26. Therefore the two lines A'B' and C'B' must be
drawn to a point B', so situated that (denoting the centres
of gravity of the respective areas by a, 5, c and d), the
areas

aV'D^de — 'K'W^'.ci BC.
O'F D' . df— K'D'B' . ch — K'B' Q' .bh-]- A' ¥' Q' . ag ~ A C

All of these quantities are readily measured and com-






ANALYSIS OF BBIDGE TRUSSES. 37

puted, as will soon be shown ; therefore we may draw
A' B' and C B' as trial lines, as near the right position as
we can, and then compute the first ratio. If it does not
equal the second ratio, move B' and try again ; a second
approximation will generally be suflBcient. Call any area,
as above, multiplied by its distance from a certain point,
an area moment

We maj^, with advantage, modify a little the applicar
tion of our method, and so obtain a rule more easily re-
membered and used. Draw the tangent M B N to the
beam at B. It is evident that NC:MA = BC:BA.
Then, from the preceding reasoning, make

area Q' V D' . dl — 'Kf'D' B' , ck _ BjCT
area K' B' G' . i^ A — A' F G' . agf ~ BA'

The deflection M A being on the opposite side of the
tangent from N C, the similar areas in the above propor-
tion are taken with the opposite signs ; that is, K' D' B'
being taken minus in the first term, K' B' G' is taken plus
in the second, and so of the others. Or we may consider
the distances to the right of B plus, and those to the left

minus.
