Advanced Methods of Structural Analysis

340 10 Influence Lines Method

P= 1

d=4m

3m

a

Design

diagram

X 1

P= 1

123

0 6

4 5

b

Primary

system

d 1 P

1 ′ 2 ′ 3 ′ 4 ′ 5 ′

d 1 P = d 1 P

dP (^1) d 1 P X 1 =1
c P= 1
Unit state
X 1 =1
+1.333 +1.333 +1.333 +1.333

• 
  
  
  
  0. 666 – 0. 666 – 1.333 –1.333 – 0. 666 – 0. 666
  
  
  
  

0.5 0.5

+0.833

–0.833

–1.0

+0.833 +0.833 –0.833

+0.833

N

d

–1/3

–0.5

+5/12

0. 25 0.25 0.25 0. 25

+5/12

–1/3

N 1

1

e

0. 25 0.25 0.25 0. 25

+1/3 +1/3

−5/12 −5/12

+ 0. 25 + 0. 25

N 2

2

f

Fig. 10.10 (a,b) Design diagram of a statically indeterminate truss and primary system. (c)
Reciprocal displacements theorem. (d) Internal forcesNcaused by unit primary unknownX 1 D 1.
(e) Design diagram for calculation of the first elastic load. (f) Design diagram for calculation of
the second elastic load