In Groningen, seismic activity has increased due to the extraction of gas in the area. A large-scale research campaign has been launched with the aim to assess and safeguard structures in the region. However, an accurate assessment of these buildings turned out to be a challenge, due to the nonlinear behaviour of the masonry and the dynamic nature of a seismic load. A Nonlinear Time History (NLTH) analysis takes into account both these factors, but the computational demand of such a method is considerable. Another method that is widely used to analyse the seismic response of a structure is the Modal Response Spectrum (MRS) method. The computational demand of this method is considerably less compared to NLTH, but nonlinear material behaviour is only taken into account in an indirect manner via a behaviour factor, and the results are considered to be too conservative. A third method is the Nonlinear Pushover (NLPO) method. It takes nonlinear material behaviour into account and compared to NLTH, NLPO is computationally more efficient. Furthermore, an advantage is that it separates capacity from demand. Even though the NLPO method is commonly applied worldwide, its validity still needs to be proven for the Groningen case. Both objectives were studied by looking into a single case study, consisting of a low-rise URM apartment building. The behaviour of the structure is characterised by a weak and strong direction, in which the weak direction is characterised by a relatively low stiffness and lateral capacity compared to the strong direction. The seismic response of the structure is determined according to the MRS, NLPO and NLTH methods. Furthermore, the NLPO analyses are executed using two different computational discretisation methods, namely continuum FEM and macro EFM. DIANA is used as a FEM solver for the MRS, NLPO and NLTH analyses and 3MURI is used for the EFM model. Moreover, a modal and uniform lateral load pattern are taken into account for the NLPO analyses. The conclusions which are drawn from the case study can generally be applied to low-rise URM apartment buildings in Groningen. However, it must be noted that significant alterations in geometry and building materials might influence the results. Furthermore, modelling assumptions have been applied, and it is important to note that the possible influence of these assumptions, may partially limit the extent of the conclusions. Moreover, several limitations are inherent to the studied methods, and cannot be accounted for somehow. All analyses are performed by incrementally increasing the seismic load until one of the near collapse limit state criteria according to NPR 9998 is met. Furthermore, three target displacement methods are evaluated: the capacity spectrum method according to NPR 9998, the regular N2-method, included in the Eurocode 8, and an adaptation of the N2-method which is developed specifically for URM structures by Guerinni. The performance of the structure according to each of the methods is studied subsequently, by looking into the force-displacement behaviour, displacement profile and damage at failure, failure mechanisms and the maximum admissible seismic load. Two significant disadvantages of macro EFM were identified when comparing the results of the NLPO analyses using 3MURI and DIANA. First, the fact that out-of-plane behaviour is not taken into account in 3MURI could significantly influence the behaviour of a structure in terms of base shear capacity, which is especially true when structures are characterised by an extremely low total length of piers in the in-plane direction. Furthermore,DIANA allows for a more gradual softening behaviour, which helps the post-peak force redistribution. As a consequence, the maximum admissible seismic load according to DIANA could be higher. However, despite the two aforementioned disadvantages of the macro EFM method as implemented in 3MURI, all other relevant results of both methods are similar. The fact that the two identified disadvantages of 3MURI can only result in more conservative results, suggests that macro EFM, as implemented in 3MURI, is a suitable computational discretisation method for the seismic assessment according to the NLPO method for low-rise URM apartment buildings in Groningen. However, it should be taken into account that the conservativeness of 3MURI could lead to a significantly larger amount of required retrofitting, in comparison with DIANA. The applicability of the NLPO method is reviewed by comparing the results of the MRS, NLPO and NLTH methods. Similar behaviour of the structure according to the NLPO and NLTH method was captured, which suggests that the NLPO method is a suitable analysis method for the studied typology. The maximum admissible seismic load using the target displacement method according to NPR 9998 is in-line with the NLTH analysis. However, the governing load case made use of a uniform load pattern, which returns a structural behaviour different than that obtained by NLTH analyses, as can be seen from the force-displacement behaviour. If only the capacity curve according to the modal load pattern would be considered, then the allowable seismic load according to NLTH is similar to that of NLPO using the target displacement method of Eurocode 8. Furthermore, from the results of the case study can be concluded that the choice of target displacement method has a significant influence on the maximum admissible seismic load. For the case study, NPR 9998 is more conservative in the strong direction, and Eurocode 8 is more conservative in the weak direction. Regarding the MRS method, very conservative results were found. A reason that was found for these conservative results is that the prescribed behaviour factor by NPR 9998 is too low for the case study when compared to that derived from the NLPO analysis. However, even with a larger behaviour factor, the results according to the MRS method would still be conservative in the weak direction.

