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312 MECHANICS.
Example.
Find the force required to act on a lever 30 inches long (see
Fig. 18) in order to lift the load W, which is 8000 pounds ? The
screw is ^-inch pitch and 1^-inch middle radius : coefficient of
friction, 0.15.
Solution :
F — 8000 X °- 5 + ° 15 x 3.1416 X 2.5 1.25
2.5 X 3.1416 — 0.15 X 0.5
X 30
F= 8000 X i’
6781
X 0.0416 =. 89.6 pounds.
7.779
F
When the screw has V thread, the frictional resistance will
be increased as -^ of the angle a (see Fig. 18), or equal to
secant of half the angle of the thread. For United States
standard screws the angle of thread is 60°, half the angle is 30°,
and secant of 30° is 1.1547, and the formula will, for United
States standard thread, become :
d- — \.\bfP R
All the letters having the same meaning as in the formulas
for the square-threaded screws.
The following table is calculated for square-threaded screws,
the pitch of the screw being double that of the United States
standard screw of same diameter. The depth of the thread is
equal to its width. We see no good reason why the depth of a
square-threaded screw should be, as frequently given in tech-
nical books, \% of the pitch of the screw ; ||, as given in pre-
vious tables, is more convenient, and also gives a little more
wearing surface to the thread. The use of this table is so
plain that it needs very little explanation. In the fourth column
is the area of the outside diameter of the screw. In the fifth
column, the sectional area of the screw at the bottom of the
thread, which may be used in calculating the tensile and crush-
ing strength of the screw. Subtracting the fifth column
from the fourth gives the sixth column, which is the projected
area of one thread; this may be used in calculating the allow-
able pressure on the thread, etc. The fourteenth column gives
the tangential force which is required to act with a leverage of
one foot in order to lift one pound by the screw if there was no
friction. The fifteenth column gives the total tangential force
required per pound of load when both load and friction are
included. The sixteenth column gives the difference between
the fourteenth and the fifteenth columns, and is the tangential
force absorbed by friction alone. The coefficient of friction in
both columns is assumed as 0.16. The last four columns in
the table give the load or axial pressure which may be allowed
on the screw corresponding to 200, 400, 600 and 1000 pounds
pressure per square inch of projected area of screw thread
when the length of the nut is twice the diameter of the screw.
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