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Putting x = lcos θ, and y = lsin θ, the equations for the several
crane corner loads are:
A = Wg/4 + Wu/4 [1+(2lcosθ)/a][1+(2lsinθ)/b]
B = Wg/4 + Wu/4 [1+(2lcosθ)/a][1-(2lsinθ)/b]
C = Wg/4 + Wu/4 [1-(2lcosθ)/a][1-(2lsinθ)/b]
D = Wg/4 + Wu/4 [1-(2lcosθ)/a][1+(2lsinθ)/b]
The relationship between the load A on crane corner "A" and angle of
inclination "θ" is shown plotted on polar coordinates in Figure 26 and from this
it will be noted that the load "OP" is a maximum when the boom is at right angles
to the diagonal "BD", that is when tan θ = a/b.  Although the boom directly over
main gudgeon "A" is often assumed to give the maximum crane corner load, this is
true only when the gudgeon spacing is equal to the gauge.  Extending the vector
"PO" to "Q" gives "OQ" as the minimum load on crane corner "A" which occurs when
the boom is rotated through an angle of 180 degrees from "OP" to "OP1".
Moment of Inertia Method.  This method assumes the crane rails to be
perfectly level and rigidly supported, and yields maximum wheel load that are
about 8 to 10 percent lower than those obtained by the beaming method.  Since the
actual condition of crane rails does not justify such assumptions, this method of
determining the maximum wheel loads is not used in the design of Navy portal
Travel Truck Systems.  The equalizers, gudgeons, gudgeon pins, float
pins, and travel trucks are designed according to the structural design
requirements for the following load combinations:
Dead load plus main hoist rated load - both multiplied by an impact
factor of 1.25, 40 mph wind, acceleration forces due to rotate and travel motion,
and spreading or squeezing forces.  The travel truck float and wheel positions are
taken in their most adverse inward or outward locations.  The upperworks and boom
are positioned to produce the maximum corner load.  The maximum stresses are
limited to 85 percent of AISC allowable values.
Dead load and non-operating wind load from the front, rear, or
side with the boom at the specified radius.  The upperworks are positioned with
the boom in the specified direction.  The maximum allowable stresses are limited
to 133 percent of AISC allowable values.
For fatigue analyses, the maximum allowable stress range is limited
to 100 percent of the AISC allowable values for Condition 2 (that is 100,000 to
500,000 cycles).  The larger of the following two stress ranges is to be used:
1) Dead load with the boom at minimum operating radius and with no
hook load.  The stress range is defined as the algebraic difference between the
stresses due to: (a) the counterweight positioned to produce the maximum corner
load, and (b) the boom positioned to produce the minimum corner load.


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