PSI - Issue 47

S. Aiello et al. / Procedia Structural Integrity 47 (2023) 668–674 S.Aiello, V. De Biagi, P. Cornetti, B. Chiaia / Structural Integrity Procedia 00 (2019) 000–000 The two-dimensional model is based on a circular plate with an anomalous thickness. This aspect was treated considering the union between a circular crown element confined at the ends, with the design thickness , and a circular plate with the anomalous thickness ℎ , which is less than the design ones as shown in Fig.2. 671 4

Fig. 2. (a) circular plate with an anomalous thickness reduction; (b) circular crown element confined at the ends; (c) circular plate with the anomalous thickness

3.1. Thermal action effect In the beam model the thermal action on a hyperstatic structure generates stress due to impeded deformation. Given a doubly confined beam, uniform heating generates an axial compressive stress, while the butterfly variation generates a bending moment that tends the extrados fiber. Also, in the circular plate model the thermal action generates some stress due to the impeded deformation. In this case the authors considered only the flexural behavior. Equation (2) shows the bending moment thermal effect term. ∗ � � � � � � � � � � � � ����� � � (2) where ��� 10 �� ° �� � the thermal expansion coefficient of the material; = material Young module; and h = thickness value. 3.2. Acting stresses The thermal effects are added to the stress generated by the vertical gravitational load. This load, defined as P, is to be considered uniformly distributed and orthogonal to the axis of the equivalent beam and to the surface oh the equivalent plate. It summarized the summarizes the self-weight contribution of the lining with thickness anomaly and the load of the overlying soil (3). ���ℎ (3) where γ is the unit weight of concrete (generally equal to 24-25 kN/m3). In the scenario of thickness anomalies, the upper soil thrust is often missing since the source of such thickness anomalies is air bubbles between the lining and the rock.