Structural Analysis and Design of Steel Railway Bridges - Design of Modern Steel Railway Bridges - page 151

and P T / n 0 for maximum shear in the panel. Therefore, the maximum shear

in spans with equal length panels occurs in panel BC when the average panel load on
the span, P T / n , equals the load in panel BC, P BC .
The relative changes in shear given by Equation 5.6 can be examined to determine
the location of the concentrated loads for maximum shear in any panel on the span.

− P BC =

5.2.1.1.3 Criteria for Maximum Bending Moment (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.
The maximum bending moment, M C , at a location, C, in a simply supported span,
of length, L , traversed by a series of concentrated loads with resultant at a distance,
x T , from one end of the span is ( Figure 5.2)

P T a

x T
L

M C = − (P L )x L , (5.7)

where P T is the total load on the span and P L is the load to the left of location C.
The change in bending moment,

Δ M C , at location C as the constant force P T

moves from x T + Δ x T is

P T a

P L

Δ M C =

L −

Δ x T , (5.8)

where x T is a small increment of movement of load assuming no change in

concentrated forces on the span.
When P T / L

Δ

P L / a , maximum bending moment at location C occurs as the change
in bending moment changes sign (positive to negative). Therefore, the maximum
bending moment occurs at location C when the average distributed load on the span,
P T / L , equals the average distributed load to the left of location C, P L / a .
The relative changes in bending moment given by Equation 5.8 can be examined
to determine the location of the concentrated loads for maximum bending moment at
any location, C, in the span.

=

5.2.1.1.4 Criteria for Maximum Bending Moment (with Loads Applied
to the Superstructure through Transverse Members)
A series of concentrated loads applied through longitudinal members (stringers) to
transverse members (floorbeams) to the steel beam or girder is typically assumed in
the design of open deck through spans. Ballasted deck superstructures that transfer
load to the beams or girders by closely spaced transverse members without stringers
may be treated as outlined in Section 5.2.1.1.3.
The maximum bending moment, M BC , in panel BC in a simply supported span
of length, L , traversed by a series of concentrated loads (with resultant force at x T )
transferred to the span by stringers and transverse floorbeams is ( Figure 5.3)

(P BC ) c
s p

d .

P T a

x T
L

M BC = − (P L )b − (5.9)