The growing need to understand the behaviour of un-reinforced masonry URM), subjected to repeated light man-made earthquakes caused by the extraction of gas in the north-eastern part of The Netherlands has resulted in intense research to determine the exact process of crack initiation and propagation. The historical masonry buildings and Dutch terraced houses in Groningen are prone to light damages which become severe upon repeated lateral earthquake loading. Although there are material models that describe the behavior of modern brick masonry, they do not accurately represent the mechanical properties of 19th century clay brick masonry. This led to a large-scale research into the mechanical behavior of un-reinforced masonry and an orthotropic continuum macro-model called the Engineering Masonry Model (EMM) was proposed. The existing tension constitutive model in EMM assumes a secant unloading-reloading branch which does not consider the strength degradation of URM under repeated loading. Since tension mode-I fracture results in cracking of URM, it is important to study the effects of repeated loading on the propagation of the crack and its effects on the capacity of the structure. This thesis presents a degradation model to represent the strength deterioration of URM observed during repeated loading. The constitutive model formulated in this thesis is based on hyperbolic functions along with a secant slope for the unloading-reloading branch. To justify the model assumptions, a single linear 4-node element is analysed with the new model and the effect of varying different components of the constitutive equations is established. The window bank spandrel sample modeled as a 4-point bending test is analysed using the new model for 10, 30 and 100 repetitions. It is shown that the hyperbolic model can predict accurately the stress reduction within each repetition displacement set and also represent the crack width widening and crack propagation accurately when compared to the experimental results. The new model is tested on a wall with a window opening sample and the results closely matched that of the experiment. Finally, recommendations are provided for further development of the hyperbolic model and calibration of the material properties.

Increasing housing demand in Europe and the need to be more sustainable are asking the construction industry to leave the traditional pathways and innovate. An emerging construction method with volumetric timber modules potentially offers the solution. However little is known about the robustness of this new innovation. Therefore, this thesis aims to advance the current research regarding collapse resistance in volumetric modular timber buildings. To achieve that goal, first, in this thesis, a literature study into robustness and modular buildings was performed. The study identified the importance of redundancy, proper connection design, ductility, and tying in modular structures for robustness. Secondly a case study was performed. The case study provided the structural design concept of a newly developed volumetric timber post and beam module by Lister Buildings, structurally designed by Pieters Bouwtechniek. The modules consist of glued laminated beams and columns with cross-laminated floor and ceiling slabs. With the modules, a hypothetical residential building of 5 storeys was created, which consecutively was decomposed into equivalent two-dimensional frame structures suited for 2D finite element analysis. To account for the mechanical behaviour of the connections in the models, nonlinear springs were used. To establish the springs, the component method was adopted. The spring behaviour was determined from the elastic, plastic and failure performance of the individual components of a connection in translational and rotational degrees of freedom. Then based on a notional element removal concept, multiple possible loss events of load bearing elements were analysed in the finite element software of Abaqus to examine the existence and development of alternative load paths. To do that, both nonlinear static and nonlinear dynamic analyses were performed. The results of this study indicate that the new design concept performs quite well on robustness. Several alternative load paths were identified, among which cantilever action, bridging action, and catenary action, depending on the removal event and scenario. In addition this thesis investigated the dynamic amplification factor (DAF) of the modular system. The results of this research imply that for alternative load path analysis of timber structures, a DAF of 2.0 should be applied in a (non)linear static analysis. More research will be necessary to examine whether a lower value than 2.0 can be used.

