Advanced Methods of Structural Analysis

4.3 Influence Lines for Reactions and Internal Forces 91

4.3.2.3 Axial Force

This influence line may be constructed according to equation

IL.Nk/Dsin'kIL



Q^0 k



cos'kIL.H / : (4.13c)

Step 1.Influence line for shear at sectionkfor reference beam is shown in Fig.4.7.
The first term sin'kIL



Qk^0


of (4.13c) presents a similar graph with spec-
ified ordinates sin'kD0:30at supportsAandB, so at the left and right of
sectionkordinates are 0.09375 and0:20625, while at crownCis0:15.
Step 2.Influence line for thrust is shown in Fig.4.7; the specified ordinates at crown
Cequals to 1.0. The second term cos'kIL.H /of (4.13c) presents a similar
graph with specified ordinates0:95391:0D0:9539at crownC. Specified
ordinate at sectionkis 0.59618.
Step 3.Procedure (4.13c) is presented in Fig.4.10.Bothtermsin(4.13c)hassame
signs, therefore both graphs, sin'kIL



Q^0 k



and cos'kIL.H /, should

be plotted on thedifferent sideson the basic line. Ordinates for required

IL.Nk/are locatedbetweenthese both graphs.

Specified ordinates of final graph (4.13c) left and right at sectionkare

.0:596180:09375/D0:50243 and

.0:59618C0:20625/D0:80243:

At crownCordinate of influence lineNkis.0:9539C0:15/D1:1039.

A

C

B

1

(^23)
k
P= 1
jk
0.80243 Connecting line

• 1.1039
  0.2759
  sinjk 0.5519
  −
  0.40194
  Inf. line Nk
  0.50243
  Construction
  Inf. line Nk
  0.9539
  sinjk⋅IL(QkO)
  cosjk⋅IL(H)
  0.3
  −
  0.59618
  0.09375
  sinjk=0.3
  0.20625 0.15
  Fig. 4.10 Three-hinged arch. Design diagram and construction of influence line for axial force at
  sectionkof the arch