Limiting maximum crack widths is a serviceability limit state, which ensures the durability of reinforced structures. In current practice, maximum crack widths are limited by using additional reinforcement, on top of the amount of reinforcement required for the designed ultimate bearing capacity. Reducing the amount of reinforcing steel used, could make the construction industry more sustainable. Recent studies showed that, hybrid reinforced beams with a 70 mm thick bottom layer of strain hardening cementitious composite (SHCC), so-called hybrid R/SHCC beams, are promising in controlling crack widths under pure bending, without using additional reinforcement (Huang, 2017; Singh, 2019). SHCC is made from a binder, fine particles and PVA fibers, which leads to ductile material properties and crack bridging. The beams studied in these previous studies were limited to a height of 200 mm. In practice larger heights are demanded. Increasing the height of a hybrid R/SHCC beam, by keeping the thickness of the SHCC layer constant, reduces the relative contribution of SHCC. In addition, cementitious materials exhibit strong size effects. Therefore, the effect of height scaling on the flexural crack width controlling behavior of hybrid R/SHCC beam is studied in this thesis. In addition, the optimization potential of the crack controlling behavior of the hybrid R/SHCC beams is studied, by the delamination of the SHCC-rebar interface. The effect of height scaling on the flexural crack width controlling behavior of the hybrid R/SHCC beams is studied both experimentally and numerically, by 200 mm, 300 mm and 400 mm high hybrid R/SHCC beams, with a constant 70 mm thick bottom layer of SHCC. Reinforced concrete beams of the same heights are used as reference. The length of the higher beams are increased, to prevent direct force transfer. The experimental results of the 200 mm high beams are used from a previous study by (Singh, 2019). To study the effect of delamination of the SHCC-rebar interface, a 300 mm high hybrid R/SHCC beam with smooth and Vaseline treated longitudinal reinforcement bars is used. The beams are tested in a four-point bending configuration, with a 500 mm constant bending moment region. All the beams have the same amount of longitudinal reinforcement. The numerical study is performed with the Delft Lattice Model. As lattice models are only recently used for the modelling of structural behavior, the use of the Delft Lattice model in this study is a contribution to the development of lattice models. Analytical calculations, with use of the multi-layer model (Yassiri, 2020), are used in the comparison of the numerical and experimental results. From the performed experiments, it is found that, the load, at which the 0.3 mm crack width limit is reached, decreases from 109% to 97% and 91% of the yielding load, upon increasing the height from 200 mm to 300 mm and 400 mm, respectively. Whereas, the beam with smooth and Vaseline treated longitudinal reinforcement bars, reached the crack width limit already at 59% of the yielding load. Increasing the height of the reinforced concrete beams does not lead to a reduction in the crack width limit load, relative to the yielding load (76%-78%). From the cracking patterns, it is found that, upon increasing the height, the number of propagated concrete cracks decrease, both in the reinforced concrete beams and in the hybrid R/SHCC beams, whereas the hybrid beam with smooth and Vaseline treated reinforcement bars showed a single propagated crack in the concrete layer. An effective tensile area is developed for the 300 mm and 400 mm high beams, which was not observed in the 200 mm high beams. Uniform cracking distributions are found in all the SHCC layers of the hybrid beams, except for the hybrid beam with smooth and Vaseline treated reinforcement bars. The delamination of the concrete-SHCC interface increases, upon increasing the height, whereas the ultimate bearing capacity is similar for the 300 mm and 400 mm high hybrid R/SHCC beams. On the contrary, the hybrid beam with smooth and Vaseline treated reinforcement bars shows very limited delamination. From the out of plane measurements, it is found that, hybrid R/SHCC beams show out of plane displacements, which are highly correlated to the applied vertical forces. This is not observed for the reinforced concrete beams. The numerical models are able to simulate the trends in the cracking patterns, as observed in the experiments. In addition, the numerical models are able to simulate the trends in delamination. Increasing the concrete-SHCC bond strength, in the 400 mm high hybrid R/SHCC numerical model, leads to the formation of an additional propagated crack in the concrete layer. In addition, the deformation capacity and the delamination of the concrete-SHCC layer reduces, for the beam with the stronger concreteSHCC interface bond strength. Using a coarser 25 mm voxel size in the numerical models, instead of the 10 mm voxel size used in previous studies (Mustafa et al., 2022), leads to similar simulated structural behavior of the beams. The voxel size limits the crack spacing, which is of larger importance for the SHCC, compared to conventional concrete. For the reinforced concrete beams, the numerical models are able to predict the yielding load, whereas for the hybrid beams, the