Steel trusses are the preferred structures when large distances are required to span due to its lightweight, the reduced deflection and its load bearing capacity. Although nowadays with the help of computational tools more efficient designs can be achieved, the geometrical shape of trusses has barely changed. This is mainly due to the ease of the required structural calculations and due to the available standard manufacturing and assembly procedures. Although a standard shape could be seen as an advantage, studies suggest that the relationship between the efficient use of material and design rationalization is not balanced, leading to design-overcapacity of the structure. The use of optimization procedures provides new opportunities to engineers. New design solutions and near-optimal structures can be achieved when implementing optimization processes. Optimization processes could generate economical alternatives in terms of weight reduction. Despite optimization techniques are becoming increasingly available, optimized structures are not commonly used in real practice due to the complex configuration an optimized structure might have, especially when using layout optimization. Due to the non-conventional node-members configuration, realizing these optimized trusses in real practice with conventional joining mechanisms, such as bolted and welded connections, will probably lead to complex designs and higher costs. Therefore, innovative joining technologies are required to be implemented. Snap-fit connections are widely used connecting mechanism for joining plastic components. Due to its simplicity and efficiency while connecting two or more elements together are suitable for different applications. Despite it is not commonly used in the building industry and it is frequently used on small scale applications, the principle based on snap-fit connections could be used to connect the structural members of optimized trusses. First, a literature study provides a clear understanding of truss structures, focusing mainly on the importance of their joints. Structural optimization is also discussed, paying special attention on a new layout-optimization approach, which is based on two steps: first, the less-weight possible layout is obtained (the benchmark) without taking into account any buildable considerations. The second step consists on rationalizing the benchmark contemplating practical and buildable restrictions. Finally, a representative case-study steel truss is presented. The second part of this research explores the structural design and the optimization procedure applied on the case-study truss. Here the layout optimization approach is applied using Peregrine (plugin for Grasshopper). After an optimized layout is generated, it is design structurally using Karamba3D. Finally, the case-study truss and the optimized truss are compared. To explore the opportunity of implementing optimized trusses in practice, the conceptual design of an innovative joint based on snap-fit connections is developed. A representative internal node from the optimized truss is chosen and based on a general concept, three design concepts are created. Extensive Finite Element (FE) analyses are carried out to study the structural behavior of the innovative joint during three main phases. All FE analysis were performed using the FE software Abaqus. To conclude, this research project is an exploratory feasibility study of the use of steel snap-fit joints as internal nodes for optimized steel trusses.

Existing sophisticated numerical micro- and macro models have already proven to be capable of simulating typical masonry behaviour. However, assessing the global response of masonry buildings using brick-to-brick micro modelling or even simplified macro modelling, in which masonry is regarded as a continuum material, takes such an amount of time that these methods cannot be considered as cost-effective. For the last two decades it has been recognized that, for the global structural behaviour of masonry buildings, simplifications have to be made. The idealization of a masonry wall as an assemblage of numerically integrated (or fibre) beam elements could considerably reduce the computational burden and therefore this study addresses the following research question: To what extent are numerically integrated beam elements applicable for assessing the global response of masonry structures? Whereas existing equivalent frame methods are usually based on lumped plasticity models, the approach discussed here considers the entire member (e.g pier or spandrel) as an inelastic element in which the sectional response is evaluated via a fibre discretization in which each fibre (or integration point over the depth) may follow a material uniaxial nonlinear stress-strain relation. Initially the shear response is kept linear, automatically idealizing the structural response as purely flexural. The proposed model will be hereinafter named FFM (Fibre Flexure Model). Additionally, an extension of the FFM has been proposed, describing the shearing behaviour by means of a structural nodal interface element. Adopting the nodal interface element, placed between two nodes of adjacent beam elements, the axial and bending behaviour is described with the fibre-section discretization and the shear behaviour is modelled via an equivalent Coulomb-type criterion describing the shear force limit. The proposed model will be hereinafter named FF-LSM (Fibre Flexure – Lumped Shear model) because it lumps shearing nonlinearities in one single interface element located in the centre of the structural component, whereas flexural and crushing behaviour is evaluated via smeared crack beam elements. To validate the numerical models, two different types of benchmarks have been investigated, respectively representing the behaviour of either a single structural component (masonry pier) or a composite façade. All numerical models have been subjected to static nonlinear (pushover) analyses and results have been compared with experimental and numerical data through the use of a reference continuum model. First, it has been demonstrated that the FFM, idealizing the structural response as purely flexural, is capable of simulating the rocking failure mode of unreinforced masonry walls, whereas it fails to simulate typical masonry shearing modes such as diagonal cracking and sliding. The use of the model for squat members that are characterized by shear failure leads to significant overpredictions, making the model not applicable for the analysis of masonry structures containing relatively squat structural components, having shear span to depth ratios less than approximately 1. Second, the shortcoming of the FFM regarding the shearing failure mode has been overcome by combining the numerically integrated beam elements with a structural nodal interface element describing the shear behaviour. The FF-LSM including the nodal interface is able to correctly predict the shear capacity of both slender and squat walls, although the observed level of accuracy depends largely on the adopted shear failure criterion. Various shear force criteria (Coulomb friction based) have been considered: the Mann and Muller (1982) criterion, the correction proposed by Magenes and Calvi (1997) and the modification according to Abrams (1992). Generally it was observed that the criteria developed by Abrams (1992) was the most accurate and that especially for a decreasing shear ratio the criterion developed by Magenes and Calvi (1997) appeared to be less precise. Third, analysing a composite façade, with respect to the reference continuum model the FFM and FF-LSM significantly reduce the number of elements, nodes and integration points, consequently minimizing the computational effort and maximizing the computational robustness. In comparison with the corresponding continuum model the computational time decreases by a factor of approximately 10. Despite the limitations of the FFM regarding the shearing failure mode, the model shows an acceptable accuracy in terms of initial stiffness, stiffness reduction and peak strength. Adopting the FF-LSM the numerical model predictions were significantly enhanced and both flexural and shearing failure modes (in piers and spandrels) were detected correctly. Therefore, the result of the investigation has proved to be very promising as with the FF-LSM an acceptable balance between computational cost and accuracy is found, applicable to the global analysis of two dimensional masonry structures constituting slender as well as squat walls. As many problems in engineering practice require solutions in three-dimensional space, a fully three-dimensional extension of the FF-LSM is highly recommended.

This research investigates if confining rubble stone masonry by timber bands and columns increases resistance against earthquake loads, by performing a number of numerical analyses in the finite element software program Diana. In order to establish a reliable model, the input parameters are investigated by means of a literature study and sensitivity study. Additionally, the numerical model is validated by comparing the results to an analytical study. From the analytical study it is determined that the failure mechanisms are correctly estimated by the numerical analysis. However, differences between the values of ultimate strength and ductility were observed. The effect of the confinement is investigated by a pushover analysis on a shear wall with two different masonry tensile strengths: ft = 0.01 N/mm2 and ft = 0.03 N/mm2. These values are selected to show how such a small difference in tensile strength results in a different failure mechanism of the wall, and therefore results in a vastly different displacement capacity and ultimate strength. Additionally, a shear wall with and without a window opening is studied. If the building is constructed with extremely low-strength masonry (ft = 0.01 N/mm2), the timber frame confinement will increase the resistance of the wall (with or without window opening) against the pushover load. If the building is constructed with masonry having a tensile strength of 0.03 N/mm2 or higher, the confinement has a negative impact on the ductility of the closed wall. For the wall with window opening the confinement triples its ultimate strength. Weather a strong or a ductile structure is more desirable, depends on the demand with respect to the seismic spectrum. If the ground motion demands a strong structure, it is advised to confine the masonry with a timber frame consisting of four timber bands, and columns at each wall junction. The design of the timber frame as recommended by the Nepali building codes is determined to not be sufficient and must be altered in order to provide this positive impact on the structure’s resistance. Firstly, the columns must be placed at both sides of the band, instead of on the inner side only, to avoid eccentric loads on the bands. Secondly, the cross-sectional dimensions of the bands and columns must be increased avoid failure of the connections and splitting of the timber. Taking these aspects into account, a new design for the confinement method is presented in this study. The limitations of the conclusions of this research follow from the investigation of a single, in-plane wall only. One of the goals of the use of bands is to improve the box behaviour, for which the out-of-plane performance must be investigated. Moreover, an analysis on a three-dimensional structure is needed to fully answer the research question. In a three-dimensional study, the closed walls and walls with opening give a combined response to the load, therefore, the advantages and disadvantages of the confinement are combined as well.

