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 supportBisD3:5m
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)