A Mofication of the Croutś Method to Simplify the Stress Calculation for Certain Building Structures

This paper proposes a precise method of obtaining the stresses in certain models widely found in building to facilitate them in the early design phases. Stresses are obtained more quickly than with other usual procedures because they are deduced from a deflection that is calculated before than the real one. The method is drawn from earlier papers that proposed possible mechanical behaviours of models to justify the operations of three classical methods (Gauss, Crout, Cholesky) that solve the equation systems of conventional equilibrium analyses. Inspired by these mechanical interpretations, the method suggests another structural response that can be justified qualitatively with Cross´ philosophy. The deflection derived is obtained as a sum of partial deflections which are determined by progressively increasing the stiffness of the bars during the balancing process without varying the original stresses. The stiffness is increased in such a way that the nodal movements of each partial deflection can be determined with few operations. Its calculation is described numerically and graphically when the model is a continuous beam and also in the case of other usual building structures. To date, the graphical version has been applied to study the behaviour of certain models as it requires only a short calculation time and the results have been found to be quite precise. As an example, the new deflection of a portico is calculated by freehand and compared with the exact result determined numerically. With this deflection, the stresses of the model are obtained by using modified Maney’s equations. Based on this work, possible lines of research are suggested for developing further graphical methods that can be used to analyse other types of structure accurately.