xxxii 
EXAMPLES TO THE SECOND SERIES. 
Weight suspended from a given point. 
and the scantlings are very readily found by the Second Series of 
Tables. 
Example 17. — Required the Scantlings of Red Pine 16 feet long to 
support 128 cwts. suspended 4 feet from the wall; the breaking weight 
of the scantlings to be 4 times that weight. 
AB=16; AC = 8; AD = 4; DB=12; W' = 128 cwts.; 
From (a) we have 
W = ^^^^ X W'= X 128 = 96 cwts. suspended from the 
middle, which being one-fourth of the breaking weight, by the Second 
Series of Tables, the Scantlings for 16 feet long are, — 
11X12J; 12X10f; 12^X10; 13X9i; 13^X8^; 14X8; 
14iX7i; 15X7; 15JX6i; 16X6. 
Multiplying the breadths by ; ^; -i^L; |; &c, ; the scantlings 
are found which break with 4i times, 5 times, 5 J times, 6 times, See- 
the tabular or given weight. 
Note. — The breadth of Trimmer Joists, to have the same strength as the joists in the same 
iloor, may be found as follows : — 
Let W= the weight at D, from one end of a trimmer fixed to AB at D ; 
W = stress at C, found as above, from the weight W'; 
W" = one half of the weight uniformly loaded upon a floor joist ; 
b = breadth of a joist ; 
then, the length and depth being the same, for a trimmer joist AB to have the same Strength 
as the joists in the same floor, the breadth of AB should be, — 
W + W" 
— w'r- ^ ^ • (»)• 