yielding deformation is underestimated, due to the overestimation of the ductility of the modelled SHCC. The analytical calculations show good comparison with the numerical models, both for the hybrid beams and for the reinforced concrete beams. The hybrid beam with smooth and Vaseline treated reinforcement leads to an unreinforced hybrid beam, which is different from the experimental results. This difference is attributed to the numerical model simulating a weak bond over the full length of the beam, whereas in the experiments Vaseline is only applied over the 700 mm central span. To conclude, upon increasing the height of the hybrid R/SHCC beams, the effectiveness of the crack controlling behavior decreases. This is both found in the numerical and in the experimental results and holds both for a 0.2 mm and 0.3 mm crack width limit. However, the hybrid beams scaled in height still lead to a significant increase in the crack controlling behavior, compared to reinforced concrete beams of the same heights. Full delamination of the rebar-SHCC interface leads to worse crack controlling behavior for the hybrid R/SHCC beams. Even more, if the full delamination occurs over the full length of the beam, the beam could be considered unreinforced. The Delft Lattice model shows large potential in the simulation of the structural behavior of both the reinforced concrete beams and the hybrid R/SHCC beams. The coarser 25 mm voxel size is found to be a time efficient and suitable modelling solution to gain insight in trends in the structural behavior of reinforced structures. The numerical model with a stronger concrete-SHCC interface showed potential in improving the crack width controlling behavior of the hybrid R/SHCC beams in height. Therefore, it is recommended to study the effect of interface roughness for hybrid R/SHCC beams scaled in height. Additionally, determining the material input for SHCC remains a challenge in numerical simulations with the Delft Lattice Model. In order to improve the simulations of the numerical models, it is recommended to study the material input possibilities for SHCC. Even more, before the beams are applied in practise, it is recommended to gain deeper understanding of the increased out of plane sensitivity of the hybrid R/SHCC beams. Studying the fiber dispersion would be logical start for this.

Strain hardening cementitious composites (SHCC) can be used to reduce the amount of reinforcement needed to control crack widths. SHCC has a strain hardening behaviour with dense micro-cracking, which makes it more ductile compared to conventional concrete. Conventional concrete can be used in the non-critical locations. An interface is formed in between the two concrete layers. The interface is the weakest link in the system, governing the structural performance. Therefore, the interface is of interest in ongoing research. The lattice model allows to investigate the effect of the fundamental parameters, the interface tensile strength and interface stiffness, on the structural behaviour in different bond tests between normal strength concrete and SHCC. Direct tension, direct shear and the notched-beam test were used to investigate the effect of the individual interface properties on the global behaviour. In all bond tests a smooth and profiled interface were simulated to investigate the effect of applying a roughness to the interface. In the small-scale tests activation of adjacent materials was found to occur at increased interface tensile strength and decreased interface stiffness. For a smooth interface a decrease in interface stiffness resulted in a scatter of failed elements over the interface in the direct tension test, increasing the ductility. Initially, a linear relation is obtained between the interface tensile strength and load capacity for the direct tension and direct shear test. With higher interface tensile strength cracking of the adjacent materials increased the load capacity, but the adjacent materials started to become governing. The application of a profile in the interface increased the capacity even further and resulted in an increased softening. For a profiled interface the effect of changing interface properties was limited in most cases compared to the effect on a smooth interface. This was due to the activation of the adjacent materials at lower interface properties compared to the smooth interface. Similar trends were found between the structural behaviour and interface properties for the notched-beam test. Only the application of a profile did not increase the load and displacement compared to the smooth interface. With the beam simulation results a data set is generated with the information about the load, displacement, interface opening and joint opening at failure. The data is classified based on the failure mode of the beams. From the classification it was found that with a smooth interface higher interface properties can be reached before the failure mode would change from interface to partial failure or from partial to concrete failure compared to a profiled interface. The range of interface properties resulting in interface failure is higher for the notched-beam test compared to the small-scale test. The notched-beam test will, therefore, be more likely to show interface failure when used for testing the interface.

