Advanced Methods of Structural Analysis

100 4 Three-Hinged Arches

Inf. line H

+

1.1428

1.71428

Inf. line Mk (m)

xk=6m

+

x 0 = 16.8m −

2.5714 1.7143

8m

C

B

A

P=10kN

H

H

ac=24m bc=18m

12m

xk=6m

3.5m

k

NP(Mk)

a

• B′ x

y

yk=3.5m

h

Fig. 4.15 Three-hinged askew arch. Design diagram and influence lines

The thrust and bending moment at the sectionkmay be calculated using the
relevant influence lines

HDPyD 10 1:1428D11:428kN;

MkDPyD 10 .1:7143/D17:143kN m:

These values coincide exactly with those calculated by formulas (4.15)and(4.17).
As before, the influence lines for thrust constructedoncemay be used for its
computation for different cases of arbitrary loads. Then, knowing the vertical reac-
tions and thrust, the internal forces at any point of the arch may be calculated by
definition without using influence line for that particular internal force.

4.5.2 Parabolic Arch with Complex Tie...........................

Analysis of such structure subjected to fixed and moving load has some features.
Design diagram of the symmetrical parabolic arch with complex tie is presented
in Fig.4.16. The arch is loaded by vertical uniformly distributed loadqD 2 kN=m.
We need to determine the reactions of the supports, thrust, and bending moment at
sectionk(akD 18 m,ykD11:25m, cos'kD0:970,sin'kD0:2425)aswellas
to construct the influence lines for above-mentioned factors.