485 



ANALYSIS OF PULL-IN AT EDGE FIXINGS 

 IN BOX MODEL TRIALS 



E. N. Fox 



September 1945 



Suma a ry . 



An approximate theory is developed for the Behaviour under impulsive loading of a 

 rectangular plate which is relatively weak at the edges, it belnj assumed that the edge fixings exert 

 a mean membrane tension T per unit length of periphery which is less than the mean membrane tension 

 T required to stretch the material In the unsupported area of the plate. 



For a given type of loading the theory Indicates that there will be a critical magnitude of 

 load and a corresponding critical final mean deflsction below which all increase of unsupported area 

 takes place at the edges. for greater final mean deflections corresponding to more severe loading 

 the- increase in area will be due both to edge pull-in and plate stretching, the fractional 

 contribution of the latter increasing steadily with increasing firal mean deflection corresponding 

 to increasing magnitude of load. 



Experimental data on edge puU-ln of the target plate in Box Model trials are in general 

 qualitative agreement with the theory and quantitative comparison leads to an estimate that 

 (T - T ) /T is of or^r 51 or less for all shots. 



It is concluded that estimates of energy absorbed by the target plate which have been given 

 in previous reports on the assinptlon that there is no edge weakness onV erred by 51 or less due 

 to neglect of this particular phenomenon. 



Object of analysis . 



in previous analyses {l)(2) of the results of Box Model trials. It was found that for some 

 shots the estimated energy absorbed in plastic deformation of the target plate was considerably 

 larger than the energy conmunlcated by the shock-wave as estimated on different theories of loading. 



Several possible sources for this difference were suggested and the present report Is 

 concerned with one of these, namely, that the energy absorbed, as calculated on the assumption that 

 the plate was raised to its yield stress everywhere, might be seriously over-estimated If pull-in 

 at the edge fixings could occur at a mean stress much lower than the yield stress for the plate. 



In order to examine this possibility, measurements of the pull-in at the edges of the 

 target plate were made as a routine procedure in all Box Model trials from Shot 174 onwards. At 

 the same time an approv'mtr thPnretical andysls was undertaken for application to these measurements 

 with a view to estimating the resistance to pull-in relative to resistance to plate stretching. 

 The present report gives the results of this application. 



Outline of theory . 



The detailed theory is given In the Appendix and we shall therefore give only the main 

 assumptions and results. 



(l) 'hysical assumptions . 



The plate is assumed to behave according to the now familiar "soap-bubble" approxlrmtiond) 

 I.e., any Increase in area occurs under a constant membrane tension 



T = s h 







where s^^ is the yield stress and h is the original thickness assured uniform over the plate. 



By 



