Civil Engineering Reference
In-Depth Information
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14.3
QUALITATIVE INFLUENCE LINES
Many methods might be used to analyze continuous structures. The most common hand
calculation method is moment distribution, but other methods are frequently used, such as
matrix methods, computer solutions, and others. Whichever method is used, you should
understand that to determine maximum shears and moments at different sections in the
structure, it is necessary to consider different positions of the live loads. As a background
for this material, a brief review of
qualitative influence lines
is presented.
Qualitative influence lines are based on a principle introduced by the German pro-
fessor Heinrich Müller-Breslau. This principle is as follows:
The deflected shape of a
structure represents to some scale the influence line for a function such as reaction,
shear, or moment if the function in question is allowed to act through a small distance.
In other words, the structure draws its own influence line when the proper displace-
ment is made.
The shape of the usual influence line needed for continuous structures is so simple
to obtain with the Müller-Breslau principle that in many situations it is unnecessary to
compute the numerical values of the coordinates. It is possible to sketch the diagram
roughly with sufficient accuracy to locate the critical positions for live loads for vari-
ous functions of the structure. These diagrams are referred to as
qualitative
influence
