This thesis investigates the potential of Basalt Fibre-Reinforced Polymer (BFRP) as an alternative to traditional steel reinforcement in concrete structures, with a focus on enhancing shear capacity. BFRP offers advantages such as higher tensile strength, superior corrosion resistance, and environmental sustainability. The study compares two alternative BFRP stirrup designs—braided BFRP rods and laminated unidirectional (UD) BFRP strips—with traditional steel stirrups through uniaxial tensile testing and displacement-controlled three-point bending tests on reinforced concrete beams. The results show that while BFRP stirrups improve the shear capacity of concrete beams, they do not yet match the performance of steel stirrups due to issues like reduced stiffness and stress concentrations in corner sections. However, BFRP stirrups demonstrated potential advantages in terms of weight efficiency, suggesting a promising role in sustainable construction. The findings underscore the need for further refinement in BFRP production methods to achieve consistent quality and better performance in structural applications.

Since a lot of bridges in the Netherlands have degraded over time, they require strengthening or (partial) replacement. Previously, the possibility to apply 3D printed fibre reinforced polymers (FRP) for strengthening of bridge decks was investigated by Arup. In this study was concluded that the field of movable bridges with timber decks has the highest potential. The timber deck, laid on steel stringers, should be replaced by an arch-shaped 3D printed FRP element, which will be placed in between the stringers. The print/material partner from the previous study retired and therefore, new research had to be done with material from another supplier, printed by another partner. This research focuses on the configuration and the properties of the new material, a recyclable thermoplastic glycol-modified polyethylene terephthalate (PETG) composite with glass fibres, and the optimization of the preliminary design.

The starting point of this research project was to investigate what the best material configuration was in terms of amount of fibres and way of printing. A fibre volume fraction (Vf) of 30% (GF30%) and 45% (GF45%) was considered. Is it possible to achieve more strength and stiffness by having a higher Vf without the material being too brittle or reducing the bond capacity of the layers? Since the fibres are orientated in the direction of printing, tensile tests in the principal direction will be performed to investigate the effect of the Vf.

With 3D printing, the element will be printed layer by layer. During the printing process, the material is melted, extruded, and cools down to harden. The longer it takes to print one layer, the more the material can cool down before the next layer is printed on top, the larger the temperature difference between the two layers will be. This difference in temperature determines the bond strength of the layers. Therefore, several layer times (80, 100, and 120 seconds) are considered to investigate what the maximum layer time should be before the bond strength decreases too much. This will be examined by tensile testing perpendicular to the print direction.

The test results showed that the structural performance of the GF45% material has a better structural performance than GF30% without being more brittle or having a significant lower strength in transverse direction. The GF45% material had a strength of 102.1 MPa and a stiffness of 22,040 N/mm2 in principal direction compared to 71.3 MPa and 13,920 N/mm2 respectively for GF30%. The two materials, printed with 80 seconds layer time, had a comparable strength in transverse direction with 20.4 MPa (GF30%) and 19.7 MPa (GF45%). The increased layer time was tested with the GF30% material. When the layer time was increased to 100 and 120 seconds, the strength decreased: 8.7 MPa for 100s and 7.7 MPa for 120s. Thus, the optimal configuration for the material is a 45% Vf and a maximum layer time of 80 seconds.

Having the optimal configuration determined, the mechanical properties of this material configuration should be established to be able to make a model for the design of the bridge deck element. These properties will be used in the finite element analysis (FEA) of the final design. The mechanical properties of the material are derived from tensile tests in longitudinal and transverse direction, compression tests in both directions, and shear tests. The investigated shear strength is the shear strength between the print layers, called the interbead shear strength (IBSS).

With these mechanical properties known, the design of the bridge deck component was optimized. The arch shape of the preliminary design is kept. The infill, design of print path and thickness of the top plate, side plates and arch will be varied. In this way, three distinctive design variants were made. From the analysis, it was derived that: the print path should have the same start and end point to enable symmetric stacking of the layers; the most extensive infill of the three variants performs the best from a structural point of view; and the thicknesses of the top plate, the arch and the side plates should be 2t, 3t, and 1t – 2t respectively. The thickness t is the thickness of a print layer, which is the width of the bead (6.0 millimetres). Since local eccentricities, due to transition points from single to double or double to triple layers, introduces unfavourable bending and thus, an increase in local stresses, local eccentricities should be avoided in the design of the print path. Lastly, the shape of the arch was varied. The circular shaped arch is preferred over a parabolic shaped arch because of better printability, although the structural design checks were comparable.

The results from the tests proved that a bridge deck element according to the final design is suitable for strengthening application. The two tested components showed consistent behaviour and were able to carry a wheel load. Moreover, a crack initiation and propagation failure mode occurred. This meant that the force remains at a certain load level above the required minimum equivalent wheel load without having collapsing failure. So, decks of movable bridges can be strengthened by the designed component with the 45% Vf and 80 s layer time configuration.

During the component tests, the failure mechanisms occurred was cracking at the intersection between the stiffeners and the arch. For follow-up, one could investigate a way to improve the connectivity between two stiffeners coming together at the arch, for example by increasing the overlap. Another issue for further research is the fatigue performance of the material and this component since this research is based on static analysis. Besides the properties and design aspect, assembly of the component should be investigated. Inverted T-girders with an additional plate on top could be an alternative to the I-girders as stringers, like in the preliminary design.

