330
DOCK ENGINEERING.
The intensity of stress due to direct compression is
.F F
7^^rf-^xi- V • • • (57)
and the maximum stress due to the bending moment is
„ F^ 6FÖCC
7 == db^^ - - - (58)
whence, combining, we obtain the maximum and minimum intensities in
the outer and inner flanges respectively,
{<3^^*j/^
Another expression for the value of I, which neglects the thickness of
the flanges and assumes their areas concentrated on a centre line in each
case situated a distance, d, apart, with k as the area of the web, is
k
If only an approximation be required, — may be ignored as very
small and
l-^ (61)
When the cross-section of the girder is not symmetrical about the
centre of gravity, the position of the latter may be obtained by dividing the
depth of the girder inversely as the ratio of the flange areas. Thus, if a± be
the area of the smaller flange and a2 that of the larger, the distance of the
centre of gravity from the larger flange will be
—il— b,
a± + a2
where b is the horizontal dimension of the girder. Or it may be obtained
graphically, thus :—Let A B (fig. 264) represent the web of the girder as a
single line ; set off horizontally A C = area of flange B, and B D = area of
flange A. Join OD, and O is the required centre of gravity.
Using the notation of (62) a fairly approximate value for I is
2
1 =6^
b2
^2
tt| + CL.->
+ a2 b2
k b2
(63)
For built girders, the moment of inertia will have to be calculated in
detail from its component parts.
Gates with Vertical Co-planar Girders.—For straight or flat gates with
discontinuous horizontal members, a different method of stress investigation
is necessary. The system of co-planar vertical girders which derive no
support from each other, such as contiguous vertical voussoirs do, involves,
as has already been poiuted out, the use of two horizontal transoms, one at
the head and the other at the sill, to afford thern the necessary support.