How to account for the bridge skew on the pier foundation design?

[Bosco89]

I am obtaining the reactions at the bottom of the pier column (longitudinal force Fx, transversal force Fy) to design the pier foundation. The pier foundation has the same skew of the bridge (alfa). What is the correct form to account for the skew on the footing(longitudinal force Fx', transversal force Fy')?

1) Fx'= Fx*cos(alfa) + Fy*sin(alfa)
Fy'= -Fx*sin(alfa) + Fy*cos(alfa)

2) Fx'= Fx/cos(alfa)
Fy'= Fy/cos(alfa)

In Case (1), the magnitude of the forces is kept the same, only the axis are rotated. While in Case (2), the magnitude of the forces increases.

Thank you.

 

[BridgeSmith]

If I'm understanding your question correctly, Case 1) would be the proper way to apply the loads - as vector components.