A History of Research and a Review of Recent Developments

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4 Structural loading from distant explosions The dynamic loading of structures from detonating explosions is due to the instantaneous or very fast increase in air pressure associated with the shock front, and to the transient forces associated with the blast winds that follow the passage of the shock front. So far we have limited our survey mainly to the ‘free field’ conditions that result from many types of explosion, but now we must introduce into this clear space structures of varying size, shape, flexibility and ductility. Some of these structures will be sufficiently stiff, or be supported in such a way that the explosive actions will not be influenced by structural behaviour under load. Other structures will deform or move in such a way that their behaviour influences the loading they receive. In the jargon of the analyst the former are decoupled, the latter coupled. Before we can consider this further we must review the pressures that arise when shock fronts are reflected or refracted by obstacles, above and below ground and under the sea. There are three settings to be considered. In the first the explosion is large and distant, so that the loading actions can be considered uniform over the faces of the structure. The Mach stem from a nuclear explosion, for example, travelling over the surface of the ground, would load the component faces of a structure in its path with a reasonably uniform distribution. The second setting, considered in Chapter 5, is when the explosion is relatively small and occurs close to, but not in contact with, a structural member. The major effects of the explosion are concentrated over a relatively small area of the surface, and the loading actions decrease in magnitude rapidly outside this area. Impulsive loads vary with distance along or across the member, and the time at which they begin is also gradually increasing with distance. These we will term concentrated loading actions; in some analytical schools these actions are designated as being ‘localized’, an ungainly adjective. The third category is the contact explosion, considered later, when the exploding charge is either in direct contact with the structure or has been buried in the material of the structure by static or dynamic penetration. An example of static penetration is the boring of holes into rock and the careful placing of a charge at the end 71
72 Structural loading from distant explosions of the hole. Dynamic penetration occurs when the warhead of a bomb or missile is contained in a shaped container that hits a structure at high velocity and enters the component before exploding. The component can have the solidity of a reinforced concrete slab, the cellular construction of an aircraft body, or the laminations of armour plate. The loading of structures by an extremely concentrated action that damages the fabric by a cutting action must also be considered. This leads us later to the consideration of hollowed or shaped charges that project molten metal linings into the structure like jets. This chapter, however, is confined to one distant explosion, and to the analytical history of the investigation of structural loading when the loading actions are assumed to be uniform. Much of this history has been set down and explained with diagrams in many earlier publications, and there is no point in repeating the details here, so what follows is a review of the major elements of the loading analysis. 4.1 UNIFORMLY DISTRIBUTED PRESSURES The fundamentals of reflected shock fronts were discussed briefly in section 2.1, but it is now necessary to look more closely at reflections from aboveground structures and components. An example often considered is the action of a shock front from a detonation on a surface structure of simple rectangular box-shape, having one face normal to the direction of propagation of a shock wave from a distant explosion. If the explosion is directly above the structure, the shock wave will strike the upper face and a reflected shock is formed. The overpressure on this face rises to pr, which as we saw in Eq. (4.1) is given by p r/p 0=2(7p a+4p 0)/(7p a+p 0), (4.1) where p 0 is the peak ‘free field’ incident pressure, p a is atmospheric pressure, and the angle of incidence of the shock front is zero. After the shock wave has impinged on the surface of the earth adjacent to the structure, the sides of the structure will be loaded by the same reflected pressure (which acts in all directions). It is assumed in this analysis that the wavelength considerably exceeds the dimensions of the structure. If the explosion is at ground level, and the centre of the explosion lies on the normal to the side face of the structure at its mid-point, then the shock wave will strike the side face normally and a reflected shock is formed having an instantaneous pressure p r. At the moment this reflected front is formed, the initial non-reflected pressure p 0, just above the top edge of the front face, initiates a rarefaction wave, travelling at the speed of sound, which heads down the front face towards the ground. This causes disintegration of the reflected shock, until it is in equilibrium with the dynamic pressures due to the following blast winds, q. Meanwhile, at a time equal to the length of the structure divided by the front velocity, ū, the incident shock front travels over the top and along the sides of
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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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Page 55 and 56: 22 The nature of explosions where I
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Page 59 and 60: 26 The nature of explosions 1.20 Ki
Page 61 and 62: 28 The detonation of explosive char
Page 83 and 84: 50 Figure 2.18 Radius/time curve of
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Page 92 and 93: 3 Propellant, dust, gas and vapour
Page 94 and 95: Dust explosions 61 as the period 19
Page 96 and 97: Gas explosions 63 reported by Palme
Page 98 and 99: Gas explosions 65 workings in very
Page 100 and 101: Vapour cloud explosions 67 the leak
Page 102 and 103: References 69 in Los Angeles Harbou
Page 106 and 107: Uniformly distributed pressures 73
Page 108 and 109: Table 4.1 Loading/time relationship
Page 110 and 111: Loading/time relationships 77 overp
Page 112 and 113: Loading/time relationships 79 side
Page 114 and 115: Loads on underground structures 81
Page 120 and 121: Loads on underwater structures 87 c
Page 122: References 89 4.12 Allgood, J. (197
Page 125 and 126: 92 Structural loading from local ex
Page 131 and 132: 98 The general empirical equation f
Page 133 and 134: 100 Structural loading from local e
Page 145 and 146: 112 Figure 5.16 Relationship betwee
Page 153 and 154: 120 Pressure measurement and blast
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122 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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146 Penetration and fragmentation w
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148 Penetration and fragmentation T
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152 Penetration and fragmentation F
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152 Penetration and fragmentation n
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158 Figure 7.16 Penetration simulat
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162 Penetration and fragmentation b
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164 Table 7.1 Penetration and fragm
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168 Penetration and fragmentation I
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170 Penetration and fragmentation l
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174 Penetration and fragmentation p
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176 Penetration and fragmentation o
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178 Penetration and fragmentation o
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180 Penetration and fragmentation 7
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182 Penetration and fragmentation 7
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184 The effects of explosive loadin
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188 Table 8.1 It is worth noting th
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200 Table 8.5 The effects of explos
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216 Response, safety and evolution
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224 In the log-normal distribution
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230 Cole, R.H. 46, 48, 53, 55, 99 C
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232 Petry 143 Philip, E.B. 13, 14,
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Subject index Aircraft damage 207 A
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A History of Research and a Review of Recent Developments

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