30 2 General Theory of Influence Lines
If loadP 1 is located to therightat sectionn,then
QnD 12 0:4C 8 .0:3/C 3 .1:8/C 2 .0:45/D3:9kN:In order to understand the obtained results, we need to calculate the shearQnfor
sectionnand show shear force diagram. Reaction of the supportAisRAD14:1kN.
If the loadP 1 is located to theleftof sectionn, then the forceP 1 mustbe taken
into account
Qn!
X
YleftD 0 !QnDRAq 1 6 P 1 D14:1 3 6 12 D15:9kN:If the loadP 1 is located to therightof sectionn, then the forceP 1 must notbe taken
into account
QnDRAq 1 6 D14:1 3 6 D3:9kN:
Shear force diagramQis presented in Fig.2.12b.
This example shows the serious advantage of influence lines: if we change the
type of loading, the amount of the load, and its locations on the beam, then a corre-
sponding reaction (or internal forces) may be calculated immediately.
Since the amount of the load and its location does not affect on the influence
lines, then influence lines should be considered as fundamental characteristics of
any structure.
2.2.2 Moving Loads
Influence line for any functionZallows us to calculateZforany positionof a
moving load, and that is very important, the most unfavorable position of the moving
loads and corresponding value of the relevant function. Unfavorable (or dangerous)
position of a moving load is such position, which leads to the maximum (positive
or negative) value of the functionZ. The following types of moving loads will be
considered: one concentrated load, aset of loads, and a distributed load.
The set of connected moving loads may be considered as a model of moving
truck. Specifications for truck loading may be found in various references, for ex-
ample in the American Association of State and Highway Transportation Officials
(AASHTO). This code presents the size of the standard truck and the distribution of
its weight on each axle. The moving distributed load may be considered as a model
of a set of containers which may be placed along the beam at arbitrary position.
The most unfavorable position of a single concentrated load is its position at
a section with maximum ordinate of influence line. If influence line has positive
and negative signs, then it is necessary to calculate corresponding maximum of the
functionZusing the largest positive and negative ordinates ofinfluence lines.