flexibility method structural analysis examples pdf

This means that a point can move (translate) in the x-direction and y-direction, or can rotate about the out-of-plane z-axis (equivalent to rotating within the 2D plane). In two dimensions (2D), each free point on a structure has three different possible DOFs: one horizontal, one vertical, and one rotational. A degree of freedom ( DOF) is simply a single direction that a point on a structure can move freely.

Degrees of Freedomīoundary conditions are typically expressed in terms of applicable degrees of freedom. A displacement boundary condition that is zero is equivalent to the structure being held in place at that location. This would be a zero force boundary condition. For example, we may know that there are locations on our structure that have no external force. The known force or displacement may have some magnitude or it may be zero.

For a structural analysis problem to be solvable, every location on the boundary of our structure must have a known boundary condition, either a known force or a known displacement. In this way, boundary conditions are where the structure interacts with the environment either through the application of an external force or through some restraint that is imposing a displacement. >When you're done reading this section, check your understanding with the interactive quiz at the bottom of the page.Ī boundary condition is a place on a structure where either the external force or the displacement are known at the start of the analysis.

Flexibility method structural analysis examples pdf