Civil Engineering Reference
In-Depth Information
Modern structural engineering software has the ability to perform moving load
analysis through stepping loads across the structure and performing the necessary
calculations to provide elastic deformations and forces in the members. Many steel
railway bridge spans are simply supported
∗
and, therefore, statically determinate.
†
Thisenablestheuseofrelativelysimplecomputerprogramsandspreadsheetstodeter-
mine the deformations and forces. For more complex superstructures (i.e., statically
indeterminate superstructures
‡
), it may be necessary to utilize more sophisticated pro-
prietary finite-element analysis software that enables moving load analysis. In any
case, digital computing has made the analysis of structures for the effects of moving
loads a routine component of the bridge design process. However, it is often necessary
that individual members of a structure be investigated (e.g., during retrofit design or
quality assurance design reviews) or relatively simple superstructures be designed.
In these cases and in general, a rudimentary understanding of classical moving load
analysis is beneficial to the design engineer.
For these reasons, the principles of moving load analysis for shear force and
bending moment are developed in the chapter (these methods are also the basis of
some software algorithms). The analyses are performed for beam and girder spans
with loads applied directly to the longitudinal members or at discrete locations via
transverse members (typically floorbeams in through girder and truss spans). The
maximum shear force and bending moment in railway truss
§
and arch
∗∗
spans are
also briefly outlined.
5.2.1.1
Maximum Shear Force and Bending Moment due to Moving
Concentrated Loads on Simply Supported Spans
5.2.1.1.1 Criteria for Maximum Shear Force (with Loads Applied Directly
to the Superstructure)
A series of concentrated loads applied directly to the steel beam or girder is typically
assumed in the design of both open and ballasted deck spans.
Themaximumshearforce,
V
C
,atalocation,C,inasimplysupportedspanoflength,
L
, traversed by a series of concentrated loads with resultant force at a distance,
x
T
,
from one end of the span is
(Figure 5.2)
x
T
L
−
V
C
=
P
T
P
L
,
(5.1)
∗
Some reasons for this are given in Chapter 3.
†
The equations of static equilibrium suffice to determine forces in the structure.
‡
Typical of continuous and some movable steel superstructures.
§
The influence lines for simple span shear force and bending moment are useful for the construction of
influence lines for axial force in truss web and chord members, respectively.
∗∗
Two-hinged arches (hinged at bases) are statically indeterminate and many steel railway arch superstruc-
tures are designed and constructed as three-hinged arches to create a statically determinate structure.
For statically determinate arches, influence lines for axial forces in members may be constructed by
superposition of horizontal and vertical effects. The influence lines for simple span bending moment
are useful for the construction of the influence lines for the vertical components of axial force in arch
members.
