A Method for Determination of Moment Contribution Ratio under Foundation Rotation in Shear Wall-Frame Systems

Abstract

In shear wall-frame systems, the foundation rotation that may occur under the shear walls changes the displacements and interstory drift ratios and changes the internal force distribution. This study investigates the effect of foundation rotations under shear walls on internal force distribution in shear-frame systems. The originality of the study lies in considering parabolic loads and dynamic analysis (first mode), in addition to static uniform or triangular distributed loads, when determining the shear wall moment contribution ratio under the influence of foundation rotation. The shear wall contribution ratio, a key parameter in many earthquake codes, is defined as the ratio of the sum of bending moments taken by the shear walls at the base to the overturning moment. It plays a crucial role in determining the building’s behavior. Depending on this ratio, the load-reduction coefficient is changed. This study investigates the effect of foundation rotation on the moment distribution at the base for three different static load cases and the first mode in the dynamic analysis. The multi-story building is modeled as an equivalent sandwich beam. The moment contribution ratio (MCR) was calculated with the help of analytical solutions of the differential equations written for three different load cases in static conditions, and graphs were created for practical use directly calculating the MCR. In the methodology of the study, the initial step involves the calculation of the equivalent sandwich beam stiffness parameters and the foundational rotational spring. Subsequent to these calculations, the MCR values can be directly obtained with the help of graphs. This approach facilitates the rapid and practical determination of the MCR and can be used in the preliminary sizing phase to eliminate possible errors in the data entry of software that performs detailed analysis. In addition, in the presented study, it has been shown that taking a single mode into account is sufficient when calculating MCR values in dynamic analysis.