The effect of wood elements in the stiffness and base shear of wall. Base shear Stiffness model (kN) (kN/m) 376 1 31300 222 2 48600 222 3 58900 4 800 92200 5 2320 255000 6 8177 289000 Table 10. the effects of wooden elements in base shear of masonry wall. Period (sec) B* R 1 0.0778 2.167 1.155 2 0.08 2.2 3 0.0553 1.8 4 0.2 5 0.196 Group Model 1 2 𝐴𝐵𝐼 𝑅 W (kgf) Base shear (kgf) Percentage reduction of Base shear (%) 0.656 162.864 106.83 - 3.246 0.237 162.864 38.59 64 3.24 0.194 104.52 20.27 81 2.5 6.55 0.133 162.864 21.66 79.7 2.5 3.356 0.26 2222.64 577.88 - 𝐶= 6 0.181 2.5 4.319 0.202 2222.64 448.97 22.3 *In this study, the soil property had been classified as site class II accordance with standard No.2800 of Iran. 600 Base shear(kN) 500 400 300 200 100 0 1 2 3 4 5 6 Models Figure 13. The effects of wooden elements in the base shear of studied models. 7. Conclusion Masonry buildings are the most common type of structures built in Iran. In spite of their suitable compression strength, due to the fundamental weakness caused by the lack of sufficient confinement, these structures are vulnerable during earthquakes. Past earthquakes have proven the vulnerability of these structures. The majority of masonry buildings collapse completely under severe earthquakes, with only a few buildings remaining functional. The accurate evaluation of these buildings revealed that the existence of the wooden bonds causes them to respond better to applied loads. In addition, to improve the seismic performance of masonry buildings, various retrofitting methods have been recommended in recent years. There is enough evidence to show that the performance of masonry walls improves by the addition of wooden elements. Wooden framed buildings are well-known as efficient seismically-resistant structures that are popular all over the world. This is due to not only their seismic performance, but also the low-cost and accessibility. These buildings generally consist of masonry walls that are reinforced by horizontal and vertical timber elements. The main goal of this paper is to study the behavior of masonry structures with/without wooden elements. For this purpose, six masonry frames, which are samples of the historical buildings in the RASTEH and MAGSODIYE of Tabriz, have been selected. At first, the behavior of the models was determined using the shell elements. Then, the models were equipped with wooden elements and evaluated. The following conclusions can be drawn from the present study: 1- The results showed that wooden elements improve the behavior of the masonry walls, such that the status of plastic hinges change from the Collapse Prevention to Life Safety; 2- The results revealed that the wooden elements improve the ductility of the walls. The ductility of the models increases from 2 to 5 times based on the configuration of the wooden elements in the masonry walls; 3- The analyses indicated that in comparison with other configurations of wooden elements, confining masonry walls is the most efficient scheme for improving the ductility, stiffness, and ultimate bearing capacity; 4- Adding wooden elements to the masonry walls increases the ultimate capacity, stiffness, and behavior coefficient of the walls significantly. Also, the results demonstrated that the Krawinlker-Nessar method gives a smaller value for the coefficient in comparison with other techniques; 5- The results showed that wooden elements decrease the base shear of the walls in groups 1 and 2 by up to 60% and 20%, respectively. Therefore, it can be concluded that the wooden frame is an efficient structural system for retrofitting masonry walls. References .1 .2 .3 .4 .5 .6 .7 .8 .9 .10 .11 .12 .13 .14 .15 .16 .17 .18 .19 .20 Doudoumis, I.N. 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