The Locomotive - Lighthouse Survival Blog

116 THE LOCOMOTIVE. [August,
Turning now to the possible failure of the pin by bending, we have to observe
that the intensity of the bending stress on the pin (before the pin becomes deformed,
at any rate,) will depend to a considerable extent upon how well the pin fits the lug
and the brace-jaws, and upon what parts of the pin are in full contact with the
brace-jaws and the lug. For example, it is possible that, owing to imperfect workmanship,
the pin may bear as shown in Fig. 3, touching the lug only at its middle
point, and touching the brace-jaws only at their outer edges. The bending stresses
will be greater with the load falling upon the pin in this way than they would be
with any other distribution of the load. We shall not go into the theory of the
strains in a pin loaded like this, but it will be sufficient to say that they are determined
by considering the pin as a beam, supported at both ends and loaded in the
middle. If I is the length of the pin between the points shown in Fig. 3, and W
is the total pull on the brace, and S is the tensile strength of the material of the pin, in
pounds per square inch, and d is the diameter of a pin that would just be strained to
the breaking point by the pull IF on the body of the brace, then the theory of the beam
shows that we have the relation
8 Wl -^3.1416 S
which gives (/, when we know IF, I, and S. If S stands for the safe working stress on
the material of the pin, then the foregoing formula gives the diameter that the pin
should have, in order to safely resist the bending stress that would be thrown upon it
by the pull on the brace. It will be understood that this formula does not apply to a
brace pin unless the pin is quite long, so that the distances between the points of applica-
tion of the forces upon the pin are large in comparison with the diameter of the pin. In
selecting the proper value for *S to obtain the safe working diameter of the pin, we are
confronted by the same difficulty that we meet with in calculating the strength of hooks.
That is, if we assign to S a value, such as would be admissible for metal to be used in
the shell of the boiler, we find that the foregoing formula gives a pin diameter that is
materially larger than good practice has shown to be sufficient. For wrought-iron
beams subjected to a dead load, we may safely take S = 14,000; and for a structure
like a brace pin, which is very short in comparison with its thickness, we may take
S = 20,000. With this latter value for *S', the formula is easily reduced to
VWT
7 a =
20 '
where d and I are measured in inches, and IF is the total load, in pounds, on the main
body of the brace.
Referring now to Fig. 1, we see that if the workmanship of the structure there
represented were imperfect, so that the lug and the fork bore upon the pin as repre-
sented in Fig. 3, then we should have Z = 2% inches. The diameter of the body of the
brace being 1% inches, it is easily found that the safe working stress on this part of
the brace is 11,140 pounds, allowing 7,500 pounds per square inch of section, which is
all that is allowed, in conservative practice, even on braces made of open hearth steel.
AVe have then to substitute this value for IF in our formula, and we have
7 ^11.140 X 2f ^3n.«:s.1 31.29 .
O- — = — "
nft _ = 1.00 in.
20 20 20
When the workmanship on such a structure as is shown in Fig. 1 is good, our
"bending formula" will give a pin diameter which is somewhat larger than good prac-