Pile Groups Subjected to Eccentric Vertical Loads

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 Qg, the number of piles is n, then the load transmitted to each pile shall be:

Q_i = \dfrac{Q_g}{n}

load at c.g

When however, the pile cap is eccentrically loaded, as to subject the pile cap to a central vertical load Qg and additional bending moment Mx (about X – axis), and My (about y- axis), then the load transmitted to a pile is given by the equation:

Q_i = \dfrac{Q_g}{n}\pm \dfrac{M_y \times}{\Sigma x^2}\pm \dfrac{M_x \times y}{\Sigma y^2}   ———- (1)

Where, Qi – Load transmitted to a particular pile

Qg = Total vertical load acting on the pile cap (centrally)

n = Number of piles in the group

Mx = Total moment about x-axis = Q_g \times e_y

My = Total moment about y-axis = Q_g \times e_x

ey = Eccentricity along y-axis

ex = Eccentricity along x-axis

\Sigma x^2  = Sum of the squares of the distances of all the piles from y-axis

\Sigma x^2 = Sum of the squares of the distances of all the piles from x-axis

Sign Convention:

Mx = +ve (clock wise direction)

My = +ve (clock wise direction)

x = +ve (forward direction)

y = +ve (upward direction)

Examples:

For pile 1, x and y both negative as –x1, -y1

For pile 4′, x and y positive as +x1, +y1

eccentrically Loaded Pile

Pile Groups Subjected to Eccentric Vertical Loads

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