The gas production in the Groningen gas field of the Netherlands has caused a significant amount of shallowhuman induced earthquakes. Among various building typologies, Groningen is home to many Dutch historical churches constructed by unreinforced masonry which has shown to be highly vulnerable to these earthquakes. From the perspective of conservation and prevention of loss of our historical and cultural heritage, the structural assessment of these churches and their monitoring is of importance. The assessment of the seismic performance of historic churches is a challenging task because of their unique design, governed by macro element behaviour and nonlinear material behaviour. An accurate and reliable earthquake resistant assessment with appropriate numerical modelling of the structure and proper assumptions of all the uncertainties is crucial. The structural monitoring cannot be applied to all historical churches. By selecting representative case studies, indepth study regarding both numerical modelling and structural monitoring are possible. This information can then serve engineers and professionals to evaluate similar structures. The research gap lies in accurate modelling of historical churches to achieve reliable and faster results by linear dynamic modelling. The fundamental modes, eigenfrequencies and modal shapes, geometry and material properties, boundary conditions, connections between structural elements and loading variations are studied using 3D models with shell elements of the casestudy. Although, the models described cannot closely represent the real structure. Firstly, a regular thickness has been assigned to masonry walls and piers despite their irregularities. Secondly, the material properties have been estimated from similar structures in Groningen, and may not represent the actual material characteristics of this case study. Thirdly, the cavity ties has been disregarded because they have been assumed to be corroded (no actual information was available). Finally, the concrete slab at the entrance of the church is disconnected to the foundation, which was an approximation from the drawings but could not be verified. For the casestudy prior structural retrofitting (models 15); Numerical Model 3 with eliminated foundation and timber flooring and a rigid base at the ground level is expected to give the best approximation of dynamic response of the church. The fundamental frequency in X direction of the casestudy prior structural retrofitting can be approximated between 2.30Hz to 2.75Hz and the fundamental frequency in Y direction between 3.0Hz to 3.45Hz. The fundamental global modes in this model show maximum deformation in the timber roof of the mainstructure and tip of the belltower in globalnd Y directions. This indicates weakness of the casestudy prior structural retrofitting. The Old Church has undergone structural retrofitting in July 2018, to prevent further seismic damage on the structure. From the survey of the casestudy and the retrofitting measures, the recent findings (eg., cavity walls, installation of steel frame, steel and timber columns) are incorporated into the finite element model of the casestudy and various modelling variations are presented in models 6 to 10. From comparing the results of these models post structural modifications, Numerical Model8 (or Model9 which has almost similar results) with degraded material properties of masonry and timber diaphragms, a shallow masonry step foundation and a rigid base at the foundation level are predicted as the closest approximation of the dynamic properties of the church. The fundamental frequency of the casestudy post structural retrofitting can be predicted to lie between 1.5Hz2.6Hz in global X direction and between 1.1Hz1.65 Hz in global Y direction. It can be observed that the implemented measures make the church stiffer and the weakness of the structure post structural retrofitting is localised at masonry facade walls of the belltower, cavity wall between the belltower and mainstructure, tip of the belltower, lateral walls and timber roofing of the mainstructure. This research on simulating a numerical model that closely represents the dynamic properties of the Old Church in Garrelsweer for achieving reliable, computationally effective and faster results. This can be used as a basis to compare the results of ambient vibration testing and operational modal analysis, and a relevant guide to study how the numerical models can be defined for modelling similar structures.

The main motive for this research was to study the behaviour of quay walls when there is an uneven pile foundation present. This means that the number of piles varies in the thickness of the quay wall along the length. The inspiration came from the failure of the Grimburgwal (Amsterdam, the Netherlands) that collapsed in 2020, which had a length of 65 meters, according to Korff et al. (2021). Korff et al. (2021) reported that the main failure mechanisms that are considered in the case of the Grimburgwal, is the deformation of the piles due to horizontal bending, in the section where there were only two instead of three rows of piles present in the thickness of the wall. A 2D model with a length of 22.5 meters in the longitudinal direction (along the length of the quay) wall is used in this research, to study the influence of the uneven pile foundation in the thickness of the wall. The quay wall’s out-of-plane behaviour is not considered. The masonry and timber floor are modelled with linear plane stress elements. An interface condition is used to model the interaction between masonry and the timber floor. The longitudinal support beams and kespen are modelled as one element. The piles are modelled as equivalent translational springs that are evenly distributed in the longitudinal direction. In the central area, one spring represents two piles in the cross-section, while the rest of the springs represent three piles. After the application of the deadweight of masonry and timber, a uniform distributed load was used on top of the model to cause settlement of the piles and wall. The dilatation joint was modelled with a nonlinear interface with a high dummy stiffness and no tension, and with a gap of one millimeter. If the length of the section with two rows of piles is increased, the capacity of the wall reduces. The cracks at the bottom of the masonry, still do not increase significantly if the length of the length of the section with two rows of piles is increased, but it does take less load to generate the same cracks. The boundary conditions also play a large role in the distribution of forces, since it is seen that the piles near the dilatation joint are less critical than the piles near the constrained edge. In the end, this model does give information on how the forces in the piles distribute and how the piles settle, before both brittle and ductile failure of the piles occurs and cracking within the model. However, it should be kept in mind that the model that is considered is a 2D model, whereas the problem of a quay wall is a 3D problem, so the results are not expected to be accurate.

