Method for Determining Longitudinal Stiffness of Combined Double Thin-Walled Pier Based on Train-Track-Bridge Interaction

Table 2

Notations adopted in calculations.

Notation	Description
σd	Maximum dynamic stress of the edge of rail bottom
σt	Thermal stress of rail
σb	Braking stress of rail
σa	Additional stress of rail caused by deformation of CDTWP
zr(x,t)/yr(x,t)/ϕr(x,t)	Vertical/lateral/torsional displacements of the rail
mr	Rail mass per unit length
ρr	Rail density
EIy/EIz	Rail bending stiffness to Y-axle/Z-axle
Ir0	Torsional inertia of the rail
GJt	Rail torsional stiffness
FrVi(t)/FrLi(t)	Vertical/lateral dynamic forces of the ith fastener
Pj(t)/Qj(t)	The jth wheel-rail vertical/lateral forces
MFi(t)	Moment applying on rail due to forces frvi(t) and frli(t)
Mwj(t)	Moment applying on rail due to forces Pj(t) and Qj(t)
Ns/Nw	Number of fasteners/wheelsets
δ(x)	Dirac delta function
FrV1i(t)/FrV2i(t)	Vertical/lateral fastener force acting on the left side of the rail
ar	Vertical distance between rail torsional centre and lateral fastener force
br	Half of the distance between frv1i(t) and frv2i(t)
hr	Vertical distance from rail torsional centre to lateral wheel-rail force
er	Lateral distance from rail torsional centre to vertical wheel-rail force
Zk(x)/Yk(x)/Φk(x)	Rail vertical/lateral/torsional mode function
Mz/My	Moments of rail