Advanced Methods of Structural Analysis

172 6 Deflections of Elastic Structures

Ta b l e 6. 4

Determination of displacements due to se

ttlements o

f support

Displacement of the joint

K

(Fig.

6.15

c)

Angular displacement



1

Vertical displacement



2

Horizontal displacement



3

The frame under unitload which correspondsto required displacement

A B

X^1

=^1

R^1

X^2

=

1

R^2

A B

X^3

=

1

R^3

A B

Reaction at support

B

in

direction





R

1

D

1 l

R

2

D

1

R

3

D

1

h l

Expression (

6.18

)



1

D

R

1



D





 1 l



D

l



D 2

R

 2

D

.

1/

D





3

D

R

3



D





1

h l





D

hl

In all cases the negative sign for reaction means that real direction of the reaction

R

in unit state

and settlement



are oppositely directed.

The positive results for required



means that unit loadi

X

on the displacement



perform the positive worki