Advanced Methods of Structural Analysis

88 4 Three-Hinged Arches

transmitted over the posts on the arch at discrete points. Thus, this design diagram
corresponds to indirect load application. Parameters of the arch are same as in
Fig.4.5.

4.3.1 Influence Lines for Reactions................................

According to (4.11), influence lines for vertical reactionsRAandRBof the arch do
not differ from influence lines for reaction of supports of a simply supported beam.
Influence line for thrust may be constructed according to (4.12); the maximum or-
dinate of influence line for bending moment at sectionCof the reference beam is
equal to.aCbC/=lDl=4D 8 (m). Therefore the maximum ordinate of influence
line for thrustHof the arch becomes

1

f



aCbC

l

D

l

4f

D

32

4  8

D1:

Influence lines for reactions of supports of the arch and internal forces for reference
beam are shown in Fig.4.7.

4.3.2 Influence Lines for Internal Forces at Section k

The sectionkis characterized by the following parameters:

akD 10 m;bkD 22 m;ykD7:0788m;sin'jD0:30;cos'jD0:9539:

4.3.2.1 Bending Moment

Influence line forMat sectionkmay be constructed according to (4.13)

IL.Mk/DIL



Mk^0



ykIL.H / : (4.13a)

Step 1.Influence line for bending moment at sectionkof reference beamMk^0
presents the triangle with maximum ordinate.akbk/=lD.1022/ =32D
6:875m at sectionkand 5.0 m at sectionC(Fig.4.7).
Step 2.Influence line for thrustH presents triangle with maximum ordinate
l=4fD 1 at the sectionC.TermykIL.H /presents the similar graph; the
maximum ordinate isyk 1 D7:0788m. So the specified ordinates of graph
ykIL.H /at sectionkandCare 4.42425 m and 7.0788 m, respectively.
Step 3.Procedure (4.13a) is presented in Fig.4.8, Construction Inf. LineMk.Since
both terms in (4.13a)hasdifferentsigns, then both graphs, IL



Mk^0



and