Recent advancements at TU Delft have investigated the potential of geometrically enhanced profiles to improve the performance of concrete-to-concrete interfaces, with one study focusing on the tensile behavior of single-tab Strain Hardening Cementitious Composites (SHCC)-to-SHCC interfaces through experimental testing. SHCC, an advanced fiber-reinforced cement-based material, is known for its distributed cracking and strain-hardening capabilities, offering superior ductility and crack control compared to traditional concrete. Building on this foundation, this thesis models the tensile behavior of geometrically profiled SHCC-to-SHCC interfaces using a continuum smeared cracking model in Abaqus and a lattice discrete cracking model.
The research aims to assess the predictive capability of these numerical models in capturing the behavior of geometrically profiled SHCC-to-SHCC interfaces. It focuses on understanding how interface parameters, such as strength and geometric profiles, influence tensile performance, particularly in enhancing ductility, controlling fracture response, and shifting failure modes from brittle interface failure to ductile SHCC material failure.

To evaluate the ability of numerical models to represent the tensile behavior of geometrically profiled SHCC-to-SHCC interfaces and assess the benefits of geometric enhancements for improving tensile performance, a systematic methodology was adopted. This included an analytical analysis to identify underlying failure mechanisms and develop a simplified model for quantifying their force-displacement response. A continuum smeared cracking model in Abaqus was employed to replicate experimental behaviors and investigate the influence of interface parameters through a parametric study. Finally, a lattice model was implemented to capture fracture responses in detail, enabling an in-depth analysis of the effects of interface strength and interface geometry on strength, ductility and fracture response.

The numerical models provided insights into the tensile behavior of geometrically profiled SHCC-to-SHCC interfaces, revealing the influence of interface parameters and geometric characteristics on failure mechanisms. The continuum smeared cracking model demonstrated the ability to simulate various failure mechanisms by adjusting interface parameters, but it underestimated SHCC’s strain-hardening behavior during local material-dominated failure due to the delayed introduction of damage. Conversely, the lattice discrete cracking model effectively captured distributed cracking patterns but exhibited overly brittle responses in interface-dominated failure mechanisms due to assumptions of brittle interface elements and the neglect of frictional resistance. Parametric studies confirmed that changing interface geometry and optimizing interface strength could shift failure modes from brittle, interface-dominated failure to ductile SHCC material-dominated failure.

This study highlights the capabilities and limitations of numerical models in optimizing the tensile behavior of geometrically profiled SHCC-to-SHCC interfaces. The continuum smeared cracking model in Abaqus identified critical parameters, such as tensile strength and fracture energy, influencing failure mechanisms. However, it underestimated SHCC hardening during tab failure due to delayed damage initiation, which should occur immediately after the elastic limit to accurately capture distributed cracking behavior.
The lattice discrete cracking model effectively simulated distributed cracking but exhibited overly brittle responses in interface-dominated failure mechanisms. This limitation stemmed from brittle interface assumptions and the omission of friction, resulting in a significant underestimation of displacement capacity.

Parametric studies using the analytical and lattice models revealed that modifying the interface geometry significantly reduces the interface strength required for ductile failure. For instance, the analytical model demonstrated that adjusting the geometry reduced the interface strength needed to transition from interface-dominated to material-dominated failure from 20% to 7%. In the lattice model, at low interface strengths (≤ 25%), a change in geometry of 1% enhanced SHCC damage by 3% to 6%. At higher strengths (≥ 30%), interface-dominated failure mechanisms diminished, with full SHCC material activation observed beyond 150% strength, ensuring global rather than localized failure.

These findings confirm that optimizing interface strength and geometry enables the transition from brittle, interface-driven failure to ductile, material-driven failure. Nonetheless, the models' limitations must be addressed, particularly the insufficient representation of strength-geometry-friction interactions in the analytical model and the lack of interface ductility and friction in the lattice model. Despite these challenges, the results provide a valuable foundation for refining numerical models and guiding experimental validation to optimize SHCC-to-SHCC interfaces.

As the structural engineering sector explores innovative materials such as Fibre Reinforced Polymer Composites (FRP), understanding their behavior under static and fatigue is critical. This thesis focuses on developing a numerical method to model the fatigue behavior of FRP composites, reducing the need for extensive experimental testing, resulting in a reduction of costs. Static and dynamic load tests were performed on Glass Fibre Reinforced Polymer (GFRP) coupons extracted from a vacuum-infused sandwich panel deck.

Based on these experimental test results, a numerical model was developed in Abaqus, integrating a VUSDFLD user subroutine to simulate stiffness degradation using a Continuum Damage Mechanics model. The model, which accounts for stress dependent stiffness degradation, was applied to coupons containing imperfections such as dimples from the manufacturing process, and without imperfections.

The research demonstrates promising results for higher load fatigue life predictions, with estimates within 10% of experimental results for both coupons with and without imperfections. However, at lower load levels, the model underestimates fatigue life by 85% for normal coupons and 30% for imperfection ones. These deviations highlight the need for further research, particularly at lower stress levels.

Despite the deviations at lower stress levels, this study presents an advancement in numerically predicting the fatigue life of FRP composites based on stiffness degradation, offering a cost-effective alternative to extensive experimental testing. The numerical model successfully integrates material degradation and manufacturing imperfections, providing valuable insights for the design and evaluation of composite structures subjected to fatigue loads. These findings also highlight the important role that imperfections play in fatigue performance. Future research should focus on optimizing the model, particularly at lower load levels, to enhance accuracy and increase its applicability. In conclusion, this study opens the door to more reliable, efficient, and improved use of FRP in structural applications, particularly in areas where fatigue behavior plays an important role.

