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)