Section III, 1922 [217] Trans. R.S.C. 



On the Depression of the Centre of a Thin Circular Disc of Steel under 



Normal Pressure 



By Stanley Smith, M.A., B.Sc. 



Presented by Professor R. W. Boyle, F. R.S.C. 



(Read May Meeting, 1922) 



The theory of the bending of a thin circular disc by the application 

 of a normal pressure leads, in the important case of a maximum 

 depression of the centre comparable with the thickness of the disc, 

 to a series of differential equations which are not directly soluble. 



In connection with some work the author is carrying out for the 

 Associate Air Research Committee of Canada on the bending of 

 aneroid and barograph diaphragms an attempt was made to find some 

 empirical relation between the various quantities involved in the 

 bending of a flat circular disc of steel. The disc, which was made of 

 stainless steel kindly provided by Messrs. Thos. Firth, Ltd., was of 

 fixed diameter, 6.14 cms., and of uniform thickness, .4 mm. It was 

 first supported, edge-free, on a flat annular flange (concentric with 

 the disc) of width 4 mms., the inside diameter of which was 4 cms. 

 The supporting flange formed part of a chamber which, when the 

 disc was in position, could be exhausted to any given pressure below 

 atmospheric pressure, so that the disc could be subjected to pressure 

 differences between its faces varying from zero to the barometric 

 pressure, the area of the plate exposed to this pressure difference, p, 

 being in the first instance a circle of diameter 4 centimetres. The 

 values of p were measured on a U-tube mercury manometer by means 

 of a cathetometer reading to . 1 mm. The inside diameter of the 

 manometer tubes was 1.85 cms. so that surface tension effects were 

 negligible enabling p to be measured with a maximum possible error of 

 .4 mm. In order to measure the depression, w, of the centre of the 

 disc a light aluminium pillar, A (Fig. 1) was attached by shellac to the 

 centre of the top surface of the disc and perpendicular to it. To A 

 was attached a small round brass rod, B (Fig. 2), of length 8 . 5 mm. and 

 diameter 3 mms., which operated the forked lever L by means of 

 adjustable steel pivots E and F working in jewelled bearings Cand-Dset 

 in B. L was fixed rigidly to a brass rod K of length 9 . 8 cms. and dia- 

 meter 3 mms., which could rotate about the steel pivots G and H 

 working in jewelled bearings M and N set in K. A small concave 