The use of Glass Fibre-Reinforced Polymer as a building material in structures or structural components is on the rise. Standards such as CUR96, DNV and JRC provide a basis of design with the material. However, there is a lack of confidence in the design phase with structures made of Glass Fibre-Reinforced Polymer, resulting in the use of large safety factors causing the components to be bloated in size. At the time of writing this report, the technical committee, CEN/TC 250 (responsible for developing structural Eurocodes), establishes a technical design specification for Fibre-Reinforced Polymer (FRP) structures. This technical specification describes a simplified and linear criterion to determine the capacity of a GFPR Laminate, in addition to being open for the use of Progressive Failure Analysis (PFA). However, the simplified and linear criterion is overly conservative, whereas there is a lack of faith in the use of the PFA considering the failure theories and degradation models that are currently in use. This report discusses the PFA, a non-linear, 5-step, advanced 2D analysis model, that can predict the static strength of in-plane stress dominated Glass Fibre-Reinforced Polymer laminate, with an arbitrary lay-up composition, based on existing knowledge and experiments, including the damage development under multi-axial stress states and stress redistribution. The research is limited to in-plane behavior, under tensile and compressive stresses. The static material response is characterized on a unidirectional ply level based on principal directions and based on experimental results obtained from the OptiDat program. The response predicted by the PFA for both tension and compression was in reasonable agreement with the experimental results. However, depending on the failure theory and degradation model used, there is potential for optimistic predictions of the laminate stress capacity. For future work, it is recommended to continue the research on a larger variety of laminate lay-ups and include more failure theories and degradation models.

According to experiments the fatigue damage behaviour of fibre reinforced polymers (FRP) experiences a load sequence effect. In this report the ability of the cohesive fatigue damage model of Dávila (2020) to simulate the behaviour after a load amplitude change is investigated. For this a double cantilever beam (DCB) with fictitious material properties is loaded in mode I. Two element layers with each its own cohesive law are used to take into account the different behaviour of the epoxy and the bridging fibres in the wake of the crack. The calculated crack growth rate is compared to the experiments done by Jensen et al. (2021), since the conditions of the simulations are most similar to that of their experiments.
When the base and bridge layer only differ in their quasi-static cohesive law no load sequence effect is seen, since the conditions at the start of the second load block are the same as for the constant amplitude test at the same crack length. By allowing fatigue damage to accumulate only in the base layer and the bridge layer to only experience quasi-static loading, a history effect is seen. However, the high-to-low transition does not give the same transition behaviour as seen in experiments. In addition, the results of the constant amplitude tests are unrealistic.
When the fatigue damage accumulation of the bridge layer is faster than that of the base layer, a transition behaviour comparable, although less profound, to that of experiments is seen. This difference in fatigue damage accumulation is achieved by adjusting the coefficients of the fatigue damage rate function to the values corresponding to another R-ratio. This result may indicate a possible underlying mechanism for the transition behaviour of FRP.

FRP is increasingly utilised in the built environment, following successful implementations in the aerospace and marine industry. However, it exhibits poor stiffness and stability compared to conventional materials such as steel, making it challenging to satisfy serviceability and comfort requirements. Optimising FRP to address these challenges will allow for lightweight solutions with long service lives which could contribute to a cost-efficient reduction of carbon footprint. To this end, an optimisation tool for the preliminary design of bridges using FRP is presented in this thesis report.

The research explores the feasibility of adopting FRP in the main load-carrying system of pedestrian bridges and develops a framework for the concurrent geometry and material architectural optimisation of said structures. The study aims to achieve significant cost- and carbon footprint reductions in
monocoque FRP bridges by employing a numerical optimisation approach.

The optimisation tool utilizes the computer-aided geometric design (CAGD) software Rhino® and its parametric interface, Grasshopper®, to concurrently optimise the shape and material architecture of the bridges. Through the use of genetic algorithms, the framework overcomes FRP’s poor stiffness and
stability, and maximizes its unique advantages, including lightweight and high-strength properties, enabling free-form designs. This feat is achieved by implementing hybrid sandwich panels, comprising glass fibre-reinforced polymer (GFRP) and carbon fibre-reinforced polymer (CFRP) face sheets.
Satisfactory stiffness is ensured by defining deflection constraints, whereas constraints on the fundamental frequency and critical buckling load factor ensure adequate stability.

The research demonstrates promising results, showing potential cost reductions of up to 17% and carbon footprint reductions of up to 27.4% compared to a real case design carried out by FiReCo. However, certain limitations and areas for improvement are acknowledged, including the required run-time and the complexity of the solution space. Suggestions for enhancing the framework’s efficiency are proposed, including implementing orthotropic failure criteria and reducing the solution space through adjustments to ply thicknesses and foam core configurations.

Overall, the developed optimisation tool provides valuable insights and serves as a valuable resource for researchers and practitioners seeking sustainable and economically viable bridge designs. By embracing innovative solutions and eco-friendly materials, this study contributes to global efforts towards carbon neutrality and sustainable infrastructure development in the built environment.

The development towards a circular economy has many hurdles to overcome. For the construction sector an important step in this process is the transition towards reusing structural elements. Prefabrication of elements is a significant step towards achieving this concept. However, a case where both prefabrication and reuse are limited is the replacement of bridge decks. Headed bolts are welded to the steel supporting elements and encased in grout to connect them to the concrete deck elements. This method prevents reuse of the deck elements and hinders reuse of the steel supporting elements.

Research and literature exists on a number of alternative shear connectors that increase the modularity of these elements. The best alternatives have a single limitation in common: the allowed deviation for the placement of the shear connectors and bolt holes is smaller than is feasibly possible. The variances of element placement during construction add up to make it incredibly hard for these low tolerance connections to be made. The bolt hole diameter can be increased to increase the deviation tolerances. The large nominal hole clearance this results in needs to be considered. This can be done by using either resin injected bolts or High Strength Friction Grip (HSFG) bolted connections. Using HSFG bolted connections is preferred due to the shorter time spent on site and minimal waste, but research on the subject is sparse.

A proposed HSFG bolted connection that implements significantly oversized holes, defined as bolt holes with a nominal hole clearance roughly equal to the bolt diameter, and cover plates was designed together with both a control and regular connection to compare its behaviour with. The control connection is identical to the proposed connection with the exception of its holes which are normal sized. The regular connection has normal holes and does not include cover plates. Finite Element Models (FEM) were made of these connections that were subjected to static loading in a Finite Element Analysis (FEA). Test specimens of these connections were made and subjected to fatigue loading.

