PSI - Issue 81

Olena Romashko-Maistruk et al. / Procedia Structural Integrity 81 (2026) 310–315

311

Nomenclature  stress  strain f

strength strain rate curvature stiffness coefficient

έ

1/r

D

k

dynamic increase factor

DIF

According to domestic standards (DSTU B V.2.6-156:2010 (2011)), performing such calculations is generally impossible, since they do not contain any recommendations for determining the dynamic increase factors of materials (concrete and reinforcement). As for European standards (EN 1992-1-1 (2004); CEB-FIP (1991); fib (2012)), then on their basis it would be possible to build a simplified express methodology for calculating reinforced concrete elements and structures under dynamic loads. However, this is not possible due to the following gaps: • the initial recommendations for determining the dynamic increase factors of reinforcement CEB Bulletin 187 (1988) are not included in either CEB-FIP (1991) or fib (2012); • the influence of concrete class on the dynamic increase factors of concrete in fib (2012) is completely eliminated, which prevents the construction of a universal methodology; • the dependences of the dynamic increase factors of concrete in CEB-FIP (1991) and fib (2012) are purely empirical, which prevents the construction of an analytically justified methodology. Therefore, these studies are aimed at developing a universal, analytically justified express methodology for the internal stress strain state of reinforced concrete elements and structures under dynamic loads. It is advisable to take the deformation-force model of concrete and reinforced concrete resistance as the basis of this methodology, supplement it with analytically substantiated functions of the stiffness of reinforced concrete elements and the coefficient of elastic-plasticity of concrete, as well as the dependencies of the dynamic increase factors of concrete and reinforcement. It is also worth assessing the significance of the influence of these coefficients on the change in the strength of reinforced concrete elements under the action of dynamic loads. In general, these research data should become another contribution to the development of a generalized model of deformation of reinforced concrete elements and structures under any loads. 2. Analytical research methods A simplified express method for calculating reinforced concrete elements and structures under dynamic loads will be built using the general limit state method based on the hypothesis of limit equilibrium: S R  , (1) where S - force ( s M , s N or s Q ) in the element from external load; R - strength of the element (internal force R M , R N or R Q ), which is determined by the geometric characteristics of the cross-section and the physical and mechanical characteristics of the materials. The force in the element from external dynamic load, in particular explosive, can be determined by one of the three most common methods, each of which requires different computational resources and provides different accuracy and reliability. The method of direct integration of the equations of motion (Murata (2006); Yan et al. (2009); Díaz and Rigby (2022)) uses a nonlinear pressure diagram of a shock explosive air wave as a load. In general, such a diagram allows you to establish the values of the pressures normal to the surface in a certain time range. However, for complex and advanced buildings and structures, this is extremely difficult to do, since the real parameters of the blast wave (the speed of propagation of its front, the reflected pressure from the frontal surface, the time from the beginning of reflection to the flow regime, etc.) change very much when in contact with the structure and flowing around it at all stages of diffraction. In the calculations using the shock pulse method (Huang et al. (2022)), the value of the corresponding shock wave pulse, its shape and duration are taken as the main load. Since the actual pulse shape is nonlinear, this significantly complicates the process of modeling the explosive load. Therefore, in most cases it is simplified and taken in the form of triangles or rectangles. However, even in such circumstances, difficulties remain due to the lack of clear recommendations for applying the explosive load. The quasi-static method (Anderson et al. (1983); Choi and Park (2002)) involves replacing the dynamic load with the corresponding equivalent static load, which significantly simplifies the calculations, especially for buildings and structures that are complex in terms of design. That is why the quasi-static method is most often recommended for simplified calculations (UFC 3 340-02 (2008); DBN V.2.2-5 (2023)), even despite its lower accuracy and reliability compared to others.