Question 3.22: Figure 3–19 shows a column resting on a foundation and carry...

Objective                        Determine if bearing stresses on the concrete and the soil are safe.

Given                               Foundation shown in Figure 3–19: Load = F = 116 kN = 116 000 N.

For concrete, f_{c}^{'} =138 \times 10^{6}  N/m^{2}

For soil (compact gravel), σ_{bd} = 0.38 MPa (Table 3–7).

Analysis and Results   For concrete, the load is transferred from the column to the concrete through the 200 mm square steel plate ( A_{1} = 40 000 mm²). But the concrete pier is 300 mm square

( A_{2} = 90 000 mm²). Therefore, the bearing load is on less than the full area of the concrete. Then, from Table 3–7,

\sigma_{bd} = Kf_{c}^{'} = 0.34 \sqrt{ \frac {A_{2}}{A_{1}}}f_{c}^{'} =0.34 \sqrt{ \frac {90  000}{4000}}f_{c}^{'}  = 0.510 f_{c}^{'}

Note that K < 0.68. Then,

\sigma_{bd} = 0.510(13.8 MPa) = 7.0 MPA

The bearing stress exerted on the concrete by the steel plate at the base of the column is

\sigma_{b} = \frac{F}{A_{b}} =\frac{116  000  N}{40  000  mm²} = 2.9  MPa <  \sigma_{bd}

Thus, the bearing stress on the concrete is acceptable.

For the soil (gravel) at the base of the foundation,

\sigma_{b} = \frac{F}{A_{b}} =\frac{116  000  N}{360  000  mm²} = 0.32 MPa

This is acceptable because the allowable bearing stress for compact gravel is 0.38 MPa as shown in Table 3–7.