HORIZONTAL IKON GIRDERS.
329
Typical Examples—1. Horizontal Rectangular Rib.—In this case p = 9;
b3
^ ~ \2’when the depth is unity ; and F is the total stress, divided by the
number of ribs.
The value for L P (fig. 261) is
Fïÿ 6Fæ
“T =
and the neutral axis of a rectangular beatn being assumed to coincide
with its horizontal axis of symmetry, the same value is equally applicable
to M R.
When the resultant passes through the point L—i.e., when æ= $, the
F 3F 4F
compression at L becomes — + —^- = -^-, or exactly four times the
intensity which it has when the resultant passes through the point O.
2. Vertical Voussoirs.—Here it is necessary to avoid tension in any
part of the joints, no duty being expected from the connecting bolts in
this respect.
The point Q is given from (53) by
J ____b*
q ~ n~vrx
and when q is made equal to which, as we have already demonstrated, is
the limit consistent with the absence of tension, we have
bL
2 - 12æ’
so that
b
X ~ 6’
which signifies that the line of pressures must lie within the middle third
of the thickness of the gate.
3. Horizontal Iron Girders.—Assuming the web horizontal and the
flanges vertical, so that the plane of the resultant coincides with that of
the web, supposed indefinitely thin, no difference exists between the
formulæ in this case and those for rectangular ribs, beyond the complica-
tion introduced by the somewhat involved expressions for the value of the
moment of inertia.
With flanges of equal area, symmetrically disposed about the centre of
gravity of the section, the value of I may be conveniently expressed as the
difference between the moments of inertia of two rectangles :—
1 ” 12 12’
• (56)
where d± and bt are the dimensions of the combined side recesses of the
irder.