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224 STRENGTH OF MATERIALS.
When a post or column is long compared to its diameter,
its strength will decrease as the length is increased. Anyone
will, from every-day observation, know that a short post will
support with perfect safety a load which will break a long one.
Short columns break under crushing, but long ones break
under comparatively light load by the combined effect due to
both crushing and flexure. It is, therefore, evident that the
strength of long columns follows laws very different from those
which apply to short ones.
The form of the ends has also F|G# ^ .
great influence on the strength of a
column when under crushing and
deflective stress. ( See Fig. 1).
When both ends are round the
column has least strength; if one
end is round and one end flat it is
stronger, but if both ends are flat
and square with the center-line, it is
strongest. The proportions are ap-
proximately as 1, 2 and 3.
Eccentric loading on columns will also have a very destruct-
ive effect upon their strength.
Theoretical calculations regarding the strength of columns
and posts are difficult, and such empirical formulas as the
well-known Hodgkingson’s or Gordon’s formulas are usually re-
sorted to.
The Hodgkingson formulas for long columns having square
ends well fitted are
:
•<^4&y v&%%&> dm^/
n3-55
P = 99,000 X tL— for solid cast iron columns.
P — 99,000 X
/)3-55 d 3-55
L
for hollow cast iron columns.
P— 285,000 X D’-
for solid wrought iron columns.
P = Breaking load in pounds.
D = External diameter in inches.
d = Internal diameter in inches.
L = Length in feet.
When the breaking load as calculated by these formulas
exceeds one quarter of the crushing load of a short column of
the same metal area, the result must be corrected by the for-
mula:
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