Force method in structural analysis always ensures compatibility of deformation.

The force method, also known as the method of consistent deformations, is a technique used in structural analysis to determine the internal forces and deformations in a structure. It is based on the principle of equilibrium, which states that for a structure to be in a state of equilibrium, the sum of all the forces acting on it must be zero.

However, equilibrium alone is not sufficient to determine the internal forces and deformations in a structure. This is because a structure can be in equilibrium with an infinite number of configurations. To uniquely determine the internal forces and deformations, the force method also considers the compatibility of deformation.

What is compatibility of deformation?

Compatibility of deformation refers to the condition that the deformations of all the members of a structure must be compatible with each other. In other words, the deformations at the ends of each member must be such that they can be connected together without any gaps or overlaps.

Why is compatibility of deformation important?

Ensuring compatibility of deformation is important because a structure must be able to deform as a whole in a coordinated manner when subjected to external loads. If the deformations of the members are not compatible with each other, it can lead to excessive stresses, failure, and collapse of the structure.

How does the force method ensure compatibility of deformation?

The force method ensures compatibility of deformation by considering the deformation characteristics of the structure and applying appropriate constraints. These constraints are used to relate the displacements and rotations of different points in the structure, ensuring that the deformations are compatible.

The force method involves the following steps to determine the internal forces and deformations:

1. Assume a set of unknown forces at the supports of the structure.
2. Determine the displacements and rotations of the structure using the assumed forces and the known properties of the members.
3. Check the compatibility of deformation by comparing the displacements and rotations obtained from step 2 with the assumed displacements and rotations at the supports.
4. Adjust the assumed forces at the supports to ensure that the displacements and rotations are compatible.
5. Repeat steps 2-4 until the assumed forces and the displacements and rotations are compatible.
6. Once the forces and deformations are compatible, the internal forces and deformations in the members of the structure can be determined.

By ensuring compatibility of deformation, the force method provides a more accurate and realistic analysis of the structure, taking into account the interdependence of the deformations in different members. This leads to more reliable and efficient structural designs, ensuring the overall safety of the structure.