Advanced Methods of Structural Analysis

4.3 Influence Lines for Reactions and Internal Forces 87

have been multiplied by a constant factor cos'k. The second term presents the
influence line of the thrust of the arch, all the ordinates of which have been mul-
tiplied by a constant factor (sin'k). Summation of these two graphs leads to the
required influence line for shear force at sectionk. Similar procedure should be ap-
plied for construction of influence line for axial force. Note that both terms for axial
force are negative.
Analysis of three-hinged arch subjected to moving loads is presented below. This
analysis of loads implies the construction of influence lines for reactions and internal
forces and their application for analysis in cases of fixed and moving load.

A

C

HHB

1

3 5

2

k

7

6

aC= 16m

P= 1

bC= 16m

ak= 10m Bk= 22m

acbc

acbc

akbk

l

= 8 m

Inf. line MCO (m)

+

Inf. line RA

0.5

1 0.75

0.25 0.125

+

lf

= 1

Inf. line H

0.5

0.25

0.5

+

0.25

Inf. line Qk^0

1.0

1.0

+

Inf. line Mk^0 (m)

= 6.875

l

+

5.0

RA RB

Fig. 4.7Three-hinged arch. Design diagram and influence lines for reactions of supports and
internal forces at sectionkfor substitute beam

Figure4.7presents the arched structure consists from the arch itself and overar-
ched construction, which includes the set of simply supported beams and vertical
posts with hinged ends. Unit load, which moves along the horizontal beams, is