Advanced Methods of Structural Analysis

174 6 Deflections of Elastic Structures

In fact the formula (c) is expression (6.18) in the expanded form. The required

horizontal displacement at pointKequals

D 1 0:02C0:50:03C 7 0:01D0:065m: (d)

The positive sign for required displacementmeans that the direction of real

horizontal displacement of the pointKcaused by settlements of supportAand

direction of unit loadXare same.

Example 6.12.The telescope mirror is placed on the inclinedCDelement of the

truss (Fig.6.17). Determine the angle of rotation of the support barCDdue to the

vertical settlements of supportsAandB: 1 D0:02m, 2 D0:03m.

d 0 = 5

A

D

B

3m

4m 4m

C

RB

A

D

B

3m

P = 0.2

P = 0.2

C

C ¢

A ¢ B ¢ A ¢ B ¢

D ¢

X =1

D 1 D 2 D 1 D 2

qCD

RA

Fig. 6.17 Design diagram of a truss and unit states

Solution.1.For required angle of rotationCDwe have to apply unit coupleXD 1

to the barCD. This couple is presented as two forcesPD1=d 0 D0:2,where

d 0 is the length of the barCD. Reaction of the supports caused by two forces

PD0:2are:

RB!

P

MAD 0 W RB 4 0:2dD 0 !RBD0:25;

RA!

P

YD 0 W RADRBD0:25:

2.Application of principle of virtual displacements leads to following expression

XCDCRA 1 RB 2 D0: (a)