Advanced Methods of Structural Analysis

4.5 Special Types of Arches 97

*

sinjk

−

NP(Nk)

A

C

B

1

3 5

2

k

7

6

P= 1

NP(Nk)

Tangent at k

Perpendicular

to tangent at k

LHP RHP- 1

RHP- 2

jk

b

uN

RA

RB

Inf. line Nk

Fig. 4.13 Construction of influence lineNkusing nil point method

4.5 Special Types of Arches...............................................

This section is devoted to analysis of special types of arches. Among them are arch
with support points located on the different levels and parabolic three-hinged arch
with complex tie.

4.5.1 Askew Arch...................................................

The arch with support points located on the different levels is called askew (or ris-
ing) arch. Three-hinged askew arch is geometrically unchangeable and statically
determinate structure. Analysis of askew arch subjected to the fixed and moving
loads has some features.
Design diagram of three-hinged askew arch is presented in Fig.4.14.Letthe
shape of the arch is parabola, span of the archlD 42 m and supportBisD3:5m
higher than supportA. The total height of the arch at hingeCisfCf 0 D 8 m.
The arch is loaded by forceP D 10 kN. It is necessary to calculate the reactions
and bending moment at sectionk, construct the influence lines for thrust and bend-
ing momentMk, and apply influence lines for calculation of bending moment and
reactions due to fixed load.
Equation of the axis of parabolic arch

yD4.fCf 0 /.Lx/

x

L^2

; (4.14)