Advanced Methods of Structural Analysis

332 10 Influence Lines Method

whereICcorresponds to the highest point of the arch (crownC); this law corre-
sponds to increasing the moment of inertia from crown to supports. It is necessary
to construct the influence lines for reactions of the supportAand bending moment
at the crownC.

dx = dscosj

dx

ds

jdy

X 1

X 2

X 3

X 2

P= 1

X 1

C

Primary system

x

ay b

l

f

P= 1

x

a=ul

y

IC

Ix

A B

C

jx

Inf. line RA

1.0000.9930.9720.9300.8960.8440.7840.7180.6480.5760.5000.4250.3520.2820.2160.1560.1040.0610.0280.007

+

d

Inf. line MA

(factorl)

0.03950.06070.06780.06400.05280.03680.0184

0.01740.03120.04180.04800.04980.04730.04100.03200.02150.01130.0032

−

+

e 0.4l^ 0.6l

Inf. line MC

(factorl)

+

− −

0.00160.00520.00900.01200.01270.01020.0034

0.00800.02460.04680.02460.0080

0.00340.01020.01270.01200.00900.00520.0016

0.132l 0.132l

f

Inf. line H

(factor l/f)

0.00850.03050.06100.09600.13200.19400.21600.22950.23440.22950.21600.19400.16540.13200.09600.06100.03050.0085

+

c

0.1654

u=0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

A

P= (^1) C
RA
ul
H B H
f
l/ 2 l/ 2
MA MB
0.1l
RB
Fig. 10.6(a,b) Parabolic arch with clamped ends. (a) Design diagram; (b) Primary system. (c–f)
Parabolic non-uniform arch. Design diagram and influence lines