Glass is gaining more and more popularity as a structural material and has become a big share of the building industry. Unfortunately, the building industry is the largest polluter in terms of industrial waste and is responsible for 40% of Europe’s energy demand (CIB, 1999), and glass is also playing a significant role in this number. One strategy to reduce the amount of pollution from a product or industry is by making it circular (PBL, 2019). Meaning the amount of waste is minimized and the energy needed to produce new material is also decreased. In the Netherlands, buildings have to be completely circular from 2050 (Rijksoverheid, 2016). In order for glass to contribute to this goal, elements have to be able to be reused or recycled, taking demountability into account during the design of a structure. One way of creating such a demountable joint, is by making use of portal frames, which require a rigid connection between the columns and beams. Currently, this connection is designed using either mechanical connections or adhesives. Rigid mechanical connections are visually not aesthetically pleasing and cause impurities right at the points where stresses are highest. This makes the joint more sensitive to failure. Rigid adhesive connections are very prone to execution and design errors, and are uncertain regarding their long-term strength. Currently, there is no efficient way to properly remove adhesives, making them non-demountable joints. This research will therefore design a demountable and rigid joint using contact pressure, taking inspiration from traditional Japanese joinery. To develop this joint, first, theory is studied, followed by the design and lastly by experimental testing. From literature, the Kanawa and Gooseneck joints are selected, because they have the capacity to take up both shear and a bending moment. These joints are then further optimized to determine the optimal geometry for a rigid glass joint. This means a geometry that minimizes tensile stresses in the glass, decreasing the chance an existing flaw will tear and cause the material to fail. This optimization is done using analytical and numerical analyses, followed by full-scale experiments. To determine the optimal force transfer the geometries were first schematized, and the relevant parameters were determined for later variation. From hand calculations, it follows that the optimal geometry finds a balance between the stresses resulting from normal force and the stresses resulting from the eccentricity of the internal line of force. Using a parametric Grasshopper model, the geometries are further optimized by varying dimensions and curvature. Several designs are imported into DIANA FEA and Abaqus to acquire numerical values for the expected stresses of these set parameters. The models are set up as two 2D glass panes with a polymer interlayer in between them. In DIANA FEA a lot of difficulties arose with the combination of complex geometry and multiple contact surfaces. Therefore all designs were mitigated to Abaqus, because this software is more suitable for complex contact surfaces. Comparing the heavily simplified hand calculations to the FEA, there was a constant increase of peak stresses with a factor of 4. The Gooseneck design was manufactured using a CNC milling machine and afterwards, its edge was polished, resulting in optimal edge quality. Due to the nature of the geometry, the Kanawa design had to be manufactured using a waterjet. There was a large difference between the accuracy of the two production methods, resulting in the Kanawa joint having a lot more space between the glass plates. This strongly influences the placement of the interlayer materials, but also the stiffness of the joint during the experiments. Before these models could be validated using experiments, a suitable interlayer to place between the edges of the glass panes was researched. POM, PVC, Surlyn, PA6 and PU85 are deemed suitable and are examined. Eventually, only PU85 could be fitted between the glass panes, which seemed to have the least favourable mechanical properties. The angle of the geometry was too small for most materials to bend them into, even after heating the plastics. The other issue lay with the tight tolerances of the polished glass panes. These had to be additionally polished by hand and the PU85 was treated with silicone spray, in order for the whole joint to fit. The disadvantage was that this manual polishing damaged the edge quality, increasing the probability of failure at a lower strength. Experiments were then conducted to validate earlier analytical and numerical calculations, using full-scale single-pane annealed glass. The joints were tested in pure tension and a bending moment, using polarizing filters to visualize the stress trajectories. For the Gooseneck model, the stress trajectories and expected stiffness corresponded well with the models. The samples failed at an average force of 6.0 kN. The model predicted peak stresses of 300 N/mm2 and stiffness of 2.8 N/m at this point, the experiments displayed a stiffness of 3.0 N/m. This means the model turned out to be 5.7% less stiff than the experiments. The stress trajectories coincided less clearly with the model for the Kanawa tension model. The samples failed at an average force of 4.1 kN. The expected peak stresses at this point were 150 N/mm2 and the stiffness 0.73 N/m based on the model. The experiments showed a stiffness of 1.1 N/m. The model underestimates the stiffness of the experiments by 33%. Interestingly, because the tolerances in the Kanawa joint were larger, there