Advanced Methods of Structural Analysis

Problems 13

However, the assembly of the elements is wrong and therefore, this system can-
not be considered as engineering structure. Indeed, the left and right rigid disks
(shown by solid) are connected bytwoelements 1 and 2. Therefore, this structure
is geometrically changeable.
Let us return to Fig.1.12. The system contains members with hinges at ends. The
number of joints isJD 6 , the number of members isSD 8 , and the number of
support constraints isS 0 D 3. Degrees of freedom of the system is calculated as for
truss, i.e.,WD 2  6  8  3 D 1. (The Chebushev formula leads to the same result,
i.e.,W D 3  8  2  10  3 D 1 , where 10 is a total number ofsimplehinges). There-
fore, the system does not have a required minimum of elements in order to provide
its geometrical unchangeability, and cannot beused as engineering structure. This
system is geometrically changeable, because two rigid discsACDandBEFare con-
nected incorrectly, i.e., bytwomembers 3 and 5. In other words, this system contains
the hinged four-bar linkageCDEF. Therefore, ifone morerigid element would be
introducedcorrectly, then system would become geometrically unchangeable. Such
additional element may connect jointsCandEor jointsDandF.

Problems

1.1.Perform the kinematical analysis of the following design diagrams:

a b c d

Fig. P1.1

a

A B

b

A B

c

AB

d

A B

e

AB

f

A B

Fig. P1.2

a b c d

Fig. P1.3