January 2, 1908J 



NA TURE 



209 



T 



THE STRESSES IN MASONRY DAMS. 



HE memoir ' referred to at the foot of this column 

 embodies the results of further work, mainly experi- 

 mental, on the design of masonry dams, and is a continu- 

 ation of the work of Atcherley and Pearson described in 

 an earlier memoir of the same series.' In the latter paper 

 the authors discussed the imperfections of the present 

 tlieory of masonry dams, in which the normal stress on 

 horizontal sections is assumed to be linear, and nowhere 

 tensile. This leads to the well-known condition of 

 stability, that the centre of pressure on horizontal sections 

 must fall within the middle-third, and the linearity of 

 normal stress involves a parabolic distribution of shearing 

 stress. Atcherley and Pearson criticised the action of 

 engineers in ignoring the shear stress distribution, and in 

 merely considering frictional stability as the criterion of 

 safety as regards horizontal sliding. They demonstrated 

 the existence of tension on some vertical sections of e.xist- 

 ing dams using the common theory, and showed that the 

 jDul-third rule was not followed consistently throughout 

 ihc- design. 



I In the memoir now under review, the authors point out 



the conditions for a true beam problem, viz. : — (i) the 

 dimensions of cross-section are small compared with the 

 length and with the radius of curva- 

 ture ; (2) true cross-sections, i.e. sec- 

 tions perpendicular to the line of 

 centroids, e.xist. .'\s these conditions 

 1 are not rigidly fulfilled in a masonry 



dam, the authors refuse to accept any 

 results based on a simple beam 

 analysis, and proceed to an endeavour 

 to throw experimental light on the 

 current mid-third theory, which they 

 summarise as follows : — 



(1) The dam shall not be subjected 

 to tensile stresses. 



(2) This involves the line of resist- 

 ance lying in the middle-third of hori- 

 zontal sections. 



(3) Condition (2) has meaning solely 

 on the assumption that the normal 



I stresses are linear. 



(4) Linearity of normal stress in- 

 volves the distribution of shearini; 

 ' stress being parabolic. 



The case of an infinitely long dam. 

 or a dam of finite length abutting 

 against rigid supports, is considered 

 mathematically. It is assumed to be 

 straight, to have a plane face at any 

 batter, and a flank curved in any 

 manner. Regarding it as a homo- 

 geneous isotropic material, the laws of 

 elasticity lead to a differential expression of a stress func- 

 tion V, which function has to fit the boundary conditions 

 of the dam, viz.: — (a) on face where shear = o; normal 

 stress = water pressure; (b) on top and flank, where 

 shear = 0; normal stress = o; (c) on base, where the shear 

 and normal stresses have their actual values. It is stated 

 that (<:) is generallv ignored, and its existence prevents 

 a mathematical solution being obtained. 



The memoir proceeds : — " The engineer using the middle- 

 third rule, and thus assuming the hypothesis of linear 

 normal stress, has actually (the italics are ours) assumed 

 the stresses over the base. Consciously or unconsciously 

 he has asserted that the pressure is linear and the shear 

 parabolic." The engineer has perhaps some excuse for 

 his assumption, as a mathematical difficulty cannot stand 

 in the way of building a dam. In many other cases, say 

 that of a large masonry arch, in the light of purely 

 theoretical considerations, the action of the engineer, 

 usually conscious we imagine, may savour a little of fools 

 stepping in where angels fear to tread. In saying this, 

 1 "An Fxnerlmental Study of the Stresses in Masonry- Dams." Bv Karl 

 Pearson. F.R S., and A. F. Campbell Pollard, assisted by C. W. Wheen 

 and \,. F. Richardson. Drapers' Company Research Memoirs. Technical 

 Series v. Price 7S 



- " On Some Di regarded Points in the Stability of Masonry Pams." By 

 L.W. Atcherley and Karl Peirson, F.R.S. Pp. 44-l-plates. (London: Dulau 

 and Co., 1907.) Price 3s. M. 



we would in no sense wish to convey tne nnpresaion that 

 the authors hold engineers responsible for what they re- 

 gard as the uncertainty in the design of dams. Indeed, 

 they expressly disclaim any such intention, frankly recog- 

 nismg the difficulties of the problem. Their results are 

 put forward as preliminary only to further investigation, 

 which they suggest might possibly be undertaken by some 

 such body as the Institution of Civil Engineers. Their 

 investigation shows that the boundary conditions are best 

 fitted by a triangular dam, but that the conditions cannot 

 hold for rectangular or trapezoidal sections. To quote 

 from the memoir : — " Purely mathematical researches 

 suggest no great hope of real advance in what is notwith- 

 standing an urgent practical problem. It does not seem 

 probable that they would provide any but the roughest 

 approximations to the actual conditions." The method by 

 which engineers escape from the horns of the mathematical 

 dilemma is viewed with some misgivings, and the authors 

 seek, in experimental work, a fold in which both engineers 

 and mathematicians may dwell together in harmony. 



Experimental Work. 



The object of the work was to determine the actual 

 straining actions in model dams by direct measurement. 



NO. 1992, VOL. 7'j'] 



Fig. I. — Vyrnwy-type dam, mod 



and, at the suggestion of the late Sir Benjamin Baker, 

 jelly was adopted as the material of the dams. After 

 much experiment suitable cream-white material made of 

 gelatin, glycerin, and colouring matter was obtained. 

 The size of models was as follows : — base, 45 cm. ; height, 

 35 cm. ; breadth, 9 cm. to 10 cm. ; substratum, 45 cm. ; 

 by 9 cm. or 10 cm. deep. Fig. i shows a typical model 

 with lines ruled on the face for the distortion measure- 

 ments. After much trouble in satisfactorily fixing the 

 models to a rigid wooden base, copper gauze was nailed 

 to the wood and heated. The model was then placed on 

 it, and on cooling was bonded securely to the gauze. 



Noting the experimental difficulty of attempting to use 

 a dam with rigid, parallel ends, the authors proceed to 

 a mathematical investigation of the stresses in a sheet of 

 elastic material with free sides, i.e. a vertical plate with 

 fixed base, no stress on sides, and subjected to a normal 

 stress on part of its edge only. They conclude that with 

 certain limitations there is an identity of stress equations, 

 and that an experimental plate dam without side supports 

 can be used to test the distribution of horizontal shear, by 

 measurement of the distortion of lines ruled on its sides. 

 If the distribution is not parabolic the normal stresses au 

 not linear. The difiiculty of measuring the local values 

 of the stretch and squeeze of the jelly prevented any direct 

 estimate of normal stress being obtained, and only the 