was more movement possible in this joint. This influenced the force transfer and therefore resulted in different peak stresses than expected. The Gooseneck model turned out to be almost 3 times as stiff as the Kanawa model. This has two likely reasons. First of all, the geometry of the Kanawa joint is not designed to take up pure tension in the direction that it was tested. Therefore, the geometry itself was a lot less stiff than that of the Gooseneck joint. Secondly, the tolerances were of large influence. Because the Kanawa samples were produced using a waterjet, with quite large tolerances, there was a lot of movement possible in the joint. This meant little force was necessary to displace the joint, resulting in a lower stiffness. The Kanawa design was tested under a bending moment, because the force transfer is very different compared to pure tension for this design. The full beam had dimensions of 2400mmx 400mmx 10 mm. Locations of peak stresses were similar to the models. The samples failed at an average of 4.0 kN, which corresponds with a moment of 1.1 kNm. The force-displacement graph of the experiments was not linear, but showed varying stiffness with plateaus where the stiffness was around 0. Most likely, this was caused by a combination of the plastic deformation of the PU85 and movement and/or sliding in the machine itself. It was attempted to calibrate the model to the experiments, by increasing the stiffness of the interlayer. This did not result in sufficient stiffness, which implies the stiffness originates from another element in the setup. The rotational stiffness was 611 kNm/rad, which is 9.1% of the stiffness compared to a solid beam of the same dimensions. This means the designed joint is not fully rigid, but this exploratory study shows there is great potential for such a system. Further optimizing the geometry and finding a more suitable interlayer could result in a rigid and demountable glass joint, as part of a portal frame.

Researchers of TU Delft have been designing and engineering with columns created out of multiple glass rods that are bundled together to form a single column. These aesthetically attractive and slender columns were tested to ensure safety before implementation in the real structure: the Glass Truss Bridge located at the campus of the university. However, the ultimate capacity and structural behaviour of such columns remained unknown. In this studies the structural behaviour of two designs of such columns is researched. It appeared that, among others, the differences in length between the rods within the columns caused an unequal distribution of stresses. This resulted in a large range of ultimate capacities of bundled glass columns that were designed according to the same design principles. Using a special approach in finite element modelling of the glass until failure, furthermore, resulted in more thorough knowledge regarding the failure behaviour of glass and the best way to model this behaviour.

This thesis describes the creation of the Equivalent Shear Masonry Model (ESMM). This is an orthotropic material model for low bond strength masonry that uses a smeared cracking approach. It was developed as an improvement of the Engineering Masonry Model (EMM) and adopts that model’s constitutive relations for the behaviour normal to the bed joints and for the compressive behaviour normal to the head joints. However, the shear failure criterion and the tensile head joint failure options are replaced by a new failure criterion for diagonal staircase cracks that is based on the observation that these cracks often open up horizontally. This failure criterion, the equivalent shear failure criterion, is derived from horizontal force equilibrium and evaluates both the shear stress and the tensile stress normal to the head joints. The combined constitutive relation is based on the Coulomb friction shear behaviour of the bed joints, that consists of linear loading, linear softening and a residual stress plateau. The softening is dictated by both the total shear strain and the total horizontal strain. This thesis first describes the development of this theory and its implementation into a user supplied subroutine for Diana FEA. This code was then verified for a single integration point and compared to the EMM’s Diagonal stair-case cracks option for a selection of load paths, among which combinations of shear and horizontal extension. This verification showed that the ESMM is more stable and provides more probable stress-strain diagrams. Subsequently, the model was validated against a micromodelled masonry unit cell for the same selection of load paths. This validation showed that the ESMM’s stress-strain diagrams are realistic, save some details that could be improved. Finally, the model was validated at a structural level with a macromodelled prediction of shear wall experiments. This validation showed that the ESMM is able to model post-peak behaviour, with both softening and a residual force plateau. The model featured inelastic deformation, hysteresis and even peak force reduction. Compared to the EMM’s Diagonal stair-case cracks option, it had less convergence issues and more realistic crack localisation. Some adjustments to details of the theory and the code are suggested. Also, further validations are required, for more load cases and other applications. Altogether, the Equivalent Shear Masonry Model shows promising characteristics and it is recommended that it is further improved and developed into a convenient, practical material model for low bond strength masonry.

