When group of piles are loaded centrally over the pile cap, the load is equally distributed on all piles, provided the pile system is symmetrical and the pile cap is rigid and very thick and is in contact with the ground. Thus, when the total vertical load, centrally placed, is Q_{g}, the number of piles is n, then the load transmitted to each pile shall be:

Q_{i} = Q_{g}/n

When however, the pile cap is eccentrically loaded, as to subject the pile cap to a central vertical load Q_{g} and additional bending moment M_{x} (about X – axis), and M_{y} (about y- axis), then the load transmitted to a pile is given by the equation:

Q_{i} = [(Q_{g }/ n) ± {(M_{y} Ã— x) /âˆ‘x^{2 }} ± {(M_{x} Ã— y) / âˆ‘y^{2}}] ———- (1)

Where, Q_{i }– Load transmitted to a particular pile

Q_{g} = Total vertical load acting on the pile cap (centrally)

n = Number of piles in the group

M_{x} = Total moment about x-axis = Q_{g} Ã— e_{y}

M_{y} = Total moment about y-axis = Q_{g} Ã— e_{x}

e_{y} = Eccentricity along y-axis

e_{x} = Eccentricity along x-axis

âˆ‘x^{2} = Sum of the squares of the distances of all the piles from y-axis

âˆ‘y^{2} = Sum of the squares of the distances of all the piles from x-axis

**Sign Convention:**

M_{x} = +ve (clock wise direction)

M_{y} = +ve (clock wise direction)

x = +ve (forward direction)

y = +ve (upward direction)

**Examples:**

For pile 1, x and y both negative as –x_{1}, -y_{1}

For pile 4′, x and y positive as +x_{1,} +y_{1}

**Pile Groups Subjected to Eccentric Vertical Loads**