A number of independent parameters, which define configuration of a system without deformation of its members is called the degree of freedom. The number of degrees of freedom for any structure may be calculated by the Chebushev’ formula
where D, H, and S0 are the number of rigid discs, simple hinges, and constraints of supports, respectively. For trusses the degrees of freedom may be calculated by formula
where J and S are the number of joints and members of the truss, respectively. Special cases. There are three special cases possible.
1. W >0. The system is geometrically changeable and cannot be used in engineering practice.
2. W D 0. The system has the necessary number of elements and constraints to be geometrically unchangeable structure. However, the system still can be inappropriate for engineering structure. Therefore, this case requires additional structural analysis to check if the formation of the structure and arrangement of elements and constraints is correct. This must be done according to rules, which are considered above. For example, let us consider systems, which are presented in Fig. 1.13a–c.
Degrees of freedom W for these cases according to formula (1.2) equal to zeros. Indeed
