Given the diameter _d_ of a steel shaft, and the number of revolutions
per minute _n_, to find the horse-power from:—
H.P. = _d_^3 × _n_ × 0·02.
Set 1 on C to _d_ on D, and bring cursor to _d_ on B. Bring 50 on B to
cursor, and over number of revolutions on B read H.P. on A.
EX.—Find horse-power transmitted by a 3 in. steel shaft at 110
revolutions per minute.
Set 1 on C to 3 on D, and bring cursor to 3 on B. Bring 50 on B to
cursor, and over 110 on B read 59·4 horse-power on A.
Given the horse-power to be transmitted and the number of revolutions of
a steel shaft, to find the diameter.
Set revolutions on B to horse-power on A, and bring cursor to 50 on B.
Then move the slide until the same number is found on B under the cursor
that is simultaneously found on D under the index of C. This number is
the diameter required.
To find the deflection _k_ in inches, of a round steel shaft of diameter
_d_, under a uniformly distributed load in lb. _w_, and supported by
bearings, the centres of which are _l_ feet apart (_k_ = (_w_
_l_^3)/(78,000_d_^4)).
Modifying the form of this expression slightly, we proceed as
follows:—Set _d_ on C to _l_ on D, and bring the cursor to the same
number on B that is found on D under the index of C. Bring _d_ on B to
cursor, cursor to _w_ on B, 78,800 on B to cursor, and read deflection
on A over index of B.
EX.—Find the deflection in inches of a round steel shaft 3½in.
diameter, carrying a uniformly distributed load of 3200 lb., the
distance apart of the centres of support being 9 ft.
Set 3·5 on C to 9 on D, and read 2·57 on D, under the L.H. index of
C. Set cursor to 2·57 on B, and bring 3·5 on B to cursor, cursor to
3200 on B, 78,000 on B to cursor, and over L.H. index of B read
0·199 in., the required deflection on A.
To find the diameter of a shaft subject to twisting only, given the
twisting moment in inch-lb. and the allowable stress in lb. per square
inch.
Set the stress in lb. per square inch on B to the twisting moment in
inch-lb. on A, and bring cursor to 5·1 on B. Then move the slide until
the same number is found on B under the cursor that is simultaneously
found on D under the index of C.
EX.—A steel shaft is subjected to a twisting moment of 2,700,000
inch-lb. Determine the diameter if the allowable stress is taken at
9000 lb. per square inch.
Set 9000 on B to 2,700,000 on A, and bring the cursor to 5·1 on B.
Moving the slide to the left, it is found that when 11·51 on the
R.H. scale of B is under the cursor, the L.H. index of C is opposite
11·51 on D. This, then, is the required diameter of the shaft.
(N.B.—The rules for the scales to be used in finding the cube root (page
42) must be carefully observed in working these examples.)