Advanced Methods of Structural Analysis

4.3 Influence Lines for Reactions and Internal Forces 89

ykIL.H /should be plotted on theone sideon the basic line. The ordinates

of required IL.Mk/will be locatedbetweenthese both graphs. Specified

ordinates of final graph (4.13a) at sectionkandCare

6:8754:42425D2:45075mand5:07:0788D2:0788m:

Step 4.Influence line between joints 2 and 3 presents a straight line because of in-
direct load application. Final influence line IL.Mk/is presented in Fig.4.8;
the connected line between joints 2 and 3 is shown by solid line.

6.875 7.0788

4.42425

5.0 IL(M

kO)

+ − yK⋅IL(H)

Construction

Inf. line Mk

A

C

B

HH

1

3

2

k

ak=10m

P= 1

bk= 22m

yk

2.0788

1.96 2.4507

1.0394 0.5194

+ Inf. line Mk(m)

−

Connecting line

*

RA RB

Fig. 4.8 Three-hinged arch. Design diagram and construction of influence line for bending mo-
ment at sectionkof the arch

4.3.2.2 Shear Force

This influence line may be constructed according to equation

IL.Qk/Dcos'kIL



QOk



sin'kIL.H / : (4.13b)

Step 1.Influence line for shear at sectionkfor reference beam is shown in Fig.4.7;
the specified ordinates at supportsAandBequal to 1.0. The first term
cos'kIL



Q^0 k



of (4.13b) presents a similar graph with specified ordinates

cos'kD0:954at supportsAandB, so ordinates at the left and right of

sectionkare0:298and 0.656, while at crownCis 0.477.