Advanced Methods of Structural Analysis

10.2 Construction of Influence Lines by the Displacement Method 347

Z 1

P = 1

Primary system

b

P = 1

A

B

C

ll

k

0.4l

a

EI = constant

c

r 11

3 EI

l

3 EI

l

r 11

3 EI Z 1

l

3 EI

l

M 1

Mk

Unit state

3 EI

l 2

0.4l

d

P = 1 P = 1

Load P = 1 in the left span Load P = 1 in the right span

u lul

2 u^ (^1 −u

l (^2) )
2 u^ (^1 −u
l (^2) )
ul υl
r 1 P r 1 P
2 u^ (^1 −u
r 1 P =l^2 )
2 u^ (^1 −u
r 1 P =–l^2 )
e P = 1
1345268910711
ll
k
Inf. line Z 1
(factor l^2 /EI)
0.0160.028
0.024
0.0320.024
0.0320.0280.016

+

Fig. 10.11 (a,b) Design diagram of the beam and primary system. (c) Bending moment diagram

caused by unit primary unknown and calculation ofr 11 .(d) Calculation ofr1P.(e) Continuous

beam. Influence line for primary unknownZ 1

3.Influence line of primary unknownZ 1 is obtained according to formula (10.17):
all ordinates of influence line forr1P(Table10.3) should be divided by

r 11 D6.EI=l/:

Corresponding influence line forZ 1 is presented in Fig.10.11e; all ordinates

must be multiplied by parameterl^2 =EI.