Історія виникнення та розвитку сендвіч-моделі для розрахунку мембранних, оболонкових та плитних елементів згідно з EN 1992-1-1:2023

For the first time in European design standards for concrete structures, specifically in Annex G (normative), the new version of Eurocode EN 1992-1-1:2023 pays focused attention to the design of membrane, shell and slab elements and proposes a modern approach for their calculation. As a method of optimal design for reinforced concrete shells, slabs and membranes, Annex G proposes the so-called sandwich model - where the shell is represented as a three-layer model consisting of two load-bearing layers (top and bottom) and an intermediate layer between them. When designing using the sandwich model – a spatial problem (bending + torsion + membrane forces) is transformed into two membrane problems for the top and bottom layers. That is, the transformation of a three-dimensional stress state into two layers (top and bottom) with equivalent membrane stresses. The sandwich model is a rigorous mechanical model that allows reducing a complex spatial problem (shell with combined forces) to two independent plane problems (membrane elements in the top and bottom layers) through statically equivalent transformation of forces into stresses. The sandwich model is based on transforming the combination of forces (membrane, bending and torsional) into a statically equivalent system of in-plane stresses acting in the top and bottom layers of the model. Basic assumptions of the method: three-layer model: the shell is represented as a structure with two load-bearing layers (top and bottom) and an intermediate layer between them; static equivalence: internal forces are transformed into in-plane stresses in such a way as to maintain complete static equilibrium; independent layer design: each layer (top and bottom) is designed separately as a membrane element according to clause G.3. The formulations presented in Annex G of EN 1992-1-1:2023 in clauses G.3 and G.4 are consistent with the clauses and design provisions in Section 8 (Ultimate Limit States (ULS)) of the main body of the document, and clause G.5 contains additional provisions to 9.2 (Crack Control) of these standards. Annex G covers the design of planar members without discontinuities in the concrete mass. Other, more refined design methods complying with clause 7.3.3 (Plastic Analysis) or clause 7.3.4 (Non-linear Analysis) of Eurocode 2 may be used. Thus, Annex G (Design of Membrane, Shell and Slab Elements) does not replace, but supplements the main sections of Eurocode 2, namely - general principles, materials (σ-ε diagrams), cross-section design for ULS, crack resistance and SLS.