The numerical results of the static FEA showed that the use of cover plates reduced the stiffness and slip load of the connection. The second observation was the small impact that the hole size had on the slip load when using cover plates. This small impact becomes negligible at design preload.

The experimental results showed that the impact of larger bolt holes increased the loss of preload by roughly 1% during both short term relaxation and fatigue loading. The effect of the bolt hole size on the slip after fatigue loading was also concluded to be negligible, but the effect of the cover plates was concluded to be detrimental.

It was overall concluded that the use of significantly oversized holes in HSFG bolted connections with cover plates is viable. The negative effects caused by the cover plates and required longer bolt make it preferrable for large disc springs to be used instead of thick cover plates. The viability of the concept allows for further research on the subject.

Fibre reinforced polymers (FRP) can be a solution for future bridge renovation when only the deck of the bridge needs replacement. In these cases the deck is replaced with an FRP sandwich panel deck. The main advantages are a high strength-to-weight ratio which is beneficial for the ever heavier lorries and the fast installation which prevents hindrance. To connect the FRP deck with the steel superstructure, bolted connectors are used. One of the aspects that needs to be investigated before the bolted connectors can be applied are the relevant loads on the bolted connectors. The focus of this thesis will be to investigate the relevant static and fatigue forces on the connectors.
55 existing girder and arch bridges have been selected from a database of Rijkswaterstaat. For each bridge an appropriate FRP deck has been designed with an analytical method. The bridges are modelled in SOFiSTiK to investigate the shear forces in the connectors. The layout of the bolted connectors is kept constant for all bridges, as well as the transverse stiffness of the connector. The shear forces are calculated with a linear analysis. Before the static and fatigue analyses, first the hybrid interaction of the model is investigated. The hybrid interaction is the amount of horizontal forces transferred between the FRP deck and the steel super-structure. Hybrid interaction is beneficial as it increases the strength of the structure. Two models of a generic bridge have been investigated, the first is the standard model which is supposed to use hybrid interaction. The second model is an adjusted version to create a non-hybrid model. Three parameters are investigated: the deflection, the slip and the longitudinal stress over the height of the beam. The results show that hybrid interaction is created with the bolted connectors in the standard model.
In the static analyses two loads are investigated: traffic loads and temperature loads. The shear forces in the longitudinal direction are investigated as this is the governing direction. Before the loads are applied on the existing bridges, first a generic bridge has been investigated to gain knowledge over three bridge parameters. First the facing laminate of the FRP deck is changed. Second the direction of the webs of the FRP deck, and this also changes the connector layout due to feasibility. Third the expansion coefficient of the resin is changed. For traffic loads mainly the direction of the webs influences the shear forces in the connectors. For temperature loading the shear forces are largely depending on the expansion coefficient of the laminate, the close the expansion coefficient to the expansion coefficient to the steel superstructure, the lower the shear forces. The existing bridges that have been investigated resulted in a large scatter in results. The layout of the superstructure of the bridge influences the facing laminate and the number of connectors, which influences the maximum shear forces in the connectors. For both traffic and temperature loads, the connectors close to the supports experience the highest shear forces.
Besides the static loading, also fatigue is investigated. The shear forces in the connectors are calculated for one bridge, namely the approach bridge Nieuw Vossemeer. This bridge is one of the heaviest loaded bridges in the static analyses and it is according to expect judgement facing deck problems. Two aspects are investigated in the fatigue analysis, first the magnitude and second the type of load cycles. The magnitude is important as this needs to be below the slip resistance of the bolted connectors. The type of load cycles is important as this is related to how damaging the load cycle is. Because there are no S-N curves for bolted connectors between an FRP deck with a steel superstructure, the damage cannot be calculated. The R-ratio is used to investigate the type of load cycles. To calculate the R-ratio of a load cycle, the minimum shear force is divided by the maximum shear force. The resulting number expresses the type of load cycle. For the results, distinction has been made between the connectors close to the supports and connectors in the lengthwise middle of the bridge span. Both the magnitude as the type of loading is different.
Finally, it is concluded that the shear forces in the connectors is one of the aspects to be considered when designing a bridge with hybrid interaction between the FRP deck and steel superstructure. A large scatter of shear forces can be expected, depending on the bridge layout. Incorrect deck design can result in unnecessary high shear forces. The connector layout can be optimised to make the design more cost efficient.

In recent times, composite materials are widely applied in the construction industry because of their superior properties compared to traditional materials like steel and concrete. The use of composite materials in defense and infrastructure protective applications to resist high rate dynamic loading conditions has been gaining the interest of a lot of researchers over the previous decade. The limitations involved in studying the behavior of composites when subjected to high rate dynamic loads experimentally generated a need for numerical models that could simulate such complex material behavior. These numerical models are also highly useful in situations where it is difficult to perform direct measurements in experiments. The idea of this thesis originated from an aim to study the behavior of a TNO developed composite laminate with alternate 0-degree and 90-degree ply layup when subjected to out of plane blast loads. Considering the complexities involved in such a loading situation, a simplified test setup that can approximately replicate stress conditions in the composite laminate due to out of plane blast load has been proposed to be designed. This simplified test setup is prepared by performing an angled cut from the composite laminate, thus making the plies off-axis with respect to the global coordinate system of its cross-section. The motivation behind choosing such a test setup is that the interface/s can be loaded by a combination of compressive and shear stresses with axial loading on the specimen. The behavior of the simplified test setup with off-axis angles 30-degree, 45-degree, and 60-degree, when subjected to dynamic compression loads with different rates ranging from quasi-static to high is analyzed in this thesis using the finite element method. The initial parts of the study focus on analyzing the quasi-static failure behavior of the off-axis angled composite specimens with a single critical interface at the center modelled using the rate-independent cohesive law coupled with friction. The later parts of the study focus on analyzing the dynamic failure behavior of the composite specimens. The rate-independent cohesive law with friction is improved by adding a rate-dependency feature based on a Johnson-Cook law. Finally, the dynamic behavior of different off-axis angled composite specimens with critical interface/s modelled using the rate-independent and the rate-dependent cohesive laws with friction when subjected to compression loads with different rates is analyzed. The results obtained from the quasi-static analyses indicate that an increase in the mode-II cohesive strength, mode-II cohesive fracture energy, and interface friction coefficient lead to an increase in the peak load carried by the laminates. An increase in the thickness of the plies of an off-axis angled composite specimen results in a decrease in its peak load and changes its governing failure mechanism. There will be a dominant contribution of local inertia and wave propagation effects in dictating the failure behaviors of the specimens when subjected to compression loads with higher rates. The rate-dependent cohesive law with friction developed in this thesis seemingly captured the rate effects in the off-axis angled composite specimens when loaded in compression at different rates. Finally, it is suggested to design the simplified test setup by performing a 45-degree cut from the original composite laminate to simulate delamination due to compression loads of different rates effectively. But all three simplified setups have to be tested to derive the unique set of interface parameters that dictate the failure behaviors of the specimens.

