A History of Research and a Review of Recent Developments

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Mendoza [9.15]. As these references show, comparisons between DYNA-3D and the analysis developed by Biggs have been made in conjunction with research on weapons effects on structures. But the field of offshore structures subjected to blast loads from hydrocarbon explosions has also produced comparative research. The structural response to blast of stiffened metallic panels, usually steel, involving torsional instability of the bulb-stiffeners has been examined by teams in a number of countries using DYNA-3D, ADINA, and the Biggs formulation. The use of finite element analysis has emphasized the importance of choosing correct boundary conditions. Stiffener restraint is important, as it can control the buckling mode, and it is also important to use an accurate static resistance relationship. Recent work in this area has been reported by Walker [9.16], Schleyer and Mihsein [9.17] Louca, Punjani and Harding [9.18] and Van Wees [9.19]. The non-linear response of stiffened ship panels to blast loading has been discussed by Houlston and DesRochers [9.20]. In reference [9.18] it was noted that the Biggs representation is accurate as long as a limited amount of plasticity occurs in the system. It was suggested that widespread plasticity is not reproduced by the Biggs analysis, whereas it can be accommodated in the finite element model. 9.3 LOAD FACTORS To end our examination of loading and load effects, we must now consider load factors to be used in limit state calculations that establish the safety and reliability of structures subjected to blast or fragmentation. In establishing the factors it is first necessary to investigate how peak pressures and impulses vary when nominally similar charges are detonated. This problem has been examined in recent years in the USA, where reliability-based blast-resistant design is being actively pursued, by the recording of data from a test series in which 16 general purpose conventional bombs were exploded. It was important to establish whether the scatter of results could be adequately represented by a log-normal distribution. Reports by Carson, Morrison and Hampson [9.21] and Carson and Morrison [9.22] of tests using Mark 82 and Mark 83 General Purpose Bombs were completed in 1984 and 1987, and were examined by Twisdale, Sues, Lavelle and Miller [9.23] in 1991. In their analysis they took 325 peak pressures and 320 positive impulses at various ranges and found that the peak pressure and peak impact prediction error statistics supported the use of log-normal distributions. The incident air-blast load factors for various reliability levels are given in reference [9.23] as shown in Table 9.1. Table 9.1 Load factor 223
224 In the log-normal distribution the coefficient of variation for airblast pressure was 0.3. The authors point out that for most above-ground structures, the blast pressures that load the structure are reflected pressures, and the data for these does not compare in quality or quantity to that available for incident blast. A later paper by Twisdale, Sues and Lavelle [9.24] indicated that the load factors in the above table should be slightly amended, because differences were noted in the mean prediction errors for half-buried bombs and bombs resting horizontally on the surface. They also reported advances in the analysis of reflected pressures. For structures buried below ground level, a major loading is derived from ground shock, as discussed in Chapter 5, section 5.2. The variability of ground shock loads from nominally similar explosions acting through nominally similar soils is high, mainly because of the variability of soil characteristics. On the assumption that the free-field stresses were distributed on a log-normal basis, standard deviations were found from experimental results by Sues, Drake and Twisdale [9.25], using earlier stress measurements recorded by Drake et al. (9.26). Standard deviations from experiments for which there was proper representation of bomb and site variability showed that for soils defined as dense, wet sand, loose wet sand, and sandy clay, there was a range of standard deviation between 0.31 and 0.33 for free field velocity, and between 0.28 and 0.48 for free field stress. These figures were shown to be independent of the distance between the centre of the explosion and the target (i.e. the range). Table 9.2 shows the relationships produced by the authors between reliability and the ground shock stress load factor for either ‘typical’ backfills (A) or backfills where there was much uncertainty about the soil properties (B). Thus, for a reliability of 95%, the presence of a well-defined soil increased the load factor for pressure or free-field stress from 2.09 to 2.40, and for an uncertainly defined soil from 2.09 to 3.34. Using average soil values and taking an overall view of the accuracy of the predictions and analysis we might broadly conclude that for pressurized above ground structures and a reliability of 95%, the recommended load factor is about 2, and for buried structures under ground shock, the stress factor increases to about 3 for the same reliability level. The team of Twisdale and Sues [9.27] have also reported on a reliabilitybased design procedure for penetrating fragments from an exploding bomb. The steps in this method are given by the authors in the following order: First evaluate the expected number of fragments that could be generated by the bomb, given as , where W c is the casing weight and M A is the fragment weight probability distribution parameter (Motts distribution). Then calculate the Table 9.2 Response, safety and evolution
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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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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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166 Penetration and fragmentation w
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168 Penetration and fragmentation I
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170 Penetration and fragmentation l
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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 249 and 250: 216 Response, safety and evolution
Page 255: 222 Response, safety and evolution
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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