The aim of this thesis was to objectively and quantitatively assess the accuracy and robustness of two-dimensional sequentially linear analysis (SLA) in comparison to nonlinear finite element analysis (NLFEA), for a range of experiments of reinforced concrete structures with proportional and non-proportional loading schemes. Non-proportional loading refers to when two or more load cases act on a structure that do not increase or decrease in a proportional way. Accuracy was defined as the degree to which the finite element model's results match the experimental results. Robustness was defined as the method's ease of completing the computation and objectivity with respect to user-specified input. In selecting the benchmarks, experiments with brittle or quasi-brittle failures were targeted. Two experiments with proportional loading (a shear beam and a corbel) and three with non-proportional loading (a shear wall, a flexural beam, and a frame) were selected as the benchmarks. The frame is a single-span, double-storey frame, and thus consists of more structural elements than the other benchmarks. Each experiment chosen had previously been analysed using NLFEA by either the experiment conductor or another in academia. The five benchmark cases were modelled with SLA using a consistent solution strategy. The material constitutive models were discretised using the (standard) ripple band width saw-tooth law, which defines an upper and lower band of the softening and plasticity relations via a factor (p) of the material strength. Four performance parameters were devised to assess the performance of the SLA and NLFEA for each benchmark in the pre-peak, peak and post-peak stages, by comparing the modelling of the structural stiffness, peak load, ductility and ability to model post-peak behaviour to experimental results (where applicable). Inhibitors to the method's accuracy include the inaccurate modelling of stress reversal, which creates unrealistic crack openings and closures; delayed and limited yielding of reinforcement due to the discretisation of the Von Mises plasticity, resulting in overestimation of structural capacity and underestimation of ductility; lack of consideration of geometrical non-linearity; and small inaccuracies in the modelled saw-tooth relations resulting in some overestimation of reduced strength values during material softening and spurious transverse crack strains. Additionally the accuracy was limited by the simplification of the concrete material model and use of the linear tensile softening relation. Inhibitors to the robustness of the SLA included lack of objectivity to some user-specified input and intermittent proportional loading limiting the amount of post-peak behaviour successfully modelled in the non-proportionally loaded benchmarks. Overall, SLA was found to have a comparable level of accuracy with NLFEA in modelling reinforced concrete structures in both proportional and non-proportional loading scenarios, with many benefits observed in terms of increased robustness. The inaccurate stress reversal algorithm can severely affect the robustness of non-proportionally loaded cases and resolving this inaccurate formulation of crack closure in SLA should be a priority in future developments.

This research investigates how the equivalent frame method in combination with a sequentially linear analysis can be used to model the behaviour of a façade of an unreinforced masonry structure, subjected to a lateral pushover load. The experimental data of the two-story building experiment at the University of Pavia is used.
Two different types of models are made, a continuum model and a beam model, with each two different modeling approaches, the three-zoned approach for the piers and spandrels and a uniform model. The three-zoned approach uses the bed joint tensile strength at the ends of the piers and spandrels, and the maximum tensile strength at the center of those element to simulate rocking and shear failure respectively. The most important results are:
The three-zoned approach in combination with a continuum model was able to describe the failure mechanism of the façade and perform the analysis stable, with a maximum tensile strength adjusted to f_tu=0.08 MPa. Shear failure in the piers was dominant. As a lateral push-over load was used and not a cyclic load as in the experiment, the maximum load of the structure was for most displacements somewhat higher than in the experiment, but the maximum load was 150 kN in both cases. The displacement of 22 mm in the experiment was not reached, but a displacement of 10 mm.
The beam model analysis aborted early as a result of a reduction of the initial load factor. It was found that the fixed crack approach in combination with high shear forces in the structure resulted in a fixed crack coordinate system that was rotated from the beam axis. Principal stresses could exceed the strength of the material and wrong integration points were damaged reducing their strength severely. At this stage a maximum displacement of 5 mm is reached while the force is 165 kN, higher than in the experiment. The structure responds very brittle.
Shear stresses in the beam element model exceeded the strength of the material. Adding shear interfaces in an SLA will result in a more correct failure pattern.
For the beam model, a sensitivity check was done for the mesh size, fracture energy, number of saw-teeth and number of integration points. All values were accurate enough.
A relation exists between an initial load factor reduction and the opening of a crack in the corresponding integration point that damages at an initial load factor reduction.
In conclusion, the results of this thesis confirm the potential of the SLA to accurately approximate the behaviour of an URM structure as it was possible to run a stable analysis with accurate results for the continuum model. The beam model gave similar results in terms of forces and bending moments compared with an incremental iterative approach, but the analysis was aborted early. New developments like a rotating crack approach and shear interfaces will result in a more stable analysis as the right failure behaviour will be followed resulting in a more accurate load-displacement relation.

This thesis is a study towards in-plane behaviour of masonry shear walls modelled through a predefined crack pattern at macro level. The Semi-Lumped method, proposed by Messali (2015), is analysed in detail to confirm the consequences of the SLM assumptions. This is achieved via literature and numerical validations. The final part of the thesis contains a pilot study towards a combined procedure of the Semi-Lumped Method and the Sequentially linear analysis.