Advanced Methods of Structural Analysis

10.1 Construction of Influence Lines by the Force Method 327

X 1 =1

M 1

0.4

1.0

k

0.4l

A

RA

l

1

= RC=^1 l

a

0.0320.0560.0640.048 0.0480.0640.0560.032

Inf. line d 1 P

(all ordinates must

be multiplied by

factor l^2 /EI

+ +

c

268910345 711

ul

P= 1

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

P= 1

ul ul

d 1 P d 1 P

d 1 P =

6

u−u^3 l^2

⋅EI EI

l^2

6 ⋅

d u−u^3

1 P =

A B C

1

b

ul

0.0480.0840.0960.072 0.0720.0960.0840.048

Inf. line X 1

(factor l)

−− −−

14568910711

P= 1

132

X 1

B

d

Fig. 10.2 (a) Bending moment diagram in primary system due toX 1 D 1 .(b)Locationofthe
loadPD 1 in the left and right span; (c) Influence line forı1P.(d) Primary system and influence
line for primary unknownX 1

Table 10.1 Calculation ofı1P(coefficientl^2 =EIis omitted)

PD 1 in the left span PD 1 in the right span

PointParameter ı1PD

uu^3

6

l^2

EI

Point Parameter ı1PD

^3

6

l^2

EI

1 .A/uD0:0 0.0 6 .B/ D1:0 0.0

2 uD0:2 0.032 7 D0:8 0.048

3 .k/ uD0:4 0.056 8 D0:6 0.064

4 uD0:6 0.064 9 D0:8 0.056

5 uD0:8 0.048 10 D0:2 0.032

6 .B/uD1:0 0.0 11 .C/D0:0 0.0