PSI - Issue 48

G. Gusev et al. / Procedia Structural Integrity 48 (2023) 176–182 Gusev et al / StructuralIntegrity Procedia 00 (2019) 000 – 000

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The scheme of the structure and the applied load used in the numerical simulation is shown in Figure 2b. The computational domain V=V 1 ∪ V 2 combines the concrete structure ( V 1 ) and the steel base supports ( V 2 ). The origin of the Cartesian coordinate system ( = 1,3) coincides with the base of one of the columns (at the junction of the column and the steel support). The stress-strain state in the system is determined from the solution of the boundary value problem including equations of equilibrium and geometric Cauchy relations. The model of elastic-plastic flow by Willam and Warnke (1975) was used in writing the physical equations for reinforced concrete. At the outer boundaries of the computational domain V , the following conditions are assumed (1): Γ 2 lower surface of steel supports - the condition of absence of all displacement components is set; the external surface of the concrete building Γ 1 is considered to be free from loads, except for the area of 0.5×0.5 m - Γ 3 , on which the distributed static load of variable intensity P is set: 1 ( ) = 0, 2 ( ) = 0, 3 ( ) = 0, ∈ 2 ; ( ) ( ) = 0, , = 1,3, ∈ 1 ; ( ) ( ) = ( ), , = 1,3, ∈ 3 . (1) The calculation of the stress-strain state of such a structure shows that starting from a certain level of the applied load, cracks begin to form on the underside of the floor disc, which increase as the load increases. The distribution of cracks in the floor slab obtained at the final stage of the calculation is shown in Figure 3a. When investigating the response from the damaged structure side, the defect was modelled as an artificially formed crack whose size, shape and location correspond to the results of the described numerical experiment. A 4 mm wide cross-shaped crack with dimensions of 1750×1750 mm was used (Figure 3b). It starts at the bottom surface of the floor slab and extends to a depth of 100 mm. The boundaries of the cut are separate and do not have a contiguous surface along its entire length. It should be noted that in this case the linear scale of the crack is comparable to the characteristic scale of the slab fragment. a b

Fig. 3 (a) Crack distribution of a part of the slab disc at the final stage of the calculation and (b) the shape and size of the defect that is artificially introduced into the structure.

To study the distortion of the vibration response during the evolution of the defect size (its depth), the problem of determining the response to a given dynamic impact for a structure with a crack depth of 30 mm, 60 mm, 100 mm is solved. As a result, vibrograms of accelerations in the control points of the structure have been obtained. The location of these points is shown in Figure 4a. a b