The Design of Modern Steel Bridges - TEDI

eam, with an effective area equal to the gross area of the slab between the
steel girders divided by the modular ratio (i.e. the ratio between Young’s
moduli of steel and concrete). Sometimes the transverse girders are unconnected
to the concrete deck; the grillage analysis in such cases must take into
account two separate sets of transverse members, i.e. the concrete slab and the
unconnected steel transverse girders. Shear deformation is generally ignored in
grillage analysis.
Open cross-sections like I-beams have negligible torsional stiffness. The
torsional stiffness of a concrete slab is also generally ignored, but may be taken
into account by assuming the St Venant torsional constant as d 3 /6 per unit
width in the two orthogonal directions, when d is the slab depth.
Computer programs for grillage analysis can also easily deal with multiplespan
continuous structures with constant or varying moments of inertia of the
longitudinal girders. The hogging moment over intermediate supports of the
longitudinal girders may cause transverse cracking of the concrete slab in these
regions, thus causing a reduction in the effective moments of inertia. This can
be dealt with in one of the following two ways:
(1) A new distribution of bending moments may be determined by neglecting
the concrete in the calculation of the moment of inertia of the beams over
the length over supports where tensile stress in concrete was found to
exceed 10% of its specified 28 day compressive strength, or over, say,
15% of the span lengths on each side of the support.
(2) The sagging moments in the adjacent spans are increased, without reducing
the hogging moment; the percentage increase is specified in BS
5400[13] as 40 times the ratio of the tensile stress in concrete to its
specified 28 day compressive strength.
In the AASHTO specification[1] empirical methods are authorised for
obtaining the transverse distribution of wheel loads. For internal longitudinal
beams with spacing S (metres), the bending moment may be calculated by
(1) taking S/1.676 fraction of wheel loads, if S < 4.267 m
(2) taking the flooring to act as a simple span between longitudinal beams, if
S > 4.267 m.
For external longitudinal beams, the flooring may be assumed to act as a
simple span between longitudinal beams, except that, where there are four or
more beams, the fraction of wheel loads shall not be less than:
(1) S/1.676, where S 4 1.829 m
(2) S/(1.219 þ 0.25S), where 1.829 < S < 4.267.
Rolled Beam and Plate Girder Design 95
Shear forces in all beams may be calculated in the same way as bending
moments, except that, for calculating end shear or reaction, the effect of
a wheel load placed near that end of a beam shall always be calculated by
assuming the flooring to act as a simple span. One condition for adopting this