Hybrid concrete-SHCC beams are a new development in construction techniques. SHCC stands for Strain Hardening Cementitious Composite. In such beams, the tension zone could for example consist, next to the traditional reinforcement, of a material that shows strain hardening behaviour. That helps with controlling the crack width. In traditional (non-hybrid) beams, the steel reinforcement would have to control the crack width on its own. This means that there are situations that the steel reinforcement fulfills the strength requirements, but additional steel reinforcement is needed to limit the crack width. Therefore, a certain amount of steel reinforcement is needed for meeting the SLS (Serviceability Limit State) requirements, while it is not used for the ULS (Ultimate Limit State) requirements. The use of hybrid beams consisting of an SHCC layer applied in the tension zone in which the reinforcement is embedded, solves this problem. This was shown in previous MSc studies by Huang and Singh. In this study, the concept of the hybrid beam is extended. A design was made of a reinforced U-shaped SHCC mould, to be used for casting a hybrid beam. In that way, a reinforced hybrid concrete beam is created, in which the webs of the U-shape prevent the need of temporary moulds at the side of the beam, which reduces costs. A complete design is presented which is ready for further research. Next to that, it is investigated how the bending behaviour of beams, that are made using this concept, can be modelled. This was done by extending the multi-layer model, that was first proposed by Hordijk in 1991. Different from the previous built models, the model proposed in this thesis includes additional aspects, such as imposed deformations caused by drying shrinkage, and the possibility to model hybrid beams (with a U-shape). After this model was extended using VBA in Microsoft Excel, it was successfully verified by comparing its results with experimental and analytical results from previous research. Comparing the force-to-displacement curves showed that the end-resistance of the beams is predicted well by the extended multi-layer model, and that generally the same trend of the curve is followed by the model. The bending resistance of the proposed experimental setup of a hybrid beam containing a U-shape was also modelled. However, as this experiment has not been performed before, there were no experimental results to compare with. Therefore, the results for this setup are to be compared with the results that follow after experimenting with the presented design of the beam.

Highway traffic bridges have been subjected to increasing loads over the past decades. Some of the movable bridge leafs in these highway bridges were constructed in the 1960s and they are now close to the end of their intended life span. These bridge leafs were typically designed and executed with hardwood deck boards. In the initial design calculations, traffic loads were smaller, complex calculation by computer models did not yet exist. Therefore, some phenomena like for example fatigue and global hybrid interaction were never considered. Since some movable highway bridges are now due to be re-assessed, there is a growing need to gain knowledge on the way timber decks are functioning within the movable bridge leaf. These bridge decks have sustained all loads throughout the years without significant damage, but we don’t know whether these timber deck boards help the main load bearing steel structure as well. Or in other words; do the timber deck boards interact with the steel girders in the current situation? In this research, the degree of hybrid interaction was measured in terms of the magnitude of the main girder deflection for the reference case of the Bridge across the Beneden Merwede. The main girder deflection for bolted connections, having a certain free slip and embedding stiffness, was determined by running a linear sequential secant stiffness analysis. This analysis approximates a physically non-linear analysis. The maximum deflection of the main girder was compared to the maximum main girder deflections for no hybrid interaction versus full hybrid interaction. The resulting global deflections from the Secant Stiffness Analysis have shown that practically no hybrid interaction can be found between the current deck and the steel structure. For retrofitting options, the level of hybrid interaction can be significant. An increasing or decreasing degree of hybrid interaction did not only change the forces and moments in the steel girders, but also had a considerable effect on the deck and its connections. There is a gain and a loss for every retrofitting option considered. Decision-making for retrofitting timber bridge decks should take multiple contradicting criteria into account. An optimisation could be necessary in order to take a well-advised decision.

