In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems.

Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, but they have also been developed for the study of the mechanics of deformable bodies.Ĭastigliano's method įlexibility method The work of a force on a particle along a virtual displacement is known as the virtual work. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action, and, therefore, is the one followed by the particle by the principle of least action. The work of a force acting on a particle as it moves along a displacement will be different for different displacements. Virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. Influence line is defined as the function which shows the variation of a structural quantity (shear force, bending moment, deflection etc.) due to the change in the position of unit load. The direction of the force at its point of application and k is the elastic stiffness of the part,Īgain in the direction of the force at its point of application. 2k where F is the applied force, x is the distance moved in

Work done by external forces equals the energy stored in the structure under load. These are methods based on linear elastic behavior and conservation of energy, i.e. In general, a rigid body in d dimensions has d(d + 1)/2 degrees of freedom (d translations and d(d −1)/2 rotations), 2 directions combine to 1 rotation, therefore use Binomial coefficient to determine number of rotations. In three dimension space, single part of structure have 3 displacements and 3 rotations. In two dimension space, single part of structure have 2 displacements and 1 rotation. Finally, subtract the number of equilibrium equations from the unknown forces to find the degrees of indeterminacy.ĭegrees of freedom This number is found by taking the number of joints and multiplying by 2 (two equations of equilibrium per joint). Second, count the available equations of equilibrium. This is the number of members (a single axial force for each member) summed with the number of unknown reaction forces. If you are looking at a truss, the first step is to count the number of unknown forces. When analyzing structural models, the first question to ask yourself is whether the system is determinant or indeterminate.

Calculate degree of freedom mechanics