A History of Research and a Review of Recent Developments

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The effects of explosive loading
shape, and any variations such as combined loading or unusual cross sections
will result in values of m between 1 and 3 in the strength ratio equation. For
example, a bridge component subjected to combined bending and compression
might be expected to have an m value between 2 and 3. Figure 8.7 indicates
that for damage that reduces the cross section by 25% or less, the strength
ratio is very similar for simple members in bending or compression, but this
ratio could in turn be 25% less than the strength ratio in tension or shear.
This analysis looks to have a logic about it, but is based on rather idealistic
circumstances. Also, it must be remembered that if the foundations of a pier
are undermined, bridge failure could be by overturning—a catastrophic
happening not linked to bridge ductility or loss of section, but to the explosive
destruction of external support from the ground.
The other extreme to the damage configuration assumed in Figure 8.6 would
be the vertical slicing of the section resulting in the reduction of the width
from b to b 1. In all the loading cases considered the value of m would now be
1, and the strength ratio would be directly proportional to the area ratio. In
practice cross-sectional damage would probably be somewhere between the
two extremes discussed above.
The assessment of strength reduction from a knowledge of the area reduction
of truss members was pursued during and after the Second World War by the
designers of the military ‘Bailey Bridge’ in the UK. Their results were presented
in the form of a table, given in reference [8.24], which gave a relationship
between the amount of damage to the webs and flanges of I beams and
percentage residual strength of verticals and diagonals in the bridge truss
panels. For example, the complete removal of the web in shorter members led
to a residual strength of 66%, and removal of half the web gave 73%. Complete
removal of one flange gave a residual strength of 24%, and removal of one
flange and half the other reduced the figure to 18%. Similar residual strengths
were given for main chords consisting of two back-to-back channels. The
removal of the web of the channel gave a residual percentage of 63% for the
shorter members, and removal of the webs of both channels gave 61%.
Complete removal of one channel flange and web gave a residual percentage
of only 3%.
The article in reference [8.24] on the damage assessment of military bridges
noted that in the majority of cases where bridges were damaged by enemy air
attack or shell fire, several bridge members would have been reduced in strength.
Each member was then considered separately and the final classification assessed
on the worst case. The article also stated that if a bridge member is struck by
flying metal and is deformed but not holed, it must be ‘carefully watched as
loads cross the bridge’. If further deformation occurs, the member is treated
as severed, and the bridge strength assessed accordingly.
Rapid methods of evaluating residual strength can be illustrated by taking
examples, and three areas where damage might occur to Class One bridge
components are: