The theory used in the nonlinear solution is called 3D CSFM and is outlined in the theoretical background [3]. All the presumptions for the designed calculation procedure are explained in detail there.
Assumptions and attributes of the model:
- Materially Nonlinear Analysis (MNA)
- 3D solution – volume elements.
- Mohr-Coulomb plasticity theory - zero angle of internal friction for concrete behaviour.
- Compression-only surface 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.
- Bond model and tension stiffening are considered.
- Stress triaxiality and confinement effect.
- Compression softening is not a part of the implemented solution.
- Mesh factor 1 - recommended computational settings.
23) 3D model + reinforcement bars layout
3D CSFM – Low-Stiffness-Soil (LSS)
The maximum axial force designated in the model reached -980 kN due to failure modes involving tensile rupture of the longitudinal reinforcement in the encircling area of the column. Transverse compression forces are restrained by the stirrups, which in the column zone are utilized during yielding and contribute to additional failure mode of the horizontal stirrup legs caused by transverse tensile stress evolutions that cannot be captured in the plane stress solution. Over-compression and crushing of the concrete occur at the interface area between the column and footing. The confinement effect is localized in this region, based on the reinforcement effect and the stiffness of the footing strip. The failure mechanism involves concrete crushing, tensile rupture of the longitudinal reinforcement, and the horizontal legs of the stirrups in tension.
24) Maximum applied force, failure modes, and transverse stress distribution
25) Minimum principal stress Sigma 3, confinement effect – ratio between triaxial vs uniaxial stress
26) Compressive plastic strain and stress in reinforcements
27) Detailed detection of critical stress on the longitudinal bars and stirrups
28) Nonlinear deflections
3D CSFM – High-Stiffness-Soil (HSS)
The force absorbed by the footing strip reached -2,116 kN, which is approximately 215% higher bearing capacity than in LSS. The failure mode involves concrete crushing, tensile rupture of the longitudinal reinforcement, and the horizontal legs of the stirrups in tension.
29) Maximum applied force, failure modes, and transverse stress distribution
30) Minimum principal stress Sigma 3, confinement effect – ratio between triaxial vs uniaxial stress
31) Compressive plastic strain in concrete and stress in reinforcements
The maximum shear stress exerted on the inner closed stirrups has reached a value of 298 MPa, which remains within the elastic range as defined by the material. This observation leads to the conclusion that punching shear failure was not the predominant failure mode in this particular instance.
32) Detailed detection of critical stress on the longitudinal bars and stirrups
33) Nonlinear deflections