THE KANSAS CITY BRIDGE. 143

the value of x for each tie being the assumed length of beam (290.5 feet) minus
the distance from the centre post to the foot of the tie next inside. The strains
in the ties and posts, calculated by this formula, are given in the tables in
Appendix G. As the practical centre is distant 145.25 fect from the centre post
only when both spans are fully loaded, the results thus obtained are excessive
for all but the centre ties, the others being most intensely strained under a
partial load when the practical centre will be nearer the centre post and the
practical length of beam less.

When but one arm is loaded the general equation for the moment of
flexure is

M = — 480 /? +. 1520/2 — 1040 2?
the maximum value of M corresponding to
& = .T3077 | = 183.

The strains in the ties which carry their load to the end posts will therefore be
calculated as if the centre of the beam was distant 133 feet from the centre post,
or 49 feet from the end post, the equivalent length of span being 98 feet. Sub-
stituting /—98 in the general equation for the web strains, it becomes

S = 23520 — 2.857 x? — 480 x

the value of «for each tie being the assumed length of beam (98 feet) minus
the distance from the end post to the foot of the next tie outside. The strain
in the several ties and posts, calculated by this formula, are also given in Ap-
pendix G.*

The maximum strain on the centre post will be equal to the total dead and
moving load between the points 145.25 feet on each side of that post, except-
ing the half panels adjoining, the weight of which is carried directly by the
pivot. The strain is therefore

(290.5 -15.5) X 2080 — 572,000 pounds.
In like manner the strain on each end post is found to be

(49 — 6.25) X 2080 = 87,800 pounds.

* The maximum web strains expressed in tons of 2,000 pounds are marked on the skeleton diagram on
Plate XIL, The practical centres used in calculating these strains are also designated on the same diagram.

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