72 3 Multispan Beams and Trusses
influence line, but this procedure is repetitive and bothersome; mainly, it is essen-
tially pointless.
This harmful inefficient approach is based on the calculation of the required force
for the different locations of the loadin order to showthe influence lines. In this
case the whole necessity of the influence line is lost, since by constructing influence
lines this way wealreadydetermined the internal forces for all positions of the
loadPD 1.
On the contrary, we need the influence linein order to findthe value of the re-
quired internal force foranylocation of the load. By no means should this graph be
plotted using repeated computation. In principal, such a flawed approach defeats the
purpose of the influence line as a powerful analytical tool.
This book contains an approach to the construction of influence lines, based on
accepted methods of truss analysis: using the joint and through section methods we
obtain an expression for the required force and after that we transform this expres-
sion into anequationfor the influence line. The algorithm described above allows
the influence line to be presented as afunction(in contrast to aset of numerical
ordinatesfor the influence line). Stated as functions, influence lines can realize their
full potential as extremely versatile tools for providing different types of analysis.
A very important aspect of this approach is that it allows us to find specific or-
dinates of the influence lines in terms of the parameters of the structure, such as
heights, panel dimensions, angle of inclination of diagonals, etc. This allows us to
determine the influence of each parameter on a required force and so provides opti-
mization analysis.
Both fundamental approaches, fixed andmoving loads, complement each other.
This combination is very effective for truss analysis with some peculiarities (espe-
cially for statically indeterminate trusses). Also, the combination of both approaches
is an effective way to analyze the same truss in different load cases (snow, dead, live,
etc.). For example, for a thrusted truss with supports on different levels, we can find
the thrust by considering the system of equilibrium equations. Then, knowing the
thrust, we can find all the required internal forces. This is not difficult, but if we
need to do it many times for each loading, then it would be much wiser to con-
struct the influence line for the thrust only once. Then we could find its value due
to each loading. It is obvious that in this case the influence line for the thrust should
be treated as the key influence line. In the case of a truss with a hinged chain, the
internal force in the member of the chain under analysis (or better, the thrust as
the horizontal component of such an internal force) should be considered to be the
key influence line. Clearly, for a complex truss, such as the Wichert truss, the key
influence line is the influence line for the reaction of the middle support.
Problems.......................................................................
3.1.Provide kinematical analysis for beams in Fig. P3.1. Construct interaction
scheme, point the main and suspended beams, and explain a load path.