Advanced Methods of Structural Analysis

3.1 Multispan Statically Determinate Beams 41

1

1

2

2

1

1

2

2

Fig. 3.3 Interaction schemes for simplest Gerber–Semikolenov beams

Five-span beam and its interaction diagram is presented in Fig.3.4. Since the
structure in a whole is restricted againstthe horizontal displacement owing to sup-
portA, then each part of the structure has no displacement in horizontal direction
as well. That is why the rolled supportsCandEon the interaction diagram are re-
placed by pinned supports. Restrictions for suspended beams also prevent horizontal
displacements. This replacement is conventional.

AB C D E F

H 1 H 2 H 3 H 4

Fig. 3.4 Interaction diagram of Gerber–Semikolenov beam

BeamsABH 1 andH 1 H 2 present the main and suspended beams, respectively.
It means that collapse of the main beamABH 1 leads to the collapse of suspended
beam, while collapse of suspended beam does not affect on the main beam. Collapse
of the beamH 4 EFleads to the collapse of the beamH 3 H 4 only, and does not affect
on other parts of the structure.
The entire structure contains five discs, four simple hinges, and seven constraints
of supports. Degree of freedom of the structure is

WD3D2HC 0 D 3  5  2  4  7 D0;

so entire system is statically determinate and geometrically unchangeable structure.
On the other hand, in general case of loads there are seven reactions of supports
arise in the structure. For their calculation we can use three equilibrium equations
and four additional conditions, i.e., bending moment at each hinge is equal to zero.
Therefore, the structure is statically determinate one.
Another four-span beam and its interaction diagram is presented in Fig.3.5.
The entire structure contains four discs, three simple hinges, and six constraints
of supports. Degree of freedom of the structure is

WD3D2HC 0 D 3  4  2  3  6 D0;