Strain Hardening Cementitious Composite (SHCC) is a new type of concrete that is able to control the crack-width in concrete structures. The application of this material in the tension zone of hybrid concrete structures is thus of interest in practice. The interfacial behavior for these hybrid structures is something that is of importance for the composite action. Therefore, a study is performed to investigate the behavior of the interface in hybrid SHCC-concrete beams. This is done by performing an experimental study on beams with a joint at midspan. Several parameters such as the interface roughness, coupling reinforcement cover, curing method and protruding reinforcement have been investigated. The hybrid SHCC-concrete beams are tested in a four-point bending configuration to obtain a constant-bending moment region along the interface. The crack propagation along the interface and through the SHCC/concrete has been evaluated with the use of Digital Image Correlation (DIC). Furthermore, also a numerical analysis has been performed using DIANA FEA based. The numerical analysis was used to help to determine the experimental campaign. Furthermore, also several experimental samples have been modelled to study the behavior of the beam in more detail and to make recommendations for future modelling of the interface. Based on the experimental results, the influence of the interface roughness resulted in an increased bond at the interface. This is both seen in an increased bearing capacity and a reduction of the interface and joint opening at equal loads. The profiled interface and holed interface resulted in an increased capacity due to the mechanical interlocking at the interface. The bearing capacity of these samples increased by 78.4% and 54.7% respectively compared to the reference sample (13.9 kN). In case of the profiled sample, no delamination of the interface occurred as the sample failed due to a horizontal crack at the level of the coupling reinforcement. This can be attributed to the localized tensile stresses at the reinforcement level. The last sample with a different interface roughness consisted of epoxy and sand (1-2 mm). For this sample, the bearing capacity increased by 51.8%. The failure of this sample was a combination of interface delamination (initially at the joint) and a horizontal crack through the coupling reinforcement. For all the samples with a different interface roughness, no yielding of the coupling reinforcement occurred. Several beams with a smooth interface have also been tested by adjusting the reinforcement cover, curing method and applying protruding reinforcement. The influence of the reinforcement cover didn’t have an effect on the bearing capacity. However, the interface and joint opening reduced significantly as the eccentricity of the reinforcement bars also reduced. Furthermore, also the effective height increased resulting in lower reinforcement stresses. The influence of a different curing method was investigated by placing the sample in a humidity-controlled (50 %) room to investigate the effect of shrinkage. The results showed that the bearing capacity remained similar to the reference samples. This can be attributed to the fact that the bond internally was still good, caused by the restraint of the reinforcement bars. However, the deflection of the beam increased as a result of the reduced stiffness by the shrinkage induced cracks. Finally, one sample consisted of stirrups at a distance of 50 mm from the joint to take up the tensile stresses at the interface (e.g. due to reinforcement eccentricity). The results showed an increase in bearing capacity by 102.7% compared to the reference sample. However, also in this case, no yielding of the coupling reinforcement occurred. The failure of the sample is also caused by the delamination of the interface. Furthermore, as a result of this delamination, fracture of the top part of the SHCC occurred at the location of the protruding reinforcement due to the rotational restraint of the stirrup. The 2nd part of the study consisted of a numerical analysis. A Coulomb-friction model with an interface tensile strength cut-off is used to model the interface. Based on this, a good correspondence between the experimental results and FE results is found in terms of the bearing capacity and failure mode for the sample with a smooth interface(delamination). However, the crack propagation of the flexural cracks through the concrete and SHCC was substantially different. The sample with a profiled interface has also been modelled in Diana FEA. This is done by implementing the profiled interface manually in the FE model. The model showed a good correspondence with the experimental results in terms of bearing capacity and interface and joint opening. The crack propagation in the concrete is also similar to the experimental results. The model however doesn’t show any flexural cracking in the SHCC layer as a result of the limitation of DIANA FEA. Also, an additional study is done to replicate the behavior of this beam using a smooth interface. Based on this model, it is recommended to use a perfect bond at the interface. For both these models, the FE model wasn’t able to replicate the strain hardening behavior of SHCC. This is due to the limiting material models in DIANA.

Existing reinforced concrete (RC) structures can be strengthened using Strain Hardening Cementitious Composites (SHCC). The ability of SHCC in exhibiting a ductile response under tensile load due to strain­-hardening after crack initiation makes it a viable material to be used in, both, construction and retrofitting of concrete structures. The main objective of this research is to study the shear behaviour of SHCC-strengthened RC beams using NLFEA. The shear behaviour of benchmark RC beams is analysed first. The analysis of the selected RC beams analysed using Damage-based shear retention function results in accurate predictions of peak load if a fine mesh size resulting in 30 or more elements in the height of the beam is used. However, the failure type is predicted inaccurately for both coarse and fine mesh sizes due to lack of consideration for aggregate interlock in Damage-based shear retention function. The analysis of the selected RC beams using Al-Mahaidi shear retention function results in accurate predictions of peak load if a coarse mesh size resulting in 20 elements in the height of the beam is used. The failure type is also predicted accurately using Al-Mahaidi shear retention function with the stated mesh size. The consideration for aggregate interlock implicitly in Al-Mahaidi shear retention function in the form of shear retention factor allows for accurate prediction of both peak load and failure type. After analysing the shear behaviour of RC beams, the shear behaviour of a reinforced SHCC beam is analysed using Al-Mahaidi shear retention function since it can predict both failure load and failure type accurately for RC beams. In comparison with experiment, the peak load for the reinforced SHCC beam is underestimated and the failure type is also incorrectly modelled. Use of embedded reinforcement results in excessive cracking along the reinforcement, causing convergence issues at a load lower than the experimental peak load. Such excessive cracking is not observed in RC beams since cracks more localized in concrete as compared to SHCC, which exhibits multi-cracking behaviour. Therefore, the shear behaviour of selected reinforced SHCC beam using Al-Mahaidi shear retention function is not accurately modelled. After the analysis of shear behaviour of concrete and SHCC separately, their behaviour is studied in the form of SHCC-RC hybrid beams. The solution strategy consisting of Al-Mahaidi shear retention function is used, and different types of hybrid interface are modelled. The results show that peak load and failure type are accurately predicted when a numerically perfect bond is modelled at hybrid interface for hybrid beams exhibiting no debonding during experimentation. This is in case of a mesh size resulting in 20 elements in the height of beam used. The peak load and failure type, however, are inaccurately predicted when delamination is modelled at the hybrid interface for hybrid beams failing due to delamination during experimentation, irrespective of the mesh size considered. This is due to the inability of the Coulomb friction interface model in recognising significant delamination at the hybrid interface as a reason for the failure of the hybrid beam.

