xl 
EXAMPLES TO THE THIRD SERIES. 
Example 23. — Fig. 5. — Required the Scantling of the Brest-summer 
Q, 20 feet long, upon the following 
Data. 
Weight of the raking beam AC, resting upon the middle of Q, 50 cwts.; 
Breaking weight of Q, 10 times the pressure upon Q. 
Let EC = i AB, then {Ex. 22) pressure p = q = weight of AC. 
Length 20 feet ; Breaking weight of Q, 10 X 50 = 500 cwts.; 
Factor for the pressure, TOO. 
20 X 500 X 1-00 = 10000, pressure in the middle. 
Col. XII. p. xxxviii., opposite 10976, the Scantling is 14 X 14. 
Deflection each way (p. 130), t^L^l x -8 = -j^ of an inch. 
Example 2L—Fig. 5.— Let BC = AB. Data in other respects as in 
Example 22. Required the Scantling of Q. 
Since BC = AB, we have ca = i Ec; or p = 1-00, q = -50. 
Least pressure ^ J_ ^ ^= -50 ; the breadth is found by Col. VII. 
Greatest pressure p I'OO 
Length 20 feet ; Breaking weight 50 X8=400 cwts. ; Factor V°- 
20 X 400 X y = 1 1428, the tabular number. Pressure uniform. 
Opposite 12167, Col. XI., the scantling is lU X 8-05. 
Deflection each way, (p. 130), i^lii^ = -571 of an inch. 
If the pressure 50 cwts. be in the middle of Q, — 
Opposite 12194, Col. XII., the scantling is 14i X 10-15. 
4 X "907 
Deflection each way (p. 130), — — X -8 = -362 of an inch. 
By the Table p. xxxviii., may be found the scantlings of beams, 
&c., pressed by one force only, such as beams for warehouse 
floors, &c., the sides of which shall be in any usual proportion, 
and sufficient to carry any given portion of the breaking weight. 
If the beams be square, the scantlings are found by Col. X. If 
in the proportion of 10 to 8,. by Col. VIII. ; and so on. 
Joists continued over beams, beams and brest-summers over columns, rafters oyer purlins, 
purlins over principals, &c., in all such cases where the ends are continued and fixed, the 
strength of the intermediate lengths is increased one half. In reducing the scantlings 
accordingly, it will be requisite to bear in mind the maxim, that. The strength of a floor 
OR ANY SYSTEM OF FRAMING, DOES NOT EXCEED THAT OF THE WEAKEST PART. 
Note, on the Table No. 3 in Tredgold's Elementary Principles of Carpentry. 
Let the Scantlings for Single Joisting, &c., in the Table No. 3 in Tredgold's Carpentry be 
those of Red Pine, of the standard strength and elasticity assumed throughout these tables, 
then every scantling therein, uniformly loaded with a weight of 1814 ibs. = 16-197 cwts., 
deflects in the middle -J- of an inch to the foot. If, therefore, 1814 be divided by the length 
in feet, the scantlings there given, within the limits of 20 feet long and 3 inches in breadth, 
may be found, nearly, by the Miscellaneous Tables, Nos. 3 to 9, in this work. 