Crack growth is an important failure mechanism in many engineering materials. Numerical models for crack growth have been developed within the framework of damage mechanics. All these models aim for the same goal, obtaining accurate results for crack growth under various loading conditions. Many damage models are based upon the cohesive crack approach. However, level set based models provide advantages compared to the cohesive crack models with regard to fatigue analysis. An alternative method to the existing thick level set (TLS) method was proposed, the interfacial thick level set (ITLS) model. The use of interface elements made the model more suitable to simulate several failure processes. In this thesis it is demonstrated that this method suffers from a dependency on the initial interfacial stiffness for the global response of a system by conducting a parameter study under quasi-static loading conditions. This parameter study proves that for a varying value of the initial interfacial stiffness parameter K the global response varies as well. This gives motivation to conduct further research on the removal of the initial interfacial stiffness from the current ITLS model. Two methods are developed to overcome the initial interfacial stiffness dependency. The first method assumes that the initial interfacial stiffness dependency is caused by the current formulation of the constitutive
law of the interface. A new expression for the interfacial stiffness is adapted after which all constitutive relations are updated. The new method shows a
perfect agreement with the current ITLS model, which validates the method as an accurate alternative. Compared to the current ITLS model, method 1 allows for the control of the initial stiffness of the undamaged part of the interface by changing the lower bound damage without affecting the global response. However, when executing simulations for a varying initial interfacial stiffness K the same problem as for the current ITLS is observed. It can be concluded that in a way this method removes the dependency on the initial interfacial stiffness but the initial interfacial stiffness parameter K should then remain constant. Furthermore, the calibration process is not simplified compared to the current ITLS model. For this reason method 1 is rejected as the final solution to the problem and a second method is proposed. The second method assumes a direct relation between the damage parameter c1 and the initial interfacial stiffness parameter K. This damage parameter is responsible for the steepness of the damage profile. The results from the parameter study showed that an increase of one of these parameters results in opposite behaviour for the initial stiffness of the global response. The leading hypothesis becomes that an increase in the stiffness parameter K can be neutralized by an increase in the damage parameter c1. Proportionality between both parameters is assumed. By trial and error the proportionality is found to be one to one. When using this proportionality condition, simulations with different values for the initial interfacial stiffness showed a perfect agreement for the load-displacement and the crack growth responses. Moreover, the proportionality condition is accurate for both a linear elastic (LE) material and an elastic-plastic (EP) material. The proportionality condition is proven by elaborating the interfacial stiffness over the damaged zone. This elaboration is done both numerically and analytically and proves that there is a one to one proportionality between c1 and K, which validates the replacement of c1 by a constant c multiplied with K. Lastly, the method should be compared to a response obtained through a different type of analysis. The method is compared with the solution of an analytical analysis resulting in a very good agreement for both a LE and an EP material. Therefore, method 2 can be approved as a solution to the initial interfacial stiffness dependency problem.

Offshore solar power installations can be increased in size and efficiency compared to land based installations due to the availability of space and the cooling effect of water. To increase survivability in large waves, very large floating solar platforms can be made flexible. However, a flexible structure is susceptible to wrinkling due to combinations of mooring loads, wave dynamics and the flexibility of the platform. Wrinkling is a limit state which is not commonly researched in maritime engineering, since generally structures are designed to be as stiff as possible. Wrinkling can lead to the global collapse of a very large flexible solar platform and should therefore be minimised. Very large floating platforms have an impact on the environment due to the shadow underneath. This problem can be diminished by adding holes to the platform. Furthermore, holes can be functional as manholes for maintenance of the bottom of the platform. Scientific research on the wrinkling behaviour of membranes has pointed out that wrinkling behaviour depends on the geometry of the membrane, which can for example be changed by adding holes to the membrane. The aim of this thesis is to set up a design and analysis framework for wrinkled membranes with permeability. In order to define this framework, (i) reliable computational indicators are developed; (ii) the influence of permeability on membrane wrinkling is investigated and; (iii) the framework is verified on a fictive case of an integrated stiff solar panel on a membrane. The first objective in this thesis is to find reliable computational indicators to assess the wrinkling behaviour of a membrane. Current concepts of offshore solar platforms are flexible membranes including mooring systems based on concentrated tension loads. To study the wrinkling behaviour of a (subregion) of such a flexible floating solar platform, in this study, it is modelled as a rectangular membrane subjected to uniaxial tension; following the available literature on the wrinkling problem. Numerical analysis of the wrinkling behaviour is first done by non-linear post-buckling calculations. However, it appeared that the results of this calculation are highly dependent on the initial deformation which is used. An alternative method which does not depend on user defined input was found in studying the second principal stress field: when negative second principal stress is present in the membrane, wrinkling can occur. When no negative second principal stress is present in the membrane, wrinkling will not occur. Furthermore, the distribution and the area of the negative second principal stresses region are indicators for the wrinkle distribution and amplitude. For a robust assessment of the susceptibility of a membrane to wrinkling, a study of the negative second principal stress field should thus be preferred over a post-buckling analysis. The second goal of this thesis is to research the influence of permeability on membrane wrinkling. The effect of holes on the wrinkling behaviour is researched by studying their influence on the second principal stress field. The aim is to find wrinkle free configurations and study the mechanisms which minimise wrinkling behaviour. Therefore, the size, location and shape of holes are varied systematically in membranes of different sizes. It was found that holes should be chosen so that when the membrane is strained, they deform in a way so that they bring tension in the regions of the membrane which are subjected to negative second principal stress in the non-permeable configuration. Furthermore, holes should be chosen such that the loadpaths in the membrane are not interrupted. The framework to research and design wrinkle free very large flexible solar platforms by adding permeability is verified and has proven to be effective by applying it on the configuration consisting of a stiff solarpanel mounted on a flexible membrane. In this configuration, the framework has led to holes by which the wrinkling region is localised. From the three parts of this thesis, it is concluded that a research framework for wrinkling of membranes with permeability was found in the analysis of the second principal stresses and the driving mechanisms were investigated and verified. To further develop this framework, research on the effect of stiffening the membrane and minimising wrinkling under load conditions other than tension are recommended.

