Horizontal Shear Force in RC Internal Beam-Column Connection at Initiation and Crack Growth from Linearly Distributed Load on a Cantilever Beam. Part II - Asymmetrical Cross Section

The beam-to-column connection is a particularly vulnerable element in frame structures under seismic action and is often responsible for building damages during earthquakes. Difficulties are still encountered in calculating the shear force and its constituent forces that are transmitted from the beams to the columns. In the current Eurocode 2 these forces are determined capacitively, based on the longitudinal bars of the beam passing through the beam-column joint. However, this does not answer the question for the magnitudes of the forces transmitted from the beam to the column as a result by the applied load. In this paper, a mathematical model of the beam is considered, which allows to take into account all its dimensions in height as well as the material properties of its constituent construction materials. A limit stage of crack initiation and growth between the beam and the column is considered. A cantilever beam loaded with a linearly distributed load with intensity at the support is considered in this study. A solution is performed and the beam lateral edge support responses along the height are determined. Menabrea’s theorem has been used. The shear force has been calculated with the exact forces determined by the newly derived formulas. To validate the results, the new shear force is compared with that determined by the approximate method recommended in the literature. The difference ranges from 12.89% to 38.65%. A comparison was also made with the shear force determined according to Eurocode 2. The difference ranges from -87.66% to +66.03%.