Advanced Methods of Structural Analysis

3.1 Multispan Statically Determinate Beams 43

second support of the suspended beam. This procedure is called as distribu-
tion of influence lines within the suspended beam.
Step 4.The beam distribution procedure should be applied for the following sus-
pended beam.
To illustrate this procedure for statically determinate multispan beams we will
consider a structure as in Fig3.6. It is necessary to construct the influence lines
for reactions, bending moment, and shear for indicated sections. We are starting
from kinematical analysis of a structure: this beam is statically determinate and
geometrically unchangeable structure.

Inf. line

Mn (m)

1.5

1

+

Inf. line RD

1

0.333

+

Inf. line Qn

1

0.5 1

0.5

+ 5

−

0.333

1

Inf. line Qs

+

0.4

2

Inf. line

− Ms (m)

0.8

5m 2m 3m 3m 2m 3m

A

H 1

B C D

H 2 H 3

P= 1

3m

s k n

2m

BH^2 H^3 C D

A H 1

Fig. 3.6 Multispan statically determinate beam. Influence lines for reactions, bending moment
and shears at some sections

Influence Line forRD

The structural element is beamH 3 CD. Influence line for reactionRDwithin the
spanCDis a straight line with ordinate 1 at supportD, zero at supportC,and
extended within left-hand and right-hand overhangs.