Advanced Methods of Structural Analysis

356 10 Influence Lines Method

Table 10.7

Comparison of the force and displacement methods for construction of influence linesComparison criteria

Force method

Displacement method

Primary system (PS)

Obtained by

eliminating redundant

constraints

from

a structure

Obtained by

introducing additional

constraints

to

a structure

Primary unknowns (PU)

Forces

(forces and moments), which

simulate

action

of

eliminated

constraints

Displacements

(linear and angular), which

neutralize

action of

introduced

constraints

Canonical equations in

general form

ı^11

X

C 1

ı^12

X

2

C

:::

C

ı1n

X

Cn



1P

D

0

ı^21

X

C 1

ı^22

X

2

C

:::

C

ı2n

X

Cn



2P

D

0



Number of canonical equations equals to

the number of PU

r^11

Z

C 1

r^12

Z

2

C

:::

C

r1n

Z

n

C

R

1P

D

0

r^21

Z

C 1

r^22

Z

2

C

:::

C

r2n

Z

n

C

R

2P

D

0

Number of canonical equations equals to

the number of PU

Canonical equations in case

of unit moving loadP

D

1

ı^11

X

C 1

ı^12

X

C 2

:::

C

ı1n

X

n

C

ı1P

D

0

ı^21

X

C 1

ı^22

X

C 2

:::

C

ı2n

X

n

C

ı2P

D

0



r^11

Z

1

C

r^12

Z

C 2

:::

C

r1n

Z

n

C

r1P

D

0

r^21

Z

1

C

r^22

Z

C 2

:::

C

r2n

Z

Cn

r2P

D

0



Features of coefficients and

free terms

ıik

are numbers;

ıiP

are functions of load location

rik

are numbers;

riP

are functions of load

location

Primary unknowns

X

are functions of load locationi

Z

are functions of load locationi