EXAMPLES TO THE THIRD SERIES. 
xxxix 
EXAMPLES TO THE ANNEXED TABLE. 
The Depth, is the greatest side ; the Breadth, the least side ; with- 
out reference to the position of the scantling. 
In the direction of the depth, the least pressure divided by the 
greatest, gives the pressure in the direction of the breadth. 
Multiply together 
The length in feet ; 
The breaking weight in cwts. ; and 
The factor for the pressure. 
If the pressure be uniform, the Scantling is found by Column XI. 
If the pressure be in the middle, the Scantling is found by Col. XII. 
Example 22. — Required the Scanthng of a Brest-summer to support 
a Shed Roof, fixed as in Fig. 5, {plate, p. xxxiii) upon the following 
Data. 
Length of the Brest-summer Q, clear of the supports, 20 feet. 
Weight of the Roof AC, 20 X 2-5 = 50 cwts. 
Pressure upon Q, uniform. 
Breaking weight of Q, 8 times the pressure upon Q. 
Centre of gravity G, in the middle of AC ; BC = i AB. 
Since BC = J AB ; Ec (= 1"00), = ca,= pressure p, = pressure q ; 
therefore 
The pressures p and q are each equal to the weight of the roof; 
P 
— - z= 1-00; = pressure for the breadth (Col. X.) 
Length 20 feet; Breaking weight 50 X 8 = 400 cwts.; Factor L 
20 X 400 X 1 = 8000, the tabular number. Pressure unifoim. 
Scantling, Cols. X. and I., 10 X 10. (See also page 71.) 
By Table IT. (p. 130), a Red Pine brest-summer 10 inches deep 
and 20 feet long, uniformly loaded with one-eighth of the breaking 
weight, deflects each way ^ ^' ^ = -657 of an inch. 
8 
If the deflections be too great, the scantling for any other deflection 
may be found by Table VI. in the Third Series of Tables, thus :— 
Let the deflection each way of the brest-summer be I of an inch ; 
P = 20 X 2-5 = 50 cwts. ; D = i. 
P 50 
^ = — = 50 X4i=: 200 cwts. Pressure uniform. 
By Col. VIIL (p. 119), -^ = 223'21 cwts. Scantling 13-09 X 13-09. 
