A pin effectively restrains the structure in place at the support point, but allows it to rotate around that point. The second common type of support shown in Figure 1.5, a pin, restrains two DOFS, both of the translation directions. Since there is one restrained DOF, there is also one reaction force at a roller support which is in the same direction as the restraint. There are two ways of showing a roller, either as a circle, or as a triangle supported on smaller circles, they both mean the same thing. The roller allows translation parallel to the roller support plane and also allows rotation at that point. The first type, a roller, can only restrain the structure in one DOF, the DOF that is perpendicular to the rolling direction, as shown. The three most common types of supports in 2D are shown in Figure 1.5. This force is called the reaction force or reaction. At these restraint locations, we know that the displacement of the structure in each restrained degree of freedom is zero however, we don't know what force is necessary to hold the degree of freedom in that restrained position. These restraints are also called supports. The most common displacement boundary conditions in structural analysis are those that restrain the movement of the structure in one or more degrees of freedom at a point.
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In three dimensions (3D), each free point has six DOFs, three translational and three rotational as shown in Figure 1.4. These are the same three directions that were previously used for the equilibrium expressions in equation \eqref 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.
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