Advanced Methods of Structural Analysis

10.2 Construction of Influence Lines by the Displacement Method 349

13452689107 11

k

0.081610.17280.08320.0224

+

R

bInfluence line for Mk^0

Inf. line Mk^0

(factorl l )

Mk^0 depends of position P

the left or right at k

Mk^0 = 0 for any position P

LoadP =1

in the left span

Load P =1

in the right span

P = 1 P^ =^1

P = 1

1345268910711

k

ul R =u^2 ( 3 −u)

2

ul

ul

ul

ul

11

P = 1

13452689107

k

(All ordinates

must be multiplied

by factor l )

–1.2EI

l

⋅IL(Z 1 )

0.01920.0336

0.0288

0.03840.0288

0.03840.03360.0192

−

+

a

Final

Inf. line Mk

(factor l )

+

−

0.10080.2064 0.0512

0.02880.03840.0336

0.1216

c 0.0192

Fig. 10.12 (a–c) Construction of influence line for bending momentMk

10.2.1.3 Influence Line for Shear ForceQk

This influence line should be constructed by formula (10.19).
According to Fig.10.11c, the reaction at the support 1 due toZ 1 D 1 is directed
downward, so the shear in primary system at sectionkdue to primary unknown
Z 1 D 1 isQkD 3 EI=l. Therefore, (10.19) becomes

IL.Qk/D

3 EI

l^2

IL.Z 1 /CIL



Q^0 k



: (10.23)

The first term



3 EI=l^2


IL.Z 1 /of the (10.23) is presented in Fig.10.13a. The
second term of the (10.23) presents influence line of shear at sectionkin the primary
system. For calculation of this term we need to consider location of the loadPD 1
in both spans separately.