Pin Support

Strucural Engineering

Definition

A pin support (pinned support, hinge support, hinged support مسند مفصلي leddopplager, boltopplager) restrains translation in two directions but allows rotation.

In a 2D model, there are three degrees of freedom:

\[\quad u_x\]

\[\quad u_y\]

\[\quad \theta\]

The pin support imposes:

\[\boxed{u_x=0}\]

\[\boxed{u_y=0} \]

\[\boxed{\theta\ \text{free}}\]

Therefore:

\[ \boxed{\text{2 constrained DOFs + 1 free DOF}}\]

Associated Reactions

Since there are two constrained translational DOFs, there are two associated reaction-force variables:

\[\quad R_x\]

\[\quad R_y \]

Thus:

\[\boxed{u_x=0\longleftrightarrow R_x} \]

\[\boxed{u_y=0\longleftrightarrow R_y}\]

Rotation is not restrained, so there is no associated reaction moment:

\[ \boxed{M=0}\]

Important Point

The existence of \(R_x\) and \(R_y\) as reaction variables does not mean that their values must be nonzero.

Therefore:

\[\boxed{\text{Pin Support}\rightarrow \text{2 kinematic constraints}\rightarrow \text{2 associated reaction forces}}\]

The directions of \(R_x\) and \(R_y\) in a free-body diagram are assumed initially. Their actual signs and magnitudes are determined by the equilibrium equations.