Masonry is one of the most common building materials globally due to its ease of construction, price, durability and fire resistance. Its heterogeneity and orthotropic nature make its mechanical behaviour rather complex, highlighting the importance of an appropriate constitutive model to describe such behaviour accurately. In literature, most of the existing constitutive models for masonry fall in one of the two following categories: macro-models or micro-models. The micro-models (also called block-based models), which explicitly describe masonry's geometrical and material heterogeneities, exhibit higher accuracy but require higher numerical efforts when simulating masonry's mechanical behaviour. The macro-models (also called continuum models), which model masonry as homogeneous material and smear out the damage over the continua, are less accurate but offer a good compromise between accuracy and numerical efficiency. They are therefore used more often to simulate masonry structures. However, most of the macro-models are not capturing well the damage localization occurring along the mortar joints and the energy dissipation in the bricks and mortars. To increase the applicability of continuum models, the components' damage localization and energy dissipation should be improved. This thesis presents a homogenized constitutive model for applications on masonry structures under in-plane loading. The developed homogenized material model for masonry includes the description of shearing, tensile cracking, crushing and splitting. Inspired by the micro-mechanical models of Zucchini and Lourenço, four models were developed in this thesis to describe the different types of in-plane failure of masonry, naming: tensile failure of bed joints, horizontal shear sliding of bed joints, tensile cracking of unit, diagonal tensile cracking failure, masonry crushing failure. The first model is derived for the masonry’s pure shear behaviour, where the shear sliding failure is introduced. The second one is derived for the horizontal tensile behaviour, where the vertical tensile cracking of brick units and the vertical joints is proposed. The third one is derived for the vertical compression behaviour, where masonry crushing failure is adopted. The fourth one is coupling the failure mechanisms described in the previous three models with a novel algorithm. Additionally, the diagonal tension cracking failure and the horizontal tensile cracking of horizontal joints are incorporated in the fourth and final material model. To derive these models, first, a representative volume element (RVE) was selected for running bond wall, where the bricks are staggered by half-length of brick from the adjoining courses above and below. Each RVE consists of two-quarters of bricks connected through a bed joint, and each one is connected to a head joint on one side. For each of the models, the active internal stresses of each component (brick, bed, head or cross joint) are calculated through the compatibility and equilibrium equations resulting from the assumed deformed mechanisms. Different damage state variables are introduced for every component in the damage model, where exponential softening is assumed for tension and shear. Additionally, a Ducker-Prager yield criterion with bi-parabolic hardening is used in combination with an explicit Euler-forward algorithm to describe the elastoplastic behaviour of the material in compression. As a result, the material model’s constitutive law is obtained with the homogenization procedures after coupling the damage and plastic model together by a specific algorithm originally introduced by Zucchini and Lourenço. The constitutive equations for model 1 (shear), model 2 (tension), model 3 (compression) and model 4 (coupled) were coded successfully in MATLAB. The components’ shearing, tensile cracking, crushing and splitting failures are correctly modelled analytically with an algorithm, which can be applied to simplify the micro-mechanical model. Besides, constitutive laws of models 1 and 2 were also implemented successfully in the finite element software DIANA version 10.4 (check). The ability of the model to capture the failure of the components in shear, tensile cracking or crushing was examined through simple analytical applications. Moreover, the model was compared against experimental results from tests performed on masonry wallets under compressive loading; the model was able to predict the strength of the specimens satisfactorily. Therefore, this alternative constitutive material model can adequately simulate masonry’s behaviours with a simpler algorithm than the previous model. Meanwhile, the component’s elastic and elastoplastic behaviours can be simulated in more detail in this model, as the case that the horizontal joint is first damaged in shear and compressive splitting effects are additionally included.