Advanced Methods of Structural Analysis

90 4 Three-Hinged Arches

Step 2.Influence line for thrust is shown in Fig.4.7; the specified ordinates at crown
Cequals to 1.0. The second term sin'kIL.H /of (4.13b) presents a sim-
ilar graph with specified ordinates0:31:0D0:3at crownC. Specified
ordinate at sectionkis 0.1875.
Step 3.Procedure (4.13b) is presented in Fig.4.9. As in case for bending mo-
ment, both terms in (4.13b)hasdifferentsigns, therefore both graphs,
cos'kIL



Q^0 k



and sin'kIL.H /should be plotted on theone sideon

the basic line. Ordinatesbetweenboth graphs present the required ordinates

for influence line for shear. Specified ordinates of final graph (4.13b)left

and right at sectionkare

0:298C0:1875D0:4855 and 0:6560:1875D0:4685:

At crownCordinate of influence lineQkis0:4770:3D0:177.
Step 4.Influence line between joints 2 and 3 presents a straight line; this connected
line is shown by solid line. Final influence line IL.Qk/is presented in
Fig.4.9.

A

C

B

1

(^23)
k
P= 1 Tangent at k
jk
0.298 cosjk
cosjk=0.954
0.3
0.477
sinjk⋅IL(H)
cosφk⋅IL(QkO)

• −
  Construction
  Inf. line Qk
  0.656
  0.1875
  Inf. line Qk
  0.3883
  0.177
  cosjk 0.4685
  0.04425
  0.0885
  −


• 
  

  Connecting line

  
  

• 0.4855
  Fig. 4.9 Three-hinged arch. Design diagram and construction of influence line for shear at section
  kof the arch