305 
1912-13.] Plane Strain in a Wedge. 
almost endless discussion amongst engineers, and many theories of stress, 
generally different from the elastic theory, have been propounded. A point 
which has caused a great deal of recent discussion is the distribution of 
stress on the base of the dam. 
(17) Messrs Pearson and Atcherley * have obtained the stresses in a 
dam by assuming the normal pressure to be linear with a parabolic distri- 
bution of shear vanishing at front and flank on a horizontal basal section — 
i.e. such a distribution as obtains in a transverse section of a beam subjected 
to a bending moment and thrust. They have also taken a linear uniform 
distribution of shear as another case. They have shown that the former 
assumption leads to large tension on vertical sections near the tip of the 
tail in a certain form of dam examined, and the latter to sensible tension ; 
but, as the writer interprets their results, the solution given does not 
satisfy the conditions at either the front or flank of the dam. 
The late Sir Benjamin Baker, in discussing j* the stresses in a masonry 
dam, has thrown doubt on the existence of such large tensions as were 
found by Messrs Pearson and Atcherley. He refers to the great difficulty 
of making proper assumptions as to the stresses on the base, owing to the 
many disturbing influences, such as temperature and workmanship. The 
remarks J of Dr Brightmore, M.Inst.C.E., on the question of large tensions 
on vertical sections near the tip of the tail of a dam seem to the writer 
very much to the point. He considers that the parabolic distribution of 
shear at the base is not justified, at least for dams with a sloping back, and 
he puts forward the plea that the old assumptions should not be abandoned 
until it has been shown that some weakness existed in designs which had 
been elaborated on their basis. 
(18) Considerable light is thrown on the question of shear by consider- 
ing the stress functions of the present paper. For example, on the plane 
x — const, the stress function of — 
Equation (9) gives xy=— 2P . 
' ,, (13) ,, xg = P(r 2 - x 2 cos 2a)/r 2 m. 
„ (15) ,, xy = ~Px/'2 sin a . 
The final of these equations gives uniform shear on the section, and it 
may easily be shown that if the loading is still further concentrated towards 
the section, up to a limit which depends on a, the shear still remains 
nearly uniform. Again, if the section x — const, is taken perpendicular to 
* Some Disregarded Points in the Stability of Masonry Dams , London, 1904 (Dulau & Co.). 
t Proc. Inst. Civil Eng., vol. clxii. p. 120. 
I Ibid., p. 112. 
VOL. XXXIII. 
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