Advanced Methods of Structural Analysis

106 4 Three-Hinged Arches

4.7.Three-hinged askew arch spanlis subjected to concentrated forcePat the
hingeC(Fig.P4.7). Determine the effect of the parameterf 0 on the thrust of the
arch. (Hint:HDZcos ̨).

A

C

B

P

l/ 2

f f

0

Z

R′A

R′B

h Z

a

a

Fig. P4.7

Ans.HD

Pl

2.2ff 0 /

4.8.Three-hinged symmetrical arch is loaded by uniformly distributed loadq(Fig.
P4.8). The span and rise of the arch arelandf, respectively. Derive the equation
of the rational axis of the arch.
(Note: the arch is called as rational if the bending moments do not arise at all the
cross sections of the arch. The equation of the rational axis of the arch depends on
the type of loading).

A

C

B

q

l/ 2

f

x

y

Fig. P4.8

Ans.yD4f

x

l



1 

x

l



4.9.Three-hinged symmetrical arch is loaded by distributed loadqasshowninFig.
P4.9. Derive the equation of the rational axis of the arch.

A

C

B

q

l/ 2

f

x

y

Fig. P4.9

Ans.yD

8

3

f

x

l



1 

x^2

l^2