The most frequently employed solution adopted by structural engineers for the current model is a beam model integrated with code compliance checks in accordance with applicable standards. The setup of the testing model remains consistent across all levels of model complexity represents a column with a square cross-section measuring 500 x 500 mm and a length of 1000 mm, a footing strip with a unit width of 1000 mm, and a length of 6000 mm. The height of the footing strip is a variable parameter. For the current verification, a height of 250 mm is utilized.
The bottom face of the footing strip is supported by compression-only springs with either low soil stiffness of 16000 kN/m³ or the high soil stiffness of 128000 kN/m³. Symmetry boundary conditions constrain the left and right ends of the footing strip.
It is essential to note that all models are design models. For simulation and code-check verification, the partial factors for materials have been applied.
11) Dimensions and analytical model
Linear beam model - Low-Stiffness Soil (LSS)
Once the simulation is conducted on the beam model, the standard code checks can be employed. The designed reinforcement adheres to the minimal detailing requirements specified by EN 1992-1-1 [1]. A minimal reinforcement ratio is applied to both longitudinal bars and stirrups. The simulation is executed using a modulus of elasticity of 10 GPa, representing the secant modulus of the designated concrete material. Due to the hyperstatic nature of the structure, the modulus influences the redistribution of internal forces.
12) Linear beam model - ultimate load for passing ULS checks
The bending moment directly beneath the column reached the ultimate value of 60.1 kNm under an axial force in the column of -245 kN. The second critical point is situated within the zone of maximum shear, where the interaction of a shear force of -86.4 kN and a corresponding bending moment of 44.8 kNm results in an interaction check, which also remains within acceptable limits with a utilization ratio of 96.6%. The most critical location on the structure is directly beneath the column, and the failure mode involves the concrete in compression and the longitudinal reinforcement bars in tension. The shear capacity notes that is not critical for this case.
13) Linear beam model - code-check for low-stiffness soil
Linear beam model - High-Stiffness Soil (HSS)
The high-stiffness soil in this scenario, dense sand with a subgrade modulus of 128000 kN/m³, significantly alters the behavior of the structure. The load is concentrated directly beneath the column area. The contact area exhibits a higher stress contact gradient and magnitude. The ultimate resistance in the column of -540 kN has increased by a factor of 2.2 compared to low-stiffness soil. The shear force profile is steeper, and the bending moment is more localized. It leads to a more prone structure to punching shear failure.
14) Linear beam model - ultimate load for passing ULS checks
The maximum bending moment concentrated beneath the column is 60.7 kNm, attributable to the maximum bearing capacity of the section in bending. The extreme shear force has been displaced proximally to the column area and has reached a magnitude of -132 kN, with the corresponding moment being 38.1 kNm. In the interaction code check, the theta angle for the concrete strut was adjusted from 21.5 degrees to 23 degrees. The Eurocode permits the adjustment of the strut angle within the range of 21.5 to 45 degrees. It has been observed that an angle of 21.5 degrees results in overutilization of capacity, primarily attributed to bending. By accommodating the variability prescribed by code requirements, the failing check has been successfully addressed through the application of an alternative strut angle.
The critical mode of failure involves the concrete in compression and the longitudinal reinforcement bars in tension.
15) Linear beam model - code-check for high-stiffness soils