(Clause 7.4.4.2) · NBC 2016 (SP 7:2016) Volume 1

Contact Pressure Distribution and Moments Below Flexible Foundation

E-1 Contact Pressure Distribution

E-1.1 The distribution of contact pressure is assumed to be linear with the maximum value attained under the columns and the minimum value at mid span.

E-1.2 The contact pressure for the full width of the strip under an interior column load located at a point i can be determined as (see Fig. 9 A):

p _ {\mathrm{i}} = \frac {5 P _ {\mathrm{i}}}{\bar {l}} + \frac {4 8 M _ {\mathrm{i}}}{(\bar {l}) ^ {2}}

where

$\bar{I} =$ average length of adjacent span, in m,

$P_{\mathrm{i}} =$ column load, in t at point $i$ , and

$M_{i} =$ moment under an interior columns loaded at $i$ .

E-1.3 The minimum contact pressure for the full width of the strip at the middle of the adjacent spans can be determined as (see Fig. 9A and 9B):

p _ {\mathrm{ml}} = 2 P _ {\mathrm{i}} \left(\frac {l _ {\mathrm{r}}}{\bar {l} _ {1} \bar {l}}\right) - p _ {i} \left(\frac {\tilde {l}}{\bar {l} _ {1}}\right)

p _ {\mathrm{mr}} = 2 P _ {\mathrm{i}} \left(\frac {l _ {\mathrm{l}}}{l _ {\mathrm{r}} \bar {l}}\right) - p _ {i} \left(\frac {\bar {l}}{l _ {\mathrm{r}}}\right)

p _ {\mathrm{m}} = \frac {p _ {\mathrm{ml}} + p _ {\mathrm{mr}}}{2}

where $l_{r}, l_{1}$ are as shown in Fig. 9A.

E-1.4 If E-2.3(a) governs the moment under the exterior columns, contact pressures under the exterior columns and at end of strip can be determined as (see Fig. 9C):

p _ {\mathrm{e}} = \frac {4 P _ {\mathrm{e}} + \frac {6 M _ {\mathrm{e}}}{C} - p _ {\mathrm{m}} l _ {1}}{C + l _ {1}}

p _ {\mathrm{c}} = - \frac {3 M _ {\mathrm{e}}}{C ^ {2}} - \frac {p _ {\mathrm{e}}}{2}

where $P_{\mathrm{e}}, p_{\mathrm{m}}, M_{\mathrm{e}}, l_{1}, C$ are as shown in Fig. 9C.

E-1.5 If E-2.3(b) governs the moment under the exterior columns, the contact pressures are determined as (see Fig. 9C):

p _ {\mathrm{e}} = p _ {\mathrm{c}} \frac {4 P _ {\mathrm{e}} - p _ {\mathrm{m}} l _ {1}}{4 C + l _ {1}}

E-2 Bending Moment Diagram

E-2.1 The bending moment under an interior column located at $i$ (see Fig. 9A) can be determined as:

PART 6 STRUCTURAL DESIGN — SECTION 2 SOILS AND FOUNDATIONS

FIG. 9 MOMENT AND PRESSURE DISTRIBUTION AT COLUMNS

M _ {\mathrm{i}} = - \frac {P _ {\mathrm{i}}}{4 \lambda} (0. 2 4 \bar {\lambda} \bar {J} + 0. 1 6)

F-1 Closed Form Solution of Elastic Plate Theory

F-1.1 For a flexible raft foundation with non-uniform column spacing and load intensity, solution of the differential equation governing the behaviour of plates on elastic foundation (Winkler Type) gives radial moment $(M_{\mathrm{r}})$ tangential moment $(M_{\mathrm{t}})$ and deflection $(w)$ at any point by the following expressions: