XXX 
EXAMPLES TO THE SECOND SEKIES. 
have the same stress upon the 
middle of the beam as the given 
weight: the scantlings for the 
uniform load so found are those 
required. 
Example 16.* — In Fig 1, let 
AB represent a beam 16 feet 
long; let C be the middle of 
the beam, and let 32 cwts. and 
64 cwts. be placed upon AB, in 
the several positions shewn in 
the figure. Required the Scant- 
lings which just break with 8 
times those weights in the seve- 
ral given positions. 
The uniform loads in Fig. 2, 
are found as below ; and the 
scantlings to break with 8 times 
those or the given weights, are 
found by the Second Series of 
Tables. 
Fig. 1. 
H ir m: 
I ! 
?> ! 
2 5tr 
Fig. 2. 
m 
Weight ( = W), upon the seve- 
ral parts of the beam AB 
in Fig. 1. 
Weight iu Fig. 2, uniformly loaded upon the 
beam AB, to have the same stress in the 
middle as the weight W iu Fig. 1. 
Scantling 
16 inches 
deep. 
Upon AD 
.. 32 cwts. 
= f X 32 = 8 cwts. 
16 X i 
Upon DE 
.. 64 
II 
AC 
= 1 X 64 = 64 " 
16 X 4 
Upon EC 
... 32 
II 
AE.AC^^ 
AC 
= y X 32 = 56 „ 
16 X3i 
Upon LC 
... 64 
II 
BL + BC „^ 
BC 
= If X 64 = 96 " 
16 X 6 
Upon BL 
... 64 
II 
— XW 
BC 
= 1 X 64 = 32 « 
16 X 2 
Upon AB 
..256 cwts. 
256 cwts. 
16 X 16 
Examples 16 and 17 shew the method of fiuding the scantlings in other cases. 
