326 DOCK ENGINEERING.
and that due to bending is
...................(50)
whence the total intensity of stress at L—
/=/+Z=Fg+y). . . . (51)
At the point M, on the other side of the neutral axis, we must give
the tensile stress, f", a negative value, and the equation becomes
/o“4-/:-i,(i-‘?^^
Graphie Représentation of Internal Stress. —Fig. 261 is a diagram showing
the combined effect of the stresses, f' and f", throughout the section, L M.
The quadrilatéral, K L MN, represents direct compression, and accordingly,
F
KL=/'=r
The two triangles, L O P, M O R, represent respectively the compres-
sive and tensile values of the bending moment; so
LP = and MR= --------
It will be noticed that, in the etched portion of the figure, the com-
pression and tension more or less neutralise one another, and that at the
point Q there is exact equilibrium. From Q to M tension predominates,
and compression from Q to L. Calling the distance O Q, q, we may obtain
its value by equating,
F Fxq
b =
whence
=b~x.....................(53)
When it is undesirable to allow a tensile stress in any part of the
section, as in the case of a curved gate built up of a series of vertical
voussoirs, evidently the section must be so arranged that
F Fa: (6 - p)
b= i’
whence
^ft^)......................<54>
This agrees with (53) when q= b- p, which is the condition for coinci-
dence of the points M and Q.
Limits of Stress.—It is manifest that there is a limiting value for the
stress intensity at L, beyond which it would be unsafe to compress the
leaf without risk of collapse. Let us call this limiting value y, and
consider its relationship to the resultant pressure.