Theory of Voussoir Arches

Cover Theory of Voussoir Arches
Theory of Voussoir Arches
Wm William Cain
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In Fig. 16, e, c a represents an unsymmet- rical arch, or an arch acted on by forces not symmetrical, vertical or inclined.
Let P resultant of the external forces acting on the arch between a and c, not including the reaction R at a. Then on combining R=a& with P, we get the centre of pressure c on the joint cc^ Similarly we could proceed for other points, b 9 d, e, of the curve of resistance, corresponding to the resultant R=. O&7 acting through a in the direction ak.
90 Let a l b c l d e^ be
...a second curve, cor- responding to the reaction R' at a^ Now if S is such a force, acting towards the left, that when combined with R, it gives R' as a resultant, we can find a point c l9 on joint cc, of the new curve of resistance, either by combining R' with P as before, or by combining its components with P : thus call the resultant of R and P, T; this combined at I with S, gives a resultant which cuts joint c c^ at t\, a point lying between Id and c, Id being in the direction of s produced.
By this construction it is seen that the new curve of resistance, corresponding to the reaction R' at a', passes through b and d, the points where k I intersects the first curve of resistance; for other joints, as ee iy the new curve lies nearer kl than the first curve; since when S acts to the left, the combination of T, for any joint, with S, gives a resultant acting between T and S, which therefore cuts the joint nearer kl than the first center of pressure.


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