Stress intensity factors for 3-D axisymmetric bodies containing cracks by p-version of F.E.M.

In this study, a simplified design method for shear wall-frame systems based on the Direct Displacement- Based Design (DDBD) approach is proposed. The method is developed using a continuous-system analytical model. For this purpose, an equivalent flexural-shear beam model is formulated based on the assumption that the frame shear force remains constant over the height of the building. By solving the differential equation governing the equivalent flexural-shear beam and applying equilibrium conditions, analytical relationships are derived for the effective mass, effective height, wall base moment ratio, and the location of the wall moment inflection point. Based on these relationships, practical design tables and charts are developed to illustrate the variation of the effective mass, effective height, wall base moment ratio, and wall moment inflection point with the frame shear ratio (defined as the ratio of the frame base shear to the total base shear). These design aids allow rapid estimation of the key design parameters required for DDBD applications. The proposed flexural-shear beam model extends the application of DDBD and enables the design of wall-frame systems to be carried out more efficiently and in a shorter time than conventional DDBD procedures. To evaluate the applicability of the proposed approach, a series of design examples was examined. The first example was presented in detail to facilitate a clearer understanding of the design procedure. The results indicate that the proposed method yields sufficiently accurate and reliable results for preliminary design applications. Consequently, the proposed approach provides a practical and efficient framework for the Displacement-Based Design (DBD) of wall-frame systems.