THE KANSAS CITY BRIDGE. 107
To obtain the actual deflection, that due to the strains in the braces and
panel ties must be added to the deflection thus obtained. The heaviest strain
caused by the moving load alone upon the braces is 240 pounds per square inch,
and upon the ties 5,000 pounds per square inch, shortening each brace .000165
of its length, and lengthening each tie .000172 of its length ; making the deflec-
tion due to each triangle .000337 of the height of that triangle; but as the
central ties and braces, which are the longest, are but slightly strained by a full
load, the average deflection due to all the triangles will not exceed .00025 of their
height. The aggregate height of the five triangles on each side of the centre, in
the system whose tie-rods meet at the centre, is 140 feet, making the deflection
due to the strains in the web .035 feet, or 43 of an inch; this, added to the
deflection due to the chord strains, gives for the total deflection .144 feet, or 143
inches.*
The unequal expansion of the wood and iron in the structure, under a
change in temperature, causes the centre of the truss to rise and fall in a man-
ner similar to the action produced by a passing train. The range of temperature
at Kansas City may be assumed at 120° Fahrenheit; in exceptional seasons it
may exceed this, but only rarely. The coefficient of expansion of pine wood,
for one degree of Fahrenheit, is .00000227, and that of wrought-iron is
-00000698 ; then give for the values of ¢ and 7’ the equation given above :—
t = .00000698 120 = .000837
i! = .00000227 120— 5g 000272 +
é
243
The values of the other known quantities will be the same as in the pre-
ceding calculation. Solving the equations as before, we have for the effects of
an increase of temperature of 120° Fahrenheit :—
@¢== 0317 i’ = .000401
7 = 50459 d = .150 = 143 inches.
The same increase of temperature acting upon the web causes a deflection in
* To secure strictly accurate results, the deflection caused in the top chord by the web strains should be
calculated separately, and the general deflections corrected to correspond with the spreading of the arch due to
them ; this difference, however, is but slight, and need not ordinarily be considered.