196 APPLIED MECHANICS 
et | tae | Ee 
Bar WwW Pp. Q ; Maximum Stress. | 
(Fig. 266).| (Fig. 263) | (Fig. 264) | (Fig. 265) | 
1 13715 | 9180 6900 | W+P | 22895 
2 | 1280 | 9180 | @900 | wir | 22000 | 
3 | 399 | 4980 | 1100 | w+q | 23020 
4 13715 | 4980 | 11100 | w+Q | 24815 4 
5 12450 | 1258 | 12598 | W+Q | 24978 
: phat HS BO ie 5031 | W+Q | 11469 
f peaineeidis Nig fi 6268) Weel oh are 
8 1789 | 3600 0 | W+P | 5389 
9 6906 | 6577 1566 | W+P | 13488 
ay one Ske 7330 | W+Q | 14736 
1 1789 0 3600 | W+Q | 5389 
181. The Method of Sections.—Conceive that a framed structure is 
divided into two parts by cutting three bars A, B, and C. Next suppose — 
that one of these parts is removed, and 
that external forces P, Q, and S are 
applied to the bars A, B, and C respec- 
tively, so as to balance the internal 
forces in these bars, then the part of the 
structure which remains (Fig. 267) will 
evidently be in equilibrium. 
If moments of all the external forces 
acting on the part of the structure under 
consideration be taken about the point 
O, where the bars A and B intersect, 
Fic. 267. 
then the moment of § will balance the resultant moment of all the 
remaining external forces; and since the moments of P and Q are 
zero, and the other forces are known, their resultant moment can be- 
determined, as in Art. 60, p. 43, and therefore the moment of 5 is- 
found, Again, since y, the ‘perpendicular distance of S from O, is known, 
therefore S can be found. If in constructing the resultant moment of 
the known external forces the pole distance be made equal to y, then the 
line which (measured with the force scale), multiplied by the pole dis- 
tance, gives the resultant moment, will, when measured with the force 
scale, give the magnitude of 8. 
Having found §, the force P may be found in like manner by taking 
moments about another point in the bar B (say at the intersection of 
and C). Lastly, the foree Q may be determined by taking momen 
about a point outside the bar B. i 
“ The forces P and Q may, however, be determined by the polygon of 
external forces after S thas been found. \ 
Another method of finding S is by means of the polygon of forces — 
