In order to show concisely the results of such a demonstration let it
be desired to find the position of a moving load which will give the
greatest stress to any web member, as _S_ in Fig. 24. Let the point of
intersection of _GK_ and _DC_ be found in the point _O_, then let _CK_
be extended, and on its extension let the perpendicular _h_ be dropped
from _O_. The distance of the point _O_ from _A_, the end of the span,
is _i_, while _m_ is the distance _AD_. Using the same notation which
has been employed in the discussion of beams, together with that shown
in Fig. 24, equation (33) expresses the condition to be fulfilled by
the train-loads in order that _S_ shall have its greatest stress. The
first parenthesis in the second member of that equation represents the
load between the panel _p_ and the left end of the span, while the
second parenthesis represents the load in panel _p_ itself.
_l_
_W₁ + W₂ + ... + Wₙ_ = - ----(_W₁ + W₂_ + etc.)
_i_
_l_(_m + i_)
+ (_W₃ + W₄_ + etc.) --------------- (33)
_pi_.
It will be noticed in equation (33) that the quantity _m_ shows in
what panel the inclined web member whose greatest stress is desired
is located, and it is important to observe that panel carefully. If,
for instance, the vertical member _KD_ were in question, the point _O_
would be located at the intersection of the panel _NK_ and the lower
chord of the bridge. In other words, the point _O_ must be at the
intersection of the two chord members belonging to the same panel in
which the web member is located.
=98. Application of Criterions for both Chord and Web Stresses.=—The
criterion, equation (33), belongs to web members only. If it is desired
to find the position of moving load which will give the greatest chord
stresses in any panel, equation (27), already established for beams,
is to be used precisely as it stands, the quantity _l′_ representing
the distance from one end of the span to the panel-point about which
moments are taken.
If the desired positions of the moving load for greatest stresses have
been found by equations (27) and (33), those stresses themselves are
readily found by taking moments about panel-points for chord members
and about the intersection-points _O_, Fig. 24, for web members.
These operations are simple in character and are performed with
great facility. Tabulations and diagrams are made for given systems
of loading by which these computations are much shortened and which
enable the numerical work of any special case to be performed quickly
and with little liability to error. These tabulations and diagrams and
other shortening processes may be found set forth in detail in many
publications and works on bridge structures. They constitute a part of
the office outfit of civil engineers engaged in structural work.
Public-domain text, read in full here on John Shaqi.
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