The Locomotive - Lighthouse Survival Blog

82 THE LOCOMOTIVE. [June,
a — net sectional area of each stay-bolt.
P=pressure of steam, per square inch.
It should be understood that 8 t and S 2 do not represent the whole stresses on the
shells. They stand for the excesses of the stresses in the curved shell, over and above
what they would be if the stayed surfaces were flat.
We have first to note that the area of the inner shell to which one stay-bolt is
allotted is less than the corresponding area on the outer shell in the proportion of R 2 to
/?,, because the vertical spacing of the stay-bolts is the same on both shells, while the
horizontal spacing (since the bolts are all radial) will be proportional to the radii of the
shells. Confining our attention to the unit consisting of one stay-bolt and the portions
of the inner and outer shells which this one stay-bolt is supposed to support, we see
that the steam pressure against the outer part is PA, and the pressure against the inner
.
part is
PAR, _
, , , .
—=-— - (because the area of the inner part is
it,
Fig. 3. — Thk Outer Sheet.
Fig. 4.
—
The Inner Sheet.
ARa " as has just been said). Consider, now,
the
*i
outer end of one stay-bolt, together with the
attached unit of plate, as shown in Fig. 3. There
is an outward steam pressure of PA pounds
against the unit of plate, and an inward pull of
Tn pounds exerted by the stay-bolt on the same
unit of plate. Hence the resultant force, acting
outward on the unit of plate, is PA— Ta. The
stay-bolts being supposed to be spaced as closely
together as is common in good practice, we may
consider that the stresses produced in the outer
shell by a force of PA— Ta pounds acting on each
unit, will be substantially the same as would be
produced if we cut away the stay bolts altogether,
and subjected the outer shell to a uniform
steam pressure just great enough to produce a total pressure of PA— Ta pounds on
every unit of the shell containing A square inches of area. That is, we may consider
the stresses on the outer shell to be due to a uniform steam pressure of P
Ta
A pounds
per square inch. The radius of the outer shell being 7?,, the usual rule for finding the
stress in such a shell when the steam pressure is known, gives us
*«, = (*-?)*.
which is easily seen to be equivalent to
(PA — Ta)R i
Si
t
t A
which is the formula given for £, in the original article. (See The Locomotive,
March, 1892, page 34.)
Turning now to the inner shell, and noting that ea