176
DOCK ENGINEERING.
will assume some intermediate trapezoidal form. For instance, let G
(fig. 96) be the point of application of the thrust : the corresponding stress
area will be H A B N. The line H N is defined by the necessity of passing
through the point F, and by the following condition:
MN=—j-,
in which a= AK, is the mean intensity of stress, æ= G E, is the, eccentricity
of the thrust, and Z=A B, is the length
H
Fig. 97.
weight w, its form is altered to
of gravity, G2, is determined by
of the base.
The demonstration of this condition
depends upon a simple theorem in
mechanics.
KABM (fig. 97) being any body
whose weight is M^ and centre of
gravity G1; if by the transposition of
any part of its volume MON with
the outline H ABN, then the new centre
the proportion
G., G, w
" W’
(34)
and the horizontal projections of G2 Gx and g^ gx follow the same law
Now, let us apply this result to the pressure diagram. Call MN y.
In fi" 96 H K F and F M N are equal triangles, and the horizontal distance
between their respective centres of gravity is, clearly, %l. Then, in the
foregoing equation (34), writing w^ and W=»Z, we have
3® _
21 ial
y=^, .................(35)
which defines the position of the point N corresponding to any assigned
value of æ. .
A table giving the resistance to compression of various kinds of stone
will be found in Chapter iv., and the safe loads on foundations are given
3 The wall may fail by shearing honzontally along some bed joint.
The amount of shear is N R (fig. 95), the horizontal component of the
resultant thrust. The resistance of masonry joints to actual shearing,
which depends largely upon their cohesion, is usually abandoned in favour
of their resistance to sliding, which depends on friction alone, and, having
a lower value, affords a margin of safety to cover defects in workmanship.
In any case this is all the duty which can be expected from the base joint
between the wall and its foundation. The amount of resistance to sliding
is CN, the vertical component in fig. 95, multiplied by the tangent of