299 
1912-13.] Plane Strain in a Wedge. 
Suppose ABCD (fig. 4) to represent a dam subjected to water pressure 
to a height ED, 0 being the point of intersection of AD and BC, and 
AB taken as horizontal. 
Let OA = a, OE = b. 
The stresses can be written down for pressure P r over OD and uniform 
tension P b over OD, and also for the weight of ODC. We have thus 
on the face OD pressure P (r — b) over ED and tension P (b — r) over OE. 
Introduce at point X, where OX — 6/3, a force = P6 2 /2 acting normal to 
0 
Fig 4 
OD and into the wedge, and at the centre of gravity of OAB introduce 
a force equal to the weight of OAB reversed, say W'. The force P6 2 /2 
at X and W' will form a set of forces in equilibrium with the tension on 
OE and the actual weight of OAB, and by the principle of equipollent 
loads the stresses due to this system are negligible at all points well 
outside area OAB, and thus the solution for the whole system of forces 
will be equivalent to the solution for pressure P (r — b) over ED and the 
weight of ABCD only. 
The force P6 2 /2 and W' can be transferred to O and suitable moments 
introduced, and the stresses due to these forces and moments can be 
written down by the aid of equations (8), (10), and (12). 
