Sequentially Linear Analysis (SLA), an event-by-event solution strategy in which a sequence of scaled linear analyses with decreasing secant stiffness is performed, representing local damage increments; is a robust alternative to nonlinear finite element analysis of quasi-brittle structures. Since it is based on a fixed smeared crack constitutive model, severe spurious stresses and inaccuracies may develop due to misalignment of the crack with the principal stress directions. To this end, the elastic-brittle fraction model was conceived. The model separates the continuum into several parallel fractions or layers, each with different properties, chosen in order to represent the overall constitutive softening behaviour as accurately as possible. The main idea is to mimick a rotating crack by a superposition of fractions, each with a fixed crack direction. In this article, the model is presented for both the 2-dimensional and 3-dimensional frameworks, with a general transition from any saw-tooth law to fraction material properties. The fraction models are then validated and compared against the fixed crack model with SLA: using single element and structural case studies. It is shown that the fraction model is able to mimick the rotating crack model, that it leads to lesser spurious cracks and narrower localisation bands, and in turn results in a more flexible post-peak response over all case studies compared to the fixed crack model.

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.