384
DOCK ENGINEERING.
which involves a quadratic in p. This formula expresses the relationship
existing between the apparent stress, p, due to the load and the maximum
stress, y, on the concave side. If, then, we insert the ultimate compressive
stress of the material in place of y and solve the equation, we find the
breaking stress, p, of the column.
It has been assumed that the ends of the column are free to move.
In dealing with a column in which both ends are fixed, the length of an
equivalent round-ended column may be taken at three-fifths of the actual
length.
The ultimate compressive stress in various materials may be taken as
follows:—
Timber, . . . . 2 to 4 tons per square inch.
Wrought iron, . . 16 tons per square inch.
Mild steel, . .. 30 „ „
Cast iron, . . . 40 ,, „
A formula very commonly used for the determination of the compressive
strength of long struts, is that devised by Professor Lewis Gordon, which,
using the same rotation as before, may be expressed thus—
P-^.........................................(80)
The fraction ^ expresses the ratio of the length of the column to its
diameter, or its least dimension in cross-section. The values of a are given
in the annexed table.
Results obtained by this formula agree fairly closely with those given by
Prof. Fidler’s method.
TABLE XXX.
Material. Cross Section. Values of a.
Both Ends Rounded. Both Ends Fixed. One End Rounded, One Fixed.
Timber, . Rectangular or circular, 777 1 IH rät
Wrought iron, Rectangular, . . .1
Circular (solid or hollow), .) ÎW 00 rAf
LT+ □ ÛI LJ . 7ÏÏÏÏ «0 70
Cast iron, Circular (solid), . rit Tit 1 ro
,, (hollow), 1 777 ■80 70
», • Rectangular, ilt tÅÖ 7T<Tr
Cross-shaped, ■so KO 3 70
Mild steel, Circular (solid), . TSO urt 777
Rectangular (solid), m ÎTSS ^Tr