Method for geometric characteristics of an arbitrary calculated punching contour calculation

Introduction. The concentrated action of loads is one of the main causes of brittle failure in reinforced concrete structures. The punching calculation of reinforced concrete slabs in domestic and international codes is based on the geometric characteristics of a contour located around the load application area. In the case of a concentrated force, the only geometric characteristic considered is the perimeter. Punching calculation provisions also require accounting of concentrated moments, which consequently necessitates the calculation of the corresponding geometric characteristics. The methodology for their calculation is described in general terms in regulatory documents. Ready-made formulas are not available for complex contours. This creates the need to develop a universal method for calculating the geometric characteristics of arbitrary contours.

Aim. To develop a universal method for calculating the geometric characteristics of arbitrary punching contour composed of straight-line segments and arcs. Materials and methods. The method proposed in the article is based on general approaches from the course of strength of materials. The main distinction is that the geometric characteristics are calculated for a contour. This leads to differences in the units of measurement of the corresponding quantities for bar cross-sections and for a contour.

Results. The geometric characteristics of elementary figures, such as a straight-line segment and an arc, are derived. These expressions are then used to determine the corresponding characteristics for the entire contour. The obtained formulas eliminate inconsistencies in units of measurement. An example calculation of a contour composed of straight-line segments and arcs is provided based on the derived formulas.

Conclusions. A universal coordinate-based method for calculating the geometric characteristics, including the rotational moment of inertia, of an arbitrary punching contour composed of straight-line segments and arcs is proposed. The approach can be implemented using commonly available software tools, spreadsheets, etc.

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