Loads and Forces on Steel Railway Bridges - Design of Modern Steel Railway Bridges - page 90

for design, the projected variable amplitude stress cycles are developed for an 80 year
life with the number of stress cycles based on the length of member influence lines
(see Chapter 5).

4.3.2 D YNAMIC F REIGHT T RAIN L IVE L OAD
A train traversing a railway bridge creates actions in longitudinal, lateral, and verti-
cal directions. Longitudinal forces and pitching rotations (rotations around an axis
perpendicular to the longitudinal axis of the bridge) are caused by applied train
braking and traction forces. Lateral forces are caused by wheel and truck yawing
or “hunting.” Lateral centrifugal forces are also created on curved track bridges.
Rocking (rotations around an axis parallel to the longitudinal axis of the bridge)
and vertical dynamic forces are created by structure-track-vehicle conditions and
interactions.

4.3.2.1 Rocking and Vertical Dynamic Forces

Lateral rocking of moving vehicles will provide amplification of vertical wheel
loads. This amplification will increase stresses in members supporting the track,
and AREMA (2008) includes this load effect as a component of the impact load.
Superstructure-vehicle interaction also creates a vertical dynamic amplification of
the moving loads. This dynamic amplification results in vibrations that also increase
stresses in members supporting the track.
The unloaded simply supported beam fundamental frequency, ω 1 , of Equation 4.1

providesabasicindicatorofsuperstructureverticaldynamicresponse,andcanbeused
to establish superstructure stiffness requirements for this serviceability criterion. The
fundamental frequency of free vibration of an unloaded simply supported beam is

EI
m ,

2
L 2

ω 1 = π

(4.1)

where L is the span length, EI is the flexural rigidity of the span, and m is the mass
per unit length of the span.
The mathematical determination of a dynamic load allowance, or impact load
(Equation 4.2), even for simply supported steel railway bridge superstructures is
complex. AREMA (2008) provides an empirical impact factor based only on length
(which appears reasonable based on Equation 4.1) in order to provide deterministic
values for vertical impact design purposes. The dynamic load effect is

LE D = I F [ LE S ] , (4.2)

whereLE D isthedynamicloadeffectandisequaltoimpactload(ordynamicresponse
for a linear elastic system), LE S is the maximum static load effect (or maximum
static response for a linear elastic system), and I F is the impact factor for the simply
supported bridge span.
Therefore, for steel railway bridges, the impact factor comprises the effects
due to vehicle rocking, RE, and the vertical effects due to superstructure-vehicle