Vertical Piles of a Group subjected to Eccentric Loading.

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In order to determine the load distribution  between the vertical piles of a group subjected to eccentric loading, we have to consider the two cases of loading:

(a) When eccentricity is about one axis only

Vpi =  V/n  +-  (V.e.Xi.A)/Ig

Where,  Vpi = Load on the ith pile

              V = Total vertical load acting on the pile group.

Accentric loading on pile group

             n = Total no. of piles.

             e= amount of eccentricity w.r.t. the centre of the pile group. 

             Xi = Distance of the centre of the ith pile from the centre of the pile group, measured parallel to e. 

             Ig = Moment of Inertia of the piles about the axis normal to the direction of eccentricity. 

                 = A.X1^2 + A.X2^2 +.... + A.Xn^2

             A = Area of the pile cross-section and 

           X1, X2, ...... Xn = Distance from centre of gravity of pile group to the line of each pile, measured parallel to e. 

Since, all the piles in the group are assumed to be identical, above equation can be written as:

Vpi =  V/n  +-  (V.e.Xi.)/Sum(Xi.^2).

(b) When eccentricity is about two axes:

When there is eccentricity about both the axes, individual pile loads may be determined by the method of superposition:

Vpi =  V/n  +-  (V.ey.Yi.A)/Ix   +-  (V.ex.Xi.A)/Iy

where, V, n and A have the same meaning. 

  

Eccentric loading on pile group

ex = Amount of eccentricity w.r.t. centre of pile group measured along x-axis.

ey = Amount of eccentricity w.r.t. centre of pile group measured along y-axis.

Ix = Moment of inertia of the piles about x-axis. == A.Y1^2 + A.Y2^2 +.... + A.Yn^2

Iy = Moment of inertia of the piles about the y-axis = = A.X1^2 + A.X2^2 +.... + A.Xn^2

Xi = distance from the centre of gravity of the pile group to the line of each pile, measured parallel to the x-axis, and 

Yi = distance from the centre of gravity of the pile group to the line of each pile, measured parallel to the y-axis.

Reference: Analysis and Design of Sub-Structures by Swami Saran

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