Advanced Methods of Structural Analysis

34 2 General Theory of Influence Lines

Fig. 2.15 Indirect load

application

Inf. line Z

A

d

B

P= 1

m n

Main beam

Stringer Floor beam

Rm Rn

ym

yn

x

Influence line for any functionZin case of direct load application is presented

in Fig.2.15by dotted line. Ordinate of influence line for parameterZat the panel

pointsmandnareymandyn, respectively. If loadPD 1 is located at pointmorn

in case of indirect load application, then parameterZequalsymoryn.IfloadPD 1

is located at any distancexbetween pointsmandn, then reactions of stringersRm

andRnare transmitted on the main beam at pointsmandn. In this case functionZ

may be calculated as

ZDRmymCRnyn:

Since

RmD

P.dx/

d

D

dx

d

;RnD

Px

d

D

x

d

;

then the required parameterZbecomes

ZD

dx

d

ymC

x

d

ynDymC

1

d

.ynym/x: (2.10)

Thus, the influence line for any functionZbetween two closest panel pointsmand

nis presented by astraightline. This is the fundamental property of influence lines

in case of indirect load application.

Influence lines for any functionZshould be constructed in the following

sequence:

1.Construct the influence line for a given functionZas if the moving load would
be applied directly to the main beam.
2.Transfer the panel points on the influence line and obtained nearest points con-
nect by straight line, which is called as theconnecting line.
This procedure will be widely used for construction of influence lines for arches and
trusses.
Procedure for construction of influence lines of bending moment and shear at
sectionkfor simply supported beam in case of indirect load application is shown
in Fig.2.16. First of all we need to construct the influence line for these functions if