EXAMPLES TO THE FIRST SERIES. 
xxi 
To find the Scantlings of Red Pine sufficient to carry a given weight 
SUSPENDED FROM THE MIDDLE, and to have with that weight a given 
deflection. 
Example 6. — Required the Scantlings of Red Pine sufficient to carry 
7i tons or 150 cwts. suspended from the middle, and deflect with that 
weight ^ of an inch. The breaking weight to be not less than 
4X150=600 cwts. 
W = 7-5 tons. D = ^L. 
W 7-5 
-p7 = — = 75 tons suspended from the middle. 
The scantlings are given by Table XXV. 
If the length clear of the supports be 7 feet, the Scantlings are, 
12-54X7; 1200X8; 11-53X9; 11-14X10; &c. 
The first five scantlings in the table are rejected, because the breaking 
weight of each is less than 600 cwts. 
The breaking weight suspended from the middle of Red Pine 7 feet 
long 12-54 X7, is 5-576 X 112-81=629 cwts ; the scantlings are 12| X7 
12X8, 1UX9, &c. 
Example 7.— Required the Scantlings of Red Pine 14 feet lono- suf- 
ficient to carry 1260 lbs. or 11-25 cwts. or -5625 tons suspended" from 
the middle, and deflect of an inch. 
W = 1260 lbs. ; or 1 1-25 cwts. ; or -5625 tons ; as the case may be. 
— To- 
= 5400 lbs. \ 
= 48-21 cwts. I suspended from the middle. 
= 2-41 tons , 
The ScantHngs are given by Table X. viz. : — 
. . 12-03X2; ll-57X2i; 11-16X2^; 10-51X3; 9-98X3^; 9-54X4; 
!)18X4i; 8-86X5; 8-34X6; 7-92X7; 7-58X8; 7-28X9; 7-03X10; 
(i-SlXll; 6-62X12. 
Deflection of each of the scantlings with the above weights, of an 
inch. 
w 
1260 
1260 X 
30 
d" 
7 
IS 
~ 7 
w 
11-25 
11-25 X 
30 
1) 
~ is 
~ 7 
w 
-5625 
■5625 X 
30 
d" 
7 
7 
