A History of Research and a Review of Recent Developments
A History of Research and a Review of Recent Developments
A History of Research and a Review of Recent Developments
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198<br />
The effects <strong>of</strong> explosive loading<br />
Safety Level 0: n=0 Extreme risk. Probability <strong>of</strong> failure as the bridge is<br />
crossed by one vehicle <strong>of</strong> maximum load class.<br />
Level 1: n=1 High risk. Probability <strong>of</strong> bridge failure after 10<br />
crossings <strong>of</strong> maximum load class.<br />
Level 2: n=2 Moderate risk, with bridge failure probable after<br />
100 crossings.<br />
Level 3: n=3 Low risk, with failure after 1000 crossings.<br />
Level 4: n=4 Minimal risk, with failure after 10 000 crossings.<br />
(The minimal risk level might well be <strong>of</strong> the same order as the annual probability<br />
<strong>of</strong> failure <strong>of</strong> an elderly undamaged civil bridge under maximum road class<br />
traffic.)<br />
The design loadings for civil bridges were compared in 1979 by the<br />
Organization <strong>of</strong> Economic Co-operation <strong>and</strong> Development (Paris) [8.23] who<br />
conducted a study in which the total bending moments caused by live loading<br />
in various codes <strong>of</strong> practice were calculated for a simply supported bridge.<br />
Calculations were made for two, three <strong>and</strong> four traffic lanes over spans from<br />
10 m to 100 m, taking account <strong>of</strong> impact <strong>and</strong> reductions for multiple lane<br />
loading. Differences in allowable stress levels were taken into account. The<br />
maximum bending moments obtained were converted into an equivalent<br />
uniformly distributed load q L. Consider, as an example, the results for American<br />
AASHTO load specifications applied to road bridges on motorways, trunk<br />
roads <strong>and</strong> principal highways (A roads), given in Table 8.4.<br />
From these figures it is possible to calculate the maximum live load bending<br />
moment that can be applied to an undamaged bridge under working conditions<br />
( for a simply supported span <strong>of</strong> length L), or under ultimate conditions<br />
. The corresponding maximum shear forces would be q LL/2 <strong>and</strong><br />
1.5q LL/2.<br />
When assessing residual strength, a knowledge <strong>of</strong> the live loading, q L, is<br />
not enough. It is necessary to know the equivalent dead load per metre<br />
(=q D) due to the self weight <strong>of</strong> the bridge <strong>and</strong> its accessories. Various equations<br />
have been proposed for the rough calculation <strong>of</strong> total dead load, <strong>and</strong> these<br />
depend on the number <strong>of</strong> traffic lanes, an estimate <strong>of</strong> the load classification<br />
<strong>and</strong> properties <strong>of</strong> the material from which the bridge is constructed. An<br />
Table 8.4 Values <strong>of</strong> equivalent uniformly distributed load, q L , for AASHTO loading<br />
The values <strong>of</strong> q L to cause the bridges to collapse could be taken approximately as<br />
1.5 times those given in the table.