This era of science and technology has seen widespread use of composite materials for a variety of applications ranging from the defense sector to the transport and construction sectors. Composites are mainly comprised of fibres impregnated with a polymeric matrix and have a superior strength to weight ratio as compared to traditional construction materials like concrete and steel. The strength of the fibres is much larger than that of the matrix. Also, the fibres exhibits elastic brittle behaviour while the matrix shows a nonlinear plastic behavior before damage occurs. Thus the overall response of the material is subjective to which direction it is loaded. In reality a multitude of stresses act simultaneously on any structure and it is quite challenging to develop a constitutive formulation for the composite material that can predict the stresses in these mixed modes accurately. This thesis aims at providing an improved constitutive formulation for the prediction of the material behavior of unidirectional composites. The constitutive formulation builds up on the existing knowledge of an isotropic invariant based yield function. The motive is to improve the performance of this constitutive law for better predicting the behavior under combined stress states, particularly in the presence of fibre stresses. Even thought the fibres behave completely elastic, the matrix surrounding the fibres is much weaker and tends to deform inelastically. The moment at which the yield stresses are developed in the matrix is also dependant on the level of stress in the fibres. To capture this behavious, two different yield criterion are formulated and testing in this project. First an additive split of the stress tensor helps to separate the fibre and matrix stress components along the fibre(`1') direction. The fibre stress is always elastic whilst the matrix stress component can behave inelastic. This matrix stress component is taken into account in the new constitutive laws. The first constitutive law is a modified version of the transversely isotropic invariant formulations as proposed by Vogler et al. and the second constitutive law is an anisotropic yield function proposed by Tsai Wu. The invarants are reformulated with the matrix stress tensor while keeping the same functional form as that of the transversely isotropic invariant formulation . Again, the split in stress tensor is performed and used in association with the anisotropic yield function. The derivations of all the constitutive relations is presented extensively in the third chapter. Followed by the formulations is the calibration of both the constitutive laws using the hardening curves derived from the micromodel simulations. The micromodel serves as the equivalent experimental test setup for the mesomodels presented in this project. Calibration of the mesomodels is a complex task in itself and the various trials were performed to determine the yield stress parameters that calibrate the models. Having calibrated the models, both the mesomodels are subjected to basic load cases and combined load cases. The MTIF model gives more consistent results than the TW model, however TW model performs better in the combined stress state of longitudinal axial tension and longitudinal in-plane shear. Finally, the effect of the fibre stresses on the plastic behavior of the matrix is being captured but to different extents in both the models. Neither of the models is able to match the micromodel results for all simulations. The sensitivity of the yield stress parameters is brought to light and are the main cause for the overestimating behavior of the TW model. Lastly, all the observations were concluded followed by some recommendations for the future work.

The use of the Classical Laminate Theory (CLT) is limited to laminates where all the fibres in a ply are oriented in the plane of the laminate. In some applications, it is possible that the plies will start at the bottom of a laminate and end at the top of the laminate. This means an inclination is added to the plies, which creates an extra rotation in the fibre direction with respect to the plane of the laminate. Such a laminate with inclined plies is found for example in the skin of InfraCore panels. In the regular CLT, this extra rotation cannot be taken into account, thus the elastic behaviour of a laminate with inclined plies cannot be described properly. The extra rotation that occurs in a laminate with inclined plies has analytically been implemented in the regular CLT to obtain a modified CLT, which has been verified using Finite Element analyses. Using the modified CLT, a reduction in equivalent stiffness can be observed for a single unidirectional ply with an inclination in the fibre direction. The exact value of stiffness reduction strongly depends on the material properties and the lay-up of the laminate. For InfraCore skins, the stiffness reduction is very small (0.15%). Due to the inclination in the plies, the lay-up of the laminate differs along the length of the plate. As a result, the output of the modified CLT is only applicable to one location along the plate. Due to the lay-up differences, the equivalent stiffness will also differ along the inclination direction. The in-plane equivalent stiffnesses will be the highest for symmetric laminates, where the flexural equivalent stiffness will be the highest when the plies with the stiffest fibre direction are located on the outside of a laminate.

For a housing project in Sirdal, Norway, a bridge is required in order to reach the construction site. Royal HaskoningDHV is interested in the possibilities that FRP composites might offer in terms of bridge design for this situation. Added to this, the fact that construction is mainly possible from one side of the river lead to the idea of an FRP cable-stayed bridge (the deck is made from FRP composite, however the cables and the pylon are respectively madefrom steel and concrete). The main span is 64 meters, which is large for an FRP bridge.Combined with its lightweight, low stiffness and structural damping, the structural response to wind excitation might be an issue. Next to designing an FRP cable-stayed bridge, this thesis therefore focuses in a second part on the dynamic behaviour to wind excitation of the bridge. To have a point of comparison with a more ’traditional’ cable-stayed bridge, in parallelto the FRP bridge, a steel-concrete alternative has been designed and analyzed. To push the comparison further, long span alternatives of the two bridges have been designed and analyzed to see their response to dynamic wind excitation. The dynamic analyses in this thesis only take buffeting (turbulence-induced vibrations) into account. Flutter (motion-induced vibrations) are considered through simple approximations from Eurocode.

