### Concrete in bearing

Two options for check of concrete in bearing are available:

- According to IS 800, Cl. 7.4
- According to IS 456, Cl. 34.4

#### Concrete in bearing checked according to IS 800, Cl. 7.4

The maximum bearing pressure should not exceed the bearing strength equal to \(0.6 f_{ck}\), where \(f_{ck}\) is characteristic cube strength of concrete. Strength of grout is assumed higher than that of concrete foundation. Cl. 7.4.3.1 provides formula for minimum thickness of column bases:

\[ t_s = \sqrt{2.5 w c^2 \gamma_{m0} / f_y} > t_f \]

where:

- \(w\) – uniform pressure from below on the slab base under the factored load axial compression
- \(c\) – overlap of the column base over the column
- \(f_y\) – yield strength of the column base
- \(t_f\) – column flange thickness
- \(\gamma_{m0} = 1.1\) – partial safety factor for resistance governed by yielding – IS 800, Table 5; editable in Code setup

The formula can be rewritten to determine the overlap with the assumption that \(w = 0.6 f_{ck}\):

\[ c = t_s \sqrt{\frac{f_y}{1.5 f_{ck} \gamma_{m0}}} \]

The area \(A_{c,eff}\) is determined by offsetting the column (with stiffeners) cross-sectional area intersecting the base plate by overlap \(c\). Another area, \(A_{FEM,eff}\) determining the area in contact between the base plate and concrete foundation (grout) by finite element analysis. The area resisting the compressive forces, \(A_{eff}\) is intersection of these two areas, \(A_{c,eff}\) and \(A_{FEM,eff}\). Bearing strength \(0.6 f_{ck}\) on this area \(A_{eff}\) is assumed at the ultimate limit state.

The check of concrete in bearing is performed in a form of stresses:

\[ \sigma_c \le w \]

where:

- \(\sigma_c = \frac{N_c}{A_{eff}}\) – average bearing stress below the base plate
- \(N_c\) – compressive force
- \(w = 0.6 f_{ck}\) – bearing resistance of the concrete

#### Concrete in bearing checked according to IS 456, Cl. 34.4.

The maximum bearing pressure should not exceed the bearing strength equal to \(0.45 f_{ck} \cdot \min \left \{ \sqrt{\frac{A_1}{A_2}}, \, 2 \right \} \), where:

- \(f_{ck}\) – characteristic cube strength of concrete; strength of grout is assumed higher than that of concrete foundation
- \(A_1\) – supporting area taken as the area of the lower base of the largest frustum of a pyramid or cone contained wholly within the footing and having for its upper base, the area actually loaded and having side slope of one vertical to two horizontal
- \(A_2\) – bearing area determined by finite element analysis (equal to \(A_{FEM,eff}\))

The check of concrete in bearing is performed in a form of stresses:

\[ \sigma_c \le w \]

where:

- \(\sigma_c = \frac{N_c}{A_{2}}\) – average bearing stress below the base plate
- \(N_c\) – compressive force
- \(w = 0.45 f_{ck} \cdot \min \left \{ \sqrt{\frac{A_1}{A_2}}, \, 2 \right \}\) – bearing resistance of the concrete

## Transfer of shear

The shear action at the base plate is assumed to be transferred from the column to the concrete foundation by:

- Friction between base plate and concrete/grout
- Shear lug
- Anchor bolts

### Anchors

The tensile forces in anchors include prying forces and are determined by finite element analysis.

Anchors are not checked in the software.