The rotational restraint coefficient at the top of a pier and the rotational restraint coefficient at the bottom of the pier (that is, the degree of fixity in the foundation of the pier) are used to determine the effective length factor of the pier. Moreover, the effective length factor of a pier is used to determine the slenderness ratio of the pier, while the degree of fixity in the foundation of a pier is used to perform the first-order elastic analysis in order to compute the pier deflection. Finally, the slenderness ratio of the pier is used to determine if the effect of slenderness shall be considered in the design of the pier, while the magnitude of the pier deflection resulting from the first-order analysis is used to determine if the second-order force effect (the p-∆ effect) shall be considered in the design of the pier. The computations of the slenderness ratio and the deflection of a pier, however, have conventionally been carried out by assuming that the base of the pier is rigidly fixed to the footing, and the footing in turn, is rigidly fixed to the ground. Other degrees of footing fixity have been neglected by the conventional approach. In this paper, two examples are demonstrated for the slenderness ratio computation and the first-order deflection analysis for bridge piers with various degrees of footing fixity (including footings anchored on rock, footings not anchored on rock, footings on soil, and footings on multiple rows of end-bearing piles) recommended by the AASHTO LRFD Bridge Design Specifications. The results from the examples indicate that the degree of footing fixity should not be neglected since it significantly affects the magnitude of the slenderness ratio and the deflection of the pier.
Hsiao, Jen-kan K. and Jiang, Yunyi. "FOOTING FIXITY EFFECT ON PIER DEFLECTION." International Journal of Bridge Engineering (IJBE) Vol. 2, No. No. 2 (Fall 2014): pp. 01-20.