The Locomotive - Lighthouse Survival Blog

84 THE LOCOMOTIVE. [June,
present case the stretch due to the force S l in the outer shell is given by the following
equation :
3.1416 A/?, = 3.1416i?j x S x h, or
x
AR =R S k.
1 1 l
In the same way we find that the stretch of the inner sheet is
A 7? 2 = B. 2 SJ:
Passing now to the stay-bolt, we note that its original length (neglecting the ends
that are within the sheets) is li — R , and that the tension to which it is subjected, per
1 2
square inch of its sectional area, is T. Hence, if we assume that the material of which
the stay-bolt is made has substantially the same resistance to stretching as the material
of the sheets, we shall find that the increase in the length of the stay-bolt is
Fig. 5.
—
,..,_
Illustrating the Stretch
op the Shells.
(R 1 — B!l)Tk
But since the stay-bolt is secured to the
sheets, its stretch must be precisely
equal to A if, — A R .
2 as will be seen
upon examining the diagram, Fig. 5.
Hence
(/?! — R ) 2 Tk= Ai?!— Ai? -
2
But we have already obtained the values
of AR t and AR 2 , and
(i?,-i? 2
) T=R S - R S .
l l 2 2
if we substitute
these in the equation last given, we have
(./?, — R%) -T k = Z?j Si k— R 2 S 2 kj
or, dividing through by k,
Substituting in this equation the values of 8 t and S 2 already found, we have
{R X -R
2)T t 1 A t., A
(PA — Ta) « " (TaR — t :
and upon solving this equation for T we have
PAR.) R s .
PA(t 2 2V + *i -K 2
3 )
T =
a ifj (*, i?x + t
t Rs ) + ht s A (i? — x R2 )
which is the formula given for T in the earlier article.
These formulae may be tested for special cases, if their trustworthiness is doubted.
Thus if we make a = ,
we see that T remains finite, and hence the total pull on the
stay-bolt (Ta) vanishes, as it should. Making a — in the formulas for S x and S 2 , we
find (since Ta — 0) that
PR —PR X
2
Si = — f— and S = s 1—
which are correct ,for this case. (It will be observed that S 2 , being negative, is now
xomj)ressive stress.)
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