Assessment of the Bill Emerson Memorial Bridge - FTP Directory ...

For a round pile, the translational parameters along x and y axis areidentical. In the case of a sliding mode along x direction, the stiffness anddamping coefficients (k x , c x ) can be evaluated by⎡E pIp ⎤kx= ⎢ ⎥fr ,3 x 1⎣ o ⎦⎡E pI p ⎤c x= ⎢ fr 2 ⎥⎣ oVs ⎦x 2(A.3)Similarly, the formulations for both rocking modes about φ and θ areidentical. In the case of a rocking mode about φ, the coefficients (k φ , c φ ) can bedetermined by⎡EI⎤k = p pφ ⎢ ⎥ fr ,⎣2 ⎦φ1 o⎡ EIpc =p⎤φ ⎢ rV2 ⎥ f (A.4)φ 2The translational motion along x (or y) axis and the rocking motion about y(or x) is inherently coupled in one plane as shown in Figure A.1. These couplingsare denoted as xφ (or yθ). In the case of coupling mode between translation xand rotation φ, the stiffness and damping of (k xφ , c xφ ) can be evaluated by⎡EIpk = xφ ⎢⎣ r 2op⎤⎥ f⎦xθ1⎣ os ⎦⎡EI⎤, c = p pxφ ⎢ ⎥ f⎣ rVo s ⎦xφ 2(A.5)In Eqs. (A.3 - A.5), I p is the moment of inertia of a pile about x axis, r o is the pileradius, and f x1, f x2, f φ1, f φ2, f xφ1, and f xφ2 , are the Novak’s parameters determinedfrom Table A.1 for ν = 0.25 and parabolic soil profile for the bridge site.Table A.1 Stiffness and damping parameters of a pile: l/r o >25 forhomogeneous soil profile and l/r o >30 for parabolic soil profile102