Throughout the years, incremental iterative approaches have been shown to be excellent tools in describing the complex behaviour of structures under a wide range of circumstances. However, robustness issues arise for quasi-brittle structures due to the potential lost of convergence during the development of abrupt fracture mechanisms. In order to overcome these robustness issues, the framework of sequentially linear analysis (SLA) has been proposed: an event-by-event strategy in which a sequence of scaled linear analyses with decreasing secant stiffness is performed, representing local damage increments. The current SLA-framework is based on a fixed crack approach, potentially causing the development of severe spurious stresses and inaccuracies due to the misalignment of the crack with the principal stress directions. To this end, Hendriks and Rots proposed a model consisting of several parallel fractions or layers, from now on called the sublayer model. Each of the layers is elastic-perfectly brittle, but has different properties, chosen such to represent the overall constitutive softening behaviour as accurate as possible. The layers fail independent of each other and have their own specific crack direction. The main idea is to mimick a rotating crack by a superposition of sublayers with a fixed crack direction. The main goal of this thesis is to further elaborate, generalize and verify the sublayer model for quasi-brittle materials and capture the influence of rotating cracks on the structural response within the framework of existing regular sequentially linear analysis. In this thesis, the frameworks of regular SLA and the sublayer model were connected by a general transition from any saw-tooth law to sublayer material properties. An externalized procedure was created to automatically generate an input file for DIANA FEA and thereby facilitate verification of the sublayer model. Furthermore, the 2-dimensional framework of the sublayer model has been extended towards 3-dimensional structures to broaden the range of application. On top of that, concepts were proposed to improve the sublayer model: the tapered ripple band, reducing the required number of sublayers to reach a specific state by adding more saw-teeth near the end of the softening curve, and an improved algorithm, making use of the fact that the order of brittle fracture of the sublayers is known in advance, such that only those integration points that can actually become critical are monitored, thereby reducing computational efforts significantly. In this thesis, the sublayer model is proved to mimick a rotating crack within the framework of existing regular sequentially linear analysis based on a set of structural case studies (notched beam, shear notched beam, DEN-beam, full scale facade and full scale concrete dam). Compared to regular SLA, effects of stress locking are reduced, less wide localization bands are found and a more realistic collapse pattern is observed, thereby making the sublayer model more interesting for application in engineering practice. Furthermore, it has been shown that for the 3-dimensional framework of the sublayer model the same conclusions as for 2D can be made. In the authors opinion, the contributions of this thesis are a step towards a robust generally applicable computational method to simulate the complex structural behaviour of quasibrittle materials.

In the past decades, great progress has been made in analyzing lateral torsional buckling of slender beams. The phenomena has been accurately described by differential equations, closed form solutions are available for specific cases and the solution for any load and any boundary condition can be obtained by finite element analysis. Timber and steel design standards provide a procedure based on equivalent moment factors. With this procedure, beams can be designed straightforwardly. However, modern designers continue to push the envelope and more irregular load patterns are found, on which the design standards do not provide solutions. Consequently, designers are forced to determine the equivalent moment factors based on case-specific literature and/or conservative assumptions. Unfortunately, this makes many challenging modern designs uneconomical. Furthermore, significant inconsistencies between the different design procedures are found. For that purpose, this paper proposes a solution in the form of a general formulation to determine equivalent moment factors for any loading on a single-span beam for both free and restrained lateral bending and/or warping at the supports, for both I-sections and rectangular slender sections loaded in the shear center. It is shown that the obtained moment factors are accurate and in good agreement with design standards and literature, and a wide range of irregular load patterns is considered.