When concrete is subjected to imposed deformations, stresses may develop. If at any point in time this stress exceeds the tensile strength of the material, the concrete will crack. Early-age cracking of concrete structures may lead to problems with durability, serviceability and aesthetics. During hardening of concrete the material properties are still in development. Therefore, to be able to predict the crack width, understanding of the stress- and strength development is required. In addition, concrete is a visco-elastic material which means that stresses are affected by phenomena such as creep or relaxation. If the design codes predict the crack width in concrete structures under imposed deformations accurately remain subject of debate. The CROW report published in 2021 [9] provided the starting point for this research. The aim of this study was to gain more insight on the background of the design codes, and to explain the fundamentals of the crack width prediction in case of imposed deformations. For this purpose, the following research question was formulated: ”What is the applicability of the design codes regarding the crack width prediction of reinforced concrete structures under imposed deformations?” From the literature study it became clear that the main difference between the design codes was related to which boundary conditions and cracking theory were applied. The majority of the design codes applied the well known tension bar model theory where both ends are fully restrained. In addition, there were also codes using the continuous base restraining theory in which the tensile member is continuously restrained along one edge. This made a huge difference in the prediction of the crack width. From the finite element analysis which was performed, it turned out that there is a difference between the steel stress development of imposed loading and imposed deformations. In addition, in case of imposed loading less cracks were developed than under imposed deformations. However, from this specific numerical analysis it turned out that the maximum crack spacing and crack width is smaller in the imposed loading model in comparison to the imposed deformation model. The only explanation for this is that in case of imposed loading the cracks are more evenly distributed. A case study was used to simulate the hardening process of concrete in combination with autogenous shrinkage as imposed deformation and compared with a finite element analysis. The goal was to determine a set of model properties that are useful for future engineers. The accuracy of the input parameters was verified with the experimental work carried out by M. Sule. Overall, when performing a non-linear finite element analysis a lot of knowledge was required. It turned out that specific choices such as the constitutive model type, the kinematic and equilibrium condition have a major impact on the outcome. Using the modified Bar model of Lokhorst in combination with this numerical approach resulted in good agreement with the experimental findings. The parameter study showed that regarding the tension bar models, the bar diameter has the largest influence on the crack width prediction. While with respect to the continuous models there was no onesided answer to the question which parameter had the largest influence on the crack width prediction. In one of the design codes based on the continuous model theory named CIRIA [8] the degree of restraint clearly stands out as the most important parameter. Whereas in the another design code based on this theory, namely the ICE [4], all parameters that were investigated in this thesis have limited effect on the crack width prediction. The design codes considered in this master thesis do not yet fully represent the crack width due to the hardening of concrete or due to autogenous shrinkage. The design codes are applicable for the crack width prediction of reinforced concrete structures under imposed deformations if conservative assumptions such as a weak bond between concrete and steel reinforcement are taken into account. It is clear that the problem treated in this report has more complexity than what one initially may think. Opinions on how to determine the crack width of reinforced concrete tensile members under imposed deformations differ. The difference is related to the type of restraint and the cracking theory which are suggested in most used analytical design models. This report contributes to a better understanding of the crack width development under imposed deformations through non-linear finite element analyses and verification with experiments. The results from this master thesis suggest that an approach to a more consistent crack width prediction under imposed deformations should investigate how bond in the interface between concrete and steel influences cracking. This has lacked attention in the current formulas in the design codes.