The goal of this research is to optimize the fiber layup of a carbon windsurfing boom for weight and stiffness. A windsurfing boom should be stiff to provide an efficient basis for the energy transfer from the sail through the surfer to the board. The weight of the boom is important as the total weight of the rig influences the performance, especially during movements where the swing weight of the rig is important. To optimize the fiber layup the FEM simulation software of SolidWorks is used. This software allows the user to divide the part in sections and specify the layup per section in terms of orientation, thickness, and material. The output of the FEM simulation is the mass and the displacement under different load cases. The load cases are based on an experiment where the loads during sailing are determined with load cells and strain gauges.
The FEM simulation is validated and scaled based on two experimentally determined force-displacement relations. The FEM is scaled with the force-displacement relation of the first loading point by scaling the given material parameters by 0.78. The FEM is then validated with the force-displacement relation of the second loading point. New fiber layups are generated based on stress direction, previous iterations, and engineering intuition. The 50 new generated layups and their respective mass and displacement results are evaluated with a performance equation to determine which layup has the highest performance for the combination of mass and displacement. The coefficients in the performance equation are chosen so that both parameters have equal weight. The chosen layup is further evaluated with a required fiber overlap section. Two booms with the new layup are evaluated with the same experiment that is used to validate and scale the original FEM. At the first loading point, where the main loading during sailing is applied, the new layup is 16 percent stiffer than the original layup, as predicted by the FEM. The experiment results for the second loading point showed that the new layup was 5.5-7.5 percent stiffer than the original layup instead of the predicted 13 percent. This difference is due to the straight tubes that are glued to the end of the optimized boom body which are made by a different manufacturer. Changing the stiffness of these pipes makes the FEM results converge to the experimentally determined values. The experiment results of both layups are evaluated with the performance equation as the stiffness has increased but the mass has increased from 2.19 to 2.25 kg as well. The performance equation showed that the new layup outperforms the original layup for both loading points. The project goal to optimize the layup for mass and stiffness is therefore achieved. For the layup of the boom, a sandwiched layup of unidirectional fibers with biaxial fibers at the in- and outside of the circular cross-section was determined as the best performing layup for the sections loaded under bending. For sections that are loaded under both torsion and bending additional layers of biaxial fibers are added at the inside of the circular cross-section. These biaxial fibers are added at the inside as the unidirectional fibers are used at the outside to create the largest moment of inertia for these fibers as the displacement due to bending is leading in this case. Even the small translation of fibers from the inside to the outside of the layup can make a significant difference.

Fibre reinforced polymers, or FRP, are increasingly used in structural engineering applications. Permeating the construction field from the aerospace industry, FRP are applied in both the rehabilitation of existing degrading structures as well as the conception of new projects such as pedestrian and traffic bridges or building facades. The increase of interest and use in FRP in recent decades is driven by the material’s advantageous properties. Its tailorable mechanical properties, long-term durability, customizable free-form design, and its light-weight feature have engrained FRP as a noteworthy alternative to traditional construction materials such as concrete, steel, or timber. This is of paramount importance in light of the climate change challenge facing structural engineers today. While the material properties have been extensively investigated over the past decades, the structural use in FRP have remained limited to specific applications. As such, FRP, material of the future, has fallen short of its aspirations, disappointing its most ardent proponents. A rift is identified between the academic setting of laboratory testing and the pragmatic essence of the construction industry. This research situates itself as part of the efforts interrogating the industry limits and attempting to bridge these two spheres. It proposes to answer the following research question: What strategies capitalize on FRP’s favorable mechanical properties in order to promote formal exploration with the material in the preliminary phase of a design considering its durable and sustainable potential? This research proposes then a tool that capitalizes on the advantageous mechanical properties of FRP and encourages formal exploration in FRP at the conception phase of a design. Considering the climate change threat, the stakes of such a catalyst framework are high. The Wilhelminaberg Viewpoint, a landmark project in Landgraaf (NL) designed by Ney & Partners, is used as case-study to implement the proposed framework. It also allows to draw a contrast between what is structurally feasible in FRP and what is realistically buildable in FRP. A multi-step single-objective optimization is developed. First, stiffness for a certain design boundary is maximized. Using a brute force algorithm, the first level iterates through all the possible laminate layup combinations to find the combination which generates the stiffest structure. The second level of the optimization finds the lightest geometries using a genetic algorithm. This suggested framework offers an answer to the research question, mentioned hereinabove. Completely integrated in one interface (Grasshopper 3D), the developed tool stimulates formal exploration in FRP structures exhibiting shell-like behavior. The user defines the design boundaries, design constraints, load-cases, and material properties and implements the framework.

Actively bent grid shells are curved structural surfaces made of flexible members. The application is mainly in roof structures. The members, spanning between two supports on the perimeter, are connected at their intersections by joints, and assembled in an initially straight grid. By lifting at a sufficient number of points the straight grid is subsequently transformed into a bent shape and new geometry is preserved by fixing the supports. Subsequently, the curved surface is braced with a third layer of flexible members. According to this specific principle of construction, actively bent grid shells can be built within a short period of time.
ThinkShell, a research team at École des Ponts ParisTech, has developed a number of actively bent Glass Fiber Reinforced (GFRP) grid shells over the last ten years. Due to mechanical properties such as lightweight, high elastic limit strain, and high stiffness, Carbon Fiber Reinforced Polymer (CFRP) becomes an interesting material choice for construction of long-span actively bent grid shells.

In the actively bent members of the grid shells considerable amount of permanent stresses is present. The main source of stress is caused by the transformation of the straight grid into a bent shape during erection. Fiber Reinforced Polymer (FRP) is sensitive to creep behavior, which may lead to possible collapse mechanism due to creep-rupture or creep-buckling as a result of reduced stiffness of the material on a long-term. Limited knowledge is available of the time-dependent long-term creep behavior of CFRP, in the field of structural design of buildings. The main objective of this research was to define stress limits related to time-dependent long-term creep behavior of CFRP in members of actively bent grid shells, using the Stepped Isostress Method (SSM).

The most important conclusion drawn from the experiments using the SSM is that, in actively bent grid shell design, it is crucially important to stay below the sustained stress limits to avoid creep-rupture, as the CFRP fails in a brittle manner. From the SSM analysis using test data from bending experiments it was concluded that if the permanent load in the CFRP is 55% of the ultimate load, creep-rupture will happen in 40 days. This result does not seem realistic as the sustained stress limit from CUR96 corresponds to a service life of 50 years. Out of the four steps in processing of raw test data using the SSM, the rescaling step is the most critical step. There is strong dependence between the rescaling step and the horizontal shifting step. To determine the rescaling values and horizontal shifting for the bending experiments, a corresponding conventional creep tests as a reference test is proposed.
The SSM represents a promising method for accelerated creep testing and corresponding test data analysis for CFRP in members of actively bent grid shells. Sustained stress limits derived from the SSM may be used as more realistic, i.e. less conservative stress limit values to avoid creep-rupture, compared to the values defined in CUR96, for the specific design parameters.