_5- 489 



bolt-holes. The ratio of this latter to the resistance to stretching in the main body of the plate 

 would be expected to be independent of the plate thickness and dependent only on the plate material 

 and on the geometrical pattern of the bolts, both of which factors were nominally the same for all 

 targets. There remains therefore only the contribution to T of the frictlonal resistance which will 

 depend on bolt tightness while its ratio to T will probably decrease with plate thickness. However, 

 this frictlonal resistance, although variable, is probably only a small part of the resistance to 

 pull-in even initially, and, cnce the pl:ite coratences to thin due tc stretching at the bolt holes, 

 the frictlonal resistance will rapidly become negligible. On the whole, therefore, the smallness of 

 the variation of T /T from target to target is not unexpected. On the other hand, variations in the 

 small frictlonal resistance could conceivably produce appreciable variations In the small difference 

 (T - T ) and could thus be In part or even mainly responsible for the scatter of the experimental 

 points in Figure 3. 



Finally, we can now consider how neglect of pull-in affects estimates of energy absorbed by 

 the target plate. 



Thus, if we neglect the relative weakness of the energy fixings and assume all Increase in 

 area to take place ag.^.inst the mean membrane stress T , the energy absorbed is 



n = T 5 



p m 



On the other hand, the true estimate, taking account of a relative weakness at the edge, is 



0- = T^ (S„- S- ) + T S- 

 p m m 1 m 



whence 



^'o (T - TJ s- 



Since S' /S < 1 and (T - T ) /T < 0.05 we conclude that ne9lect o.f edge weaknees only 

 Implies an error of order 51 or less In the estimated energy absorbed by the target plate. In 

 particular, such neglect cannot therefore account for the much large differences, recorded 

 previously(l) (2) , between energy absorbed 6y tarjet plate and energy communicated according to 

 various theories. 



CoTic Lusions , 



(1) The agreement between the approximate theory and the experimental results is reasonable 

 bearing in mind that the large scatter of the experimental points, as plotted in Figure 3, is 

 to be expected in view of probaole variation in type of loading and/or small variations In 

 edge resistance from shot to shot, due to the large variety of charge and target conditions 

 in the experiments. 



(2) The mean membrane stress T round the periphery is estimated to differ by less than 5» from 

 the mean membrane stress in the unsupported area of plate. 



(3) Estimates of energy absorbed by the.target plate given in previous reports(l) (2) are not 

 likely to be in error by more than about 5» due tc neglect of the pull-in phenomenon. 



References, 



(1) Taylor, G.I, "The Distortion under pressure of a diaphragm which Is clamped 



along its edge and stressed beyond the elastic limit", 



(2) Fox, E.N., and Rollo, "Analysis of Box Model Trials. II'. 



W.T. 



(3) Fox, E.N., and Craig, J. "The opt imum distribut ion of weight between plating and stiffeners 



for maximum resistance to impulsive loading - first theoretical 

 analysis". 



