A History of Research and a Review of Recent Developments

Civil bridges 199
approximate relationship, used by defence engineers for spans between 10
and 100 m, is
q D =K(L+50)(1+2m)(30+c)/800 KN/m,
(8.2)
where m is the number of traffic lanes, c is an estimate of the military load
class, and K depends on the materials from which the bridge is constructed.
For a steel main structure and timber deck, K=1; for a steel main structure and
concrete deck, K=1.25; for prestressed concrete bridge K=2.4 and for other
reinforced concrete bridges K=4.0.
As an example, the dead load per metre for a reinforced concrete bridge
having two lanes of traffic and a military load class of 70 would be
q D =4(L+50)5(30+70)/800 KN/m,
(8.3)
so that for a simply supported span of 50 metres, q D=50 KN/n. This is of a
similar order to q L from Table 8.4. For a four lane bridge having a similar
span q D would rise to 90 KN/m, again of a similar order to q L.
According to Eq. (8.2) the dead load per metre for a reinforced concrete
bridge is 2.2 times that for a steel and concrete bridge having a similar capacity,
width and span, and 1.7 times that for a prestressed concrete bridge. These
figures are independent of span within the range given and imply that the effect
of prestressing a bridge is to reduce its dead weight for the same span and
loading by 40%. This is consistent with the notion that prestressing is broadly
equivalent to applying a distributed upward vertical force on the girder.
If the girder weight is reduced by 40% of its non-prestressed value, then
for a rectangular girder section of constant width the effect will be a reduction
in section depth. This in turn leads to a reduced capacity to carry a bending
moment to about 36% of its original value. If the section is an I beam or
hollow box, the reduction would be to about 60% of the original value. For a
practical bridge girder section the true reduction in moment capacity would
probably be around 50%.
This infers that if the prestressing tendons are cut by an explosion the total
capacity of the girder to carry live plus dead loading could be halved. We have
already seen that the dead load moment for concrete bridges of less than 40
metres span could well be equal to the dead load moment under working
conditions, so after the destruction of tendons the girder would just take its
dead load with a margin of safety of about 1.5. An application of live load
equal to about one half maximum would then cause complete failure, and in
fact any application of live load would begin to cause undesirable permanent
bending deflections and structural deterioration.
As the length of a single span girder bridge increases, the proportion of the
moment capacity used to support the dead load will also increase. In the limit,
for very long suspension or cable stayed bridges up to a single span of 1500 m,
it is often assumed that 80% of the total loading is due to the deadweight of