LOCI 0F CENTRES OF GRAVITY.
177
the angle of repose-^., of the steepest inclination at which a block
tlæ substance in question will remain stationary. This frictional
résistance is quite independent of the area of the surfaces in contact but
its intensity at any point corresponds to the intensity of pressure at the
same point. The following are values for the tangent of the angle ofrepose
of several surfaces, usually designated the coefficient of friction P
Dry masonry and brickwork, 0-6 to 0’7.
Masonry and brickwork, with wet niortar, 0-47.
Masonry and brickwork, with slightly damp niortar, 0-74.
Before applying the foregoing principles to a definite example it may
as well to explain one or two methods adopted for finding the centre
gravity ot the section of a dock or other retaining wall
Loci of Centres of Gravity.-The centre of gravity of a square
rectangle lies at the intersection of the diagonals (0, fig. 98).
The centre of gravity of a triangle is at two-thirds of the len^th of
median measured from the apex (0, fig. 99).
The centre of gravity of a trapezoid is at a point 0, fig. 100, on the line
be
of
or
A B, bisecting the parallel sides such that £A _ «+26
V 1 , AB ~ T^Vé)’ where a
and 6 are the lengths of the sides bisected at A and B respectively.
Fig. 98.
Fig. 99.
B
Fig. 100.
points
AG is
Let A CDB iom , 7 T"* °f a slmPle S^phical construction,
p s’ 0 J be a traPezoid- Bisect A B and CD at the
and i respectively, and join EF. Produce BA to G, so that
AB
J
Fig. 102.
equal to CD. Produce C D to H, so that D H is equal to A B. Join G H
Ihe intersection, 0, of the lines E F and G H, is the required centre of
gravity.
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