Assumptions and model assembly
The theory employed in the nonlinear solution is called CSFM (Compatible Stress Field Method) and is traced in the theoretical background[2].
Assumptions and attributes of the model:
- Materially Nonlinear Analysis (MNA)
- Plane stress model.
- Compression-only line supports (low/high stiffness).
- Symmetry constraints are positioned on the left and right edges of the footing strip.
- A thick plate 100 mm on the top of the column to stem local stress concentration underneath the point force load.
- All the material properties for concrete C30/37 and reinforcement bars B500B are engaged as design values with partial factors according to EN 1992-1-1 [1].
- Mesh factor 1 - a minimum of four elements over the shortest edge.
16) 2D model + reinforcement bars layout
2D CSFM - Low-Stiffness-Soil (LSS)
The maximum applied force capable of addressing the failure modes has reached -1340 kN. The vertical force has resulted in a contact stress of 0.59 MPa. The observed trend in contact stress indicates nonlinearity in tension, attributable to the uplift of the left and right sections near the symmetry constraints. The failure modes occurred in compression at the interface between the column edge and the face in contact with the footing. Concurrently, by the tensile rupture of longitudinal reinforcement.
17) Maximal applied force, contact stress, and failure modes
18) Principal stress in compression, compression plastic strain, stress in reinforcements
The stress in the stirrups has reached a maximum of 201 MPa, leading to the consensus that this stress level is significantly below the ultimate limit of utilization. The failure mode in shear does not pose a threat in this context.
19) Nonlinear deflections, stress in stirrups, and detailed insight into the failure modes of longitudinal bars
2D CSFM - High-Stiffness-Soil (HSS)
The maximum load at which all governing failure mechanisms can still be resisted is –2652 kN. The corresponding vertical reaction induces a contact stress of 1.99 MPa at the footing–soil interface. The evolution of contact stress exhibits marked nonlinearity in tension, resulting from the uplift of the footing edges. This loss of contact occurs primarily along the left and right ends of model.
The dominant failure mechanism is compressive crushing at the interface between the column edge and the loaded face of the footing. Simultaneously, tensile rupture of the bottom-layer longitudinal reinforcement within the footing occurs.
20) Maximal applied force, contact stress, and failure modes
21) Principal stress in compression, compression plastic strain, stress in reinforcements
The nonlinear deflections demonstrate substantially smaller displacements under higher loads compared to the LSS variants. Stress is predominantly concentrated beneath the column area, with stirrups being underutilized at approximately 186 MPa. However, the model exhibits evidence of local softening on the bottom face of the footing strip due to high tensile stress in reinforcement bars.
22) Nonlinear deflections, stress in stirrups, and localized compression softening