Advanced Methods of Structural Analysis

104 4 Three-Hinged Arches

A

C

B

1

2

3

n

P= 1

bc

k

ac

fc

Fig. P4.2

4.3.Design diagram of three-hinged arch is presented in Fig.P4.3.
(a)Find the location of uniformly distributed load so tensile fibers at section k
would be located below the neutral line and as this takes place, the bending
moment would be maximum
(b)Find the location of concentrated forcePfor shear at sectionkto be positive
and maximum value
(c)Find a portion of the arch where clockwise coupleMshould be placed for shear
at sectionkto be positive and maximum value.

A

C

B

1

2

3

n

P= 1

k

Fig. P4.3

4.4.Design diagram of three-hinged arch is presented in Fig.P4.4.

1.For the axial force at sectionnto be maximum, the uniformly distrubuted load
should be located (a) left at the sectionn; (b) right at the sectionn; and (c) within
all spanAB.
2.For the axial force at sectionnto be maximum a concentrated forcePshould be
located
(a)leftatthesectionn; (b) right at the sectionn; (c) at the hingeC;(d)leftat
hingeC; (e) right at hingeC.
3.The vertical settlement of supportAleads to appearance of internal forces at
the following part of the arch: (a) portionAC; (b) portionCB; (c) all archAB;
(d) nowhere.