- 3 _ 473 



trial and from 1.95 to 2.0it for pressures of 40 - 120 lbs. /square inch during trial. Both 

 figure 3 and TaDle 3 thus sho* that the- shap.- of the deflectod plate is in rrasonabte agreement 

 with the theory of report A. 



2. Loid-def lect ion curve . 



The relation betwci.'n applied pressure and central deflection is plotted in Figure 1 where 

 the experimrntal points frofii T-iblc I an sho.vn conntCted by a faired curve. 



If the plate Schav.^d is •'. membrane extrlinq a constiint stress the load-deflection curve 

 would be a straight line through the ori^'in given, from equation 36 of report a with changed 

 notation, oy 



Zc = £^2^ (1) 



where Zc = central deflection 



p = appl ied pressure 



a = half long span (36 inches) 



h = plate thickness (O.llia inches) 



5 = yield stress 



Comparing this equation ivitn the curve of Figure u it should first be noted that in the 

 initial stages the theory would not be expected to apply in view of the elastic nature of small 

 deflections and of the initial slackness of the plate. Considering pressures above 60 lbs,/ 

 square inch the experimental curve, while it cannot be approximated closely by a straight Tine 

 through the origin over the whole of its length, is nevertheless not in disagreement with 

 theoretical expectation if allowance fs made for strain hardening. Thus if we assume the stress 

 in the plate to be constant over the surface but, due to strain hardening, to increase with 

 increasing de'liction then equation (l) will still hold at any particular deflection. The stress 

 5 will now be, however, an increasing function of Zc, and thus the load-deflection curve will 

 become concave to the pressure axis. Conv.;rsely from Figure * we can tfstimato the variation of 

 s which would be necessary to give agreement between equation (l) and the experimental data. 

 In this way we find that for pressures from 60 lbs. /square inch to 275 lbs. /square inch the 

 calculated value of s varies from 16 tons/square inch to 23-5 tons/square inch. 



As the test was a preliminary one intended originally to explore the possibilities of 

 static tests rather than to obtain definite data, the plate used was taken arbitrarily from 

 dockyard stocks; when it was realised that the data obtained was of sufficient interest to warrant 

 analysis no spare piece of plate was available to carry out a tensile test. It can, however, be 

 said that the preceding values, deduced from Figure 4, of s increasing from 18 tons/square inch 

 to 23.5 tons/square inch seem reasonable Tn view of the ultimate strength of 26 - 30 tons/square 

 Inch required by specification for the stock of plates from which the particular plate used in 

 the trial was taken. 



If we assume as indicated by Table 3 that the deflected plate is approximately constant 

 in shape corresponding to a mean value Zc = 1.99 then the volume of the deformed plate is directly 

 proportional to the maximum deflection and from Figure H the total work done by the applied 

 pressure can then be calculated to give a value of 185,000foot lbs. This can be regarded as 

 divided between elastic strain energy, energy in permanent straining of unsupported target plate 

 area and work done in pull-in at the edges. From Table 1 and Table 2 it is seen that the 

 rreasured elastic recovery at the centre was only 0.05 inches so that even allowing for an 

 experimental error of O.l inches the work done in elastic defornation is only 1 - 2» of the total. 

 An estimate of t'le work done in pull-in at the edges is jiven by multiplying s h by the total 

 area of pull-in as given in Table «. As discussed previously s may be taken as varying 

 between 18 and 23-5 tons/square inch whence using a mean value of 21 tons/square inch we find 

 that the work done In pull-in at the edges is 25,000 foot lbs. which is about 25f of the total 

 work done. We are thus left with about 160,000 foot lbs. of work done in stretching the 

 original unsupported target plate area of 2U square feet again using s = 21 tons/square Inch on 

 the membrane assumption this work done corresponds to an increase of 370 square inches in the 

 original area. This estimated av. rage area extension of 10.74 corresponds to an average lineal 



strain 



