The unit load to be used in connection with the influence lines will be
taken at 10,000 pounds. Remembering that the panel lengths are each 30
feet, it will be seen that the panel-point _Q_ is 150 feet from _A_.
Hence the product _gx_ will be 1,500,000 foot-pounds. Similarly the
product _g_(l - _x_) will be 900,000 foot-pounds. Laying off the first
of these quantities, as _AD_, at a scale of 1,000,000 foot-pounds per
linear inch, and the second quantity, as _BK_, by the same scale, the
influence line _ACB_ can at once be completed. Vertical lines are next
to be drawn through the positions of the various weights, including
one through the centre of the uniform train-load 110 feet in length
resting on the truss. The vertical line through the centre of the
uniform train-load is shown at _O_. By carefully scaling the vertical
intercepts between _AB_ and _ACB_, and remembering that each of the
loads on the truss must be divided by 10,000, the following tabulated
statement will be obtained, the sum of the intercepts for each set
of equal weights being added into one item, and all the items of
intercepts being multiplied by 1,000,000:
.195 × 110 × .4 × 1,000,000 = 8,580,000 foot-pounds.
1.78 × 2.6 × ” = 4,628,000 ” ”
2.14 × 4 × ” = 8,560,000 ” ”
.485 × 2 × ” = 970,000 ” ”
1.525 × 2.6 × ” = 3,965,000 ” ”
.9 × 4 × ” = 3,600,000 ” ”
.12 × 2 × ” = 240,000 ” ”
----------
2⟌30,543,000 ” ”
----------
Moment for one truss = 15,271,500 ” ”
The lever-arm of _ef_, i.e., the normal distance from _Q_ to _ef_, is
39.7 feet. Hence the stress in _ef_ is
15,271,500
----------- = 384,700 pounds.
39.7
All the chord stresses can obviously be found in the same manner.
In order to place the same moving load so as to produce the greatest
shear at the same section _Q_, the criterion of equation (33) must be
employed. The dimensions of the truss shown in connection with Fig. 29
give the following data to be used in that equation: _i_ = 210 feet,
_m_ = 60 feet, and _p_ = 30 feet.
_l_(_m + i_) _l_
Hence ------------ = 10²/₇, --- = 1¹/₇.
_pi i_
[Illustration: FIG. 25_b_.]
[Illustration: FIG. 25_c_.]
[Illustration: FIG. 25_d_.]
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