Advanced Methods of Structural Analysis

46 3 Multispan Beams and Trusses

4.Connect nearest intersection points by connecting lines.
5.Influence line as a result of indirect load application is bounded by broken line
emnstf.

Inf. line RA

1

−

+

a

h

d

e

m

n s

t f

Inf. line Mk

a 0 b 0 /l

+

a −

h

e f

m k

n s

t

d

A B

E F

C

k H

P=1

m n s t D

Stringer Floor beam

Girder

a 0 b 0

Fig. 3.7 Gerber–Semikolenov beam with indirect load application, its interaction diagram and

influence lines

Influence line forMk:

If the load is applied to the beamAHDdirectly, then the influence line forMkis

bounded byakhdpoints. In case of indirect load application, the influence line is

bounded byemnstfpoints.

Discussion

1.Because of the indirect load application,the reactions and internal stresses arise
in the beamADeven if the load is applied outside the beamAD(close to sup-
portsEorF).
2.Influence lines are convenient to use for analysis of structures, with modified de-
sign diagram. For example, for the given structure the bending moment at section
kis positive, if any load is located within the stringer beamEm. It means that the
extended fibers in the sectionkare located under the neutral axis of the beam.
However, if a floor beammwill be removed and two stringersEmandmnwill
be replaced by one stringerEn, then the pointseandnon influence line forMk
should be connected. In this case bending moment at sectionkbecomes negative,
e.g., the extended fibers in the sectionkwill be located above the neutral line.