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Beaming Method.  The beaming method is described in Electric Cranes, H.H.
Broughton, (London, 1958).  It assumes that the weight of the portal base is
distributed equally among the four corners (unless there is a significant
eccentric load, which can be readily taken into consideration) and that the off-
center load from the upperworks is resolved into moment components about the
lateral and longitudinal axes.  The relative magnitudes of the moment components
vary sinusoidally as a function of the orientation of the upperworks.  The maximum
wheel (corner) load is reached when the sum of the two moment components reaches
its maximum value.
For a square portal base, the maximum wheel load occurs when the boom
axis is directly over the corner.  For a rectangular portal base, the maximum
wheel load is reached when the boom axis is normal (or nearly normal) to the
portal base diagonal.  Figure 24 shows in graphic form the variation of the wheel
load through one quadrant of rotation as a function of upperworks orientation and
hook radius (moment) for a typical portal crane with a rectangular portal base.
It is important to note that for some radii the maximum allowable wheel load for
the rail system is exceeded as the upperworks rotates over the corner; and in
order to remain within the allowable wheel load, the hook radius must be reduced
(the boom raised) before rotating over the corner.  (The dashed line in Figure 24
shows this path.)  If the counterweight is excessive, it may generate the maximum
wheel loads when the empty boom is at minimum radius; in which case the boom will
have to be lowered to reduce the corner load if the maximum allowable wheel load
of the rail system is being exceeded.
The maximum wheel load
calculated by the beaming method is used to
determine the governing load for
the design of the portal base structure and all
structural-mechanical components
below the main gudgeon connection and the
selection of wheel diameter.  In
the case of older cranes with idler wheel driven
travel trucks, the maximum wheel
load also governs the design of travel truck
gearing, bearings, and axles.
Formal Presentation of the Beaming Method.  The following subparagraphs
paraphrase (for consistency of terminology) the description of the beaming method,
titled "Truck wheel-pressures under slewing load" from
H.H. Broughton's Electric Cranes.
Figure 25 represents the portal base of a portal crane having a main
gudgeon spacing "a" and a gauge "b".  The portal base (including the travel truck
system) weighs "Wg" which weight acts centrally at the point "O", and the
upperworks, pivoted at "O", and weighing "Wu" has as its center of gravity the
point "S" which is a distance "l" from the center of rotation.  The angle of
inclination of the plane of the boom "OE" with respect to the axis "hf" is "",
and the coordinates of the point "S" referred to the two axes "CD" and "BC" are: x
+ (a/2) and y + (b/2), respectively.  To find the load A on crane corner "A" due
to the weight of the upperworks, first take moments about point "Q" and find P =
Wu{x + (a/2)}/a.  (P is the reaction at point "P" due to Wu, if Wu were located at
points "S" on an imaginary beam between Points "P" and "Q".)  Next take moments
about point "B" to obtain load A = P{y +(b/2)}/b.  To this load has to be added
Wg/4 due to the weight of the portal base.  Evidently the load on any crane corner
for any angle "θ" can be determined in the same way.


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