State the conditions under which displacement method work
The displacement method is a structural analysis technique used to determine the displacements, member forces, and reactions in a structural system. It can be applied to solve problems in both statically determinate and indeterminate structures. However, there are specific conditions under which the displacement method works effectively:
1. Linearity: The displacement method assumes that the structural behavior can be adequately described using linear material properties, such as linear elasticity assumption for determining member stiffness.
2. Small Deformations: The method assumes that the deformations or displacements within the structure are relatively small. This assumption allows the deformation effects to be linearly related to the applied loads and the resulting forces.
3. Static Equilibrium: The analysis assumes that the structure is in static equilibrium, meaning that the sum of forces acting on each node or joint is zero, and the sum of moments about any point is also zero.
4. Rigid Joints: The method assumes that the joints or connections between the structural members are idealized as perfectly rigid, transmitting forces but not moments.
5. Displacement Compatibility: The method requires that the displacement compatibility condition is satisfied, meaning that the assumed displacement or deformation profiles along the members should match at the connected nodes.
6. Appropriate Boundary Conditions: Adequate boundary conditions must be enforced to restrict the structure's degrees of freedom, preventing rigid body motions and accounting for supports or restraints.
By meeting these conditions, the displacement method can provide accurate solutions for determining the internal forces and displacements in various types of structures.