A History of Research and a Review of Recent Developments

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Civil bridges 197 It was necessary to build twin Bailey bridges, each 80 ft in length, across the gap in the deck in order to continue to use the bridge for military traffic. More recently there have been a number of demolitions, or part demolitions of civil bridges during the conflict in Bosnia. Reinforced concrete box section bridges have been destroyed or partially destroyed, mainly by charges placed at deck level; but there have been instances of damage to piers by explosives set at their bases. The problems encountered because of explosive damage to Bosnian bridges have been discussed by Pelton [8.22]. In order to classify the extent of explosive damage it has been suggested that the main load carrying components of all bridge structures can be classified as follows: Class One: Complete destruction of the component will result in the complete destruction of the load-carrying capacity of the bridge. This could apply to suspension bridge towers and cables, cable-stayed bridge towers, single piers, single box girders or abutments. Class Two: Complete or partial destruction of the component will seriously reduce the load-carrying capacity of the structure, but repair will allow a reduced capability to be maintained. This could apply to single main girders of bridges with at least two main girder systems or to the main arches of steel or concrete bridges with two or more parallel arches. It also applies to the deck slabs of composite bridges and to the cross girders of truss girder bridges. Class Three: Complete or partial destruction of the component will only have a localized effect on load-carrying capacity, and repair will allow the full capability to be restored. This could apply to the deck slabs of non-composite bridges or to single members in highly redundant trusses or frameworks. The calculation of the residual strength of bridges damaged by explosions or by penetration and fragmentation of explosive-carrying missiles can be based on safety levels and on the specification of live load capacity as an equivalent uniformly distributed load. The chances of crossing a damaged bridge safely before any repairs are made can be related to five levels of risk, each level being linked to the number of vehicles of maximum load class that can cross the damaged structure before it becomes completely unsafe. The decrease in safety with time can be linked to the growth of deep cracks around the edge of a damaged area in a concrete slab deck or to the growth of tearing in a steel plate girder that has been pierced by fragments; or to the gradual onset of instability in a supporting pier due to settlement into a nearby crater. If the bridge fails completely after 10n crossings of the heaviest vehicles, the safety level can be expressed in terms of the value of n, as follows:
198 The effects of explosive loading Safety Level 0: n=0 Extreme risk. Probability of failure as the bridge is crossed by one vehicle of maximum load class. Level 1: n=1 High risk. Probability of bridge failure after 10 crossings of maximum load class. Level 2: n=2 Moderate risk, with bridge failure probable after 100 crossings. Level 3: n=3 Low risk, with failure after 1000 crossings. Level 4: n=4 Minimal risk, with failure after 10 000 crossings. (The minimal risk level might well be of the same order as the annual probability of failure of an elderly undamaged civil bridge under maximum road class traffic.) The design loadings for civil bridges were compared in 1979 by the Organization of Economic Co-operation and Development (Paris) [8.23] who conducted a study in which the total bending moments caused by live loading in various codes of practice were calculated for a simply supported bridge. Calculations were made for two, three and four traffic lanes over spans from 10 m to 100 m, taking account of impact and reductions for multiple lane loading. Differences in allowable stress levels were taken into account. The maximum bending moments obtained were converted into an equivalent uniformly distributed load q L. Consider, as an example, the results for American AASHTO load specifications applied to road bridges on motorways, trunk roads and principal highways (A roads), given in Table 8.4. From these figures it is possible to calculate the maximum live load bending moment that can be applied to an undamaged bridge under working conditions ( for a simply supported span of length L), or under ultimate conditions . The corresponding maximum shear forces would be q LL/2 and 1.5q LL/2. When assessing residual strength, a knowledge of the live loading, q L, is not enough. It is necessary to know the equivalent dead load per metre (=q D) due to the self weight of the bridge and its accessories. Various equations have been proposed for the rough calculation of total dead load, and these depend on the number of traffic lanes, an estimate of the load classification and properties of the material from which the bridge is constructed. An Table 8.4 Values of equivalent uniformly distributed load, q L , for AASHTO loading The values of q L to cause the bridges to collapse could be taken approximately as 1.5 times those given in the table.
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EXPLOSIVE LOADING OF ENGINEERING ST
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Explosive Loading of Engineering St
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Contents Preface vii Acknowledgemen
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Preface A long time ago I walked ov
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Acknowledgements The reports from w
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xii Notation m mass of projectile m
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xiv Notation Q work done during exp
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Introduction Explosions can threate
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Introduction xix Bertram Hopkinson
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Introduction xxi in the seventeenth
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Introduction xxiii own versions of
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Introduction xxv indoor shelters an
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Introduction xxvii explosions/ stru
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Introduction xxix particularly dama
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Introduction xxxi but the feeling i
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2 The nature of explosions propelli
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4 The nature of explosions or rathe
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6 The nature of explosions ogive, a
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8 The nature of explosions mass, an
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10 The nature of explosions Figure
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12 4 lb cylinders, TNT, 3.75 lb sph
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14 The nature of explosions As Figu
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16 The nature of explosions of the
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18 1.4 THE DECAY OF INSTANTANEOUS O
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20 The nature of explosions Figure
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22 The nature of explosions where I
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24 sometimes written in psi as The
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26 The nature of explosions 1.20 Ki
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28 The detonation of explosive char
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50 Figure 2.18 Radius/time curve of
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54 and 50%, rather than by a factor
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3 Propellant, dust, gas and vapour
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Dust explosions 61 as the period 19
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Gas explosions 63 reported by Palme
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Gas explosions 65 workings in very
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Vapour cloud explosions 67 the leak
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References 69 in Los Angeles Harbou
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4 Structural loading from distant e
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Uniformly distributed pressures 73
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Table 4.1 Loading/time relationship
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Loading/time relationships 77 overp
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Loading/time relationships 79 side
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Loads on underground structures 81
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Loads on underwater structures 87 c
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References 89 4.12 Allgood, J. (197
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92 Structural loading from local ex
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98 The general empirical equation f
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100 Structural loading from local e
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112 Figure 5.16 Relationship betwee
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120 Pressure measurement and blast
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142 Penetration and fragmentation r
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144 Penetration and fragmentation p
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Page 183 and 184: 152 Penetration and fragmentation F
Page 185 and 186: 152 Penetration and fragmentation n
Page 191 and 192: 158 Figure 7.16 Penetration simulat
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Page 197 and 198: 164 Table 7.1 Penetration and fragm
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Page 209 and 210: 176 Penetration and fragmentation o
Page 211 and 212: 178 Penetration and fragmentation o
Page 213 and 214: 180 Penetration and fragmentation 7
Page 215 and 216: 182 Penetration and fragmentation 7
Page 217 and 218: 184 The effects of explosive loadin
Page 221 and 222: 188 Table 8.1 It is worth noting th
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Page 233 and 234: 200 Table 8.5 The effects of explos
Page 249 and 250: 216 Response, safety and evolution
Page 257 and 258: 224 In the log-normal distribution
Page 263 and 264: 230 Cole, R.H. 46, 48, 53, 55, 99 C
Page 265 and 266: 232 Petry 143 Philip, E.B. 13, 14,
Page 268 and 269: Subject index Aircraft damage 207 A
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