Roller Support
Structural Engineering
Definition
Roller Support (مسند حركي أو مسند دحروجي rulleopplager )
A roller support restrains translation normal to the contact surface while allowing translation tangential to the surface and rotation. Therefore, in a 2D idealized model, it imposes one kinematic constraint and is associated with one reaction force normal to the contact surface.
- Provides one reaction force, perpendicular to the surface.
- Allows tangential translation.
- Allows rotation.
- Does not resist a moment.
Sole Reaction
A roller support imposes one kinematic constraint because it restrains translation in only one direction: normal to the contact surface.
\[\boxed{\text{One constrained DOF} \rightarrow \text{One associated reaction}}\]
The reaction may be nonzero or zero depending on the loading condition.
Absence Of Tangential Reaction
A roller support does not restrain translation parallel to the contact surface.
Therefore, there is no reaction force associated with tangential translation.
In an ideal frictionless roller support:
The absence of \(R_x\) is not because the horizontal reaction happens to have a zero value; rather, there is no horizontal kinematic constraint in the idealized support model.
The absence of Reaction Moment
A roller support allows the structure to rotate about the support:
\[\theta\neq0\]
Therefore, rotation is not restrained, and there is no reaction moment associated with rotational restraint.
For an ideal roller support:
\[\boxed{M=0}\]
Thus, in a 2D model on a horizontal surface, the roller support has one restrained DOF and one associated reaction force:
\[\boxed{u_y=0\quad\longleftrightarrow\quad R_y}\]
while:
\[\boxed{u_x\text{ is free},\qquad \theta\text{ is free}}\]
Inclined Surface
The reaction force of an ideal roller support acts normal (perpendicular) to the contact surface, rather than necessarily in the vertical direction.
The restrained DOF is therefore translation normal to the surface:
\[u_n=0\]
and the associated reaction is:
\[R_n\]
The structure remains free to translate tangentially to the surface and to rotate.
If the reaction force is resolved into Cartesian components, \(R_x\) and \(R_y\), these components are not independent reactions. They are simply the two components of the single reaction force \(R_n\).
Therefore:
\[\boxed{\text{One constraint}\rightarrow\text{one reaction force}}\]
even when that reaction force is represented by multiple Cartesian components.
Ideal and Non-ideal Roller Support
An ideal roller support imposes one kinematic constraint and is therefore associated with one normal reaction force.
In reality, a roller support is not perfectly ideal. There may be friction, rolling resistance, and deformation at the contact region. As a result, the support may develop a resistance to tangential motion.
In addition to the normal reaction force,
\[R_n\]
a tangential reaction force may therefore develop:
\[R_t\]
Thus, the total contact reaction can be represented as:
\[\vec{\mathbf{R}}=R_n\vec{\mathbf{n}}+R_t\vec{\mathbf{t}}\]
However, the presence of a tangential reaction does not necessarily mean that tangential motion is completely restrained. This depends on the friction or contact model being used.
Therefore, the ideal and non-ideal models differ mainly in how the contact interaction is represented: the ideal roller is frictionless and has only a normal reaction, whereas the non-ideal roller may also develop tangential resistance due to friction and/or rolling resistance.
Rolling elements (such as balls, cylinders, or cones) between two concentric, grooved rings called races. The relative motion of the races causes the rolling elements to roll with very little rolling resistance and with little sliding.