Research Article

Implementation of an Advanced Macroelement Beam Model under Moving Load (Case Study: Iranian Railroad Projects)

Table 1

Symbol definition.

SymbolDefinition

Axial and lateral deformation in the x, y, and z directions, respectively
Axial and lateral velocity in the x, y, and z directions, respectively
Axial and lateral acceleration in the x, y, and z directions, respectively
Torsion angle around x direction
Warping factor definition
Stiffness factor per unit length of the beam in the x, y, and z directions, respectively
Rotational stiffness factor per unit length of the beam
Damping factor per unit length of the beam in the x, y, and z directions, respectively
Rotational damping factor per unit length of the beam
Mass per unit length of the beam
Rotational mass inertia per unit length of the beam
Modulus of elasticity
Area section
Warping factor
Kinetic energy
Potential energy
Nonconservative works
Mass density
Strain of beam model
The second moment of area in the x, y, and z directions, respectively
Second polar moment of area
Distance between shear center and bottom level of the rail
Moving point load in the x, y, and z directions, respectively
Concentrated rotational moment around the x axis