Annex D(Clause 7.4.4.1)

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 591

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Calculation of Pressure Distribution by Conventional Method

D-1 Determination of Pressure Distribution

The pressure distribution $(q)$ under the raft shall be determined by the following formula:

q = \frac {Q}{A} \pm \frac {Q e _ {\mathrm{y}} ^ {\prime}}{I _ {\mathrm{x}} ^ {\prime}} y \pm \frac {Q e _ {\mathrm{x}} ^ {\prime}}{I _ {\mathrm{y}} ^ {\prime}} x

where

$Q$ = total vertical load on the raft,

$A =$ total area of the raft,

$\left.\begin{array}{l}e_{x}^{\prime},e_{y}^{\prime}\\ I_{x}^{\prime},I_{y}^{\prime}\end{array}\right\} =$ eccentricities and moments of inertia about the principal axes, through the centroid of the section, and

x, y = coordinates of any given point on the raft with respect to the x and y axes passing through the centroid of the area of the raft.

$I_{\mathrm{x}}^{\prime}, I_{\mathrm{y}}^{\prime}, e_{\mathrm{x}}^{\prime}, e_{\mathrm{y}}^{\prime}$ may be calculated from the following equations:

I _ {\mathrm{x}} ^ {\prime} = I _ {\mathrm{x}} - \frac {I _ {\mathrm{xy}} ^ {2}}{I _ {\mathrm{y}}}

\overline {{I _ {\mathrm{y}} ^ {\prime} = I _ {\mathrm{y}} - \frac {I _ {\mathrm{xy}} ^ {2}}{I _ {\mathrm{x}}}}}

e _ {\mathrm{x}} ^ {\prime} = e _ {\mathrm{x}} - \frac {I _ {\mathrm{xy}}}{I _ {\mathrm{x}}} e _ {\mathrm{y}}

e _ {\mathrm{y}} ^ {\prime} = e _ {\mathrm{y}} - \frac {I _ {\mathrm{xy}}}{I _ {\mathrm{y}}} e _ {\mathrm{x}}

where

$I_{x}, I_{y}=$ moment of inertia of the area of the raft respectively about the x and y axes through the centroid,

$I_{\mathrm{xy}} = \int xy\cdot \mathrm{d}A$ for the whole area about $x$ and $y$ axes through the centroid, and

$e_{x}, e_{y} =$ eccentricities in the x and y directions of the load from the centroid.

For a rectangular raft, the equation simplifies to:

q = \frac {Q}{A} \left(1 \pm \frac {1 2 e _ {y} y}{b ^ {2}} \pm \frac {1 2 e _ {x} x}{a ^ {2}}\right)

where

a and b = dimensions of the raft in the x and y directions, respectively.

NOTE — If one or more of the values of $(q)$ are negative as calculated by the above formula, it indicates that the whole area of foundation is not subject to pressure and only a part of the area is in contact with the soil, and the above formula will still hold good, provided the appropriate values of $I_{x}$ , $I_{y}$ , $I_{xy}$ , $e_{x}$ and $e_{y}$ , are used with respect to the area in contact with the soil instead of the whole area.