Applications to Beam Problems and Mechanics Vocabulary

Vocabulary flashcards covering beam classifications, support types, loading conditions, and fundamental principles of statics from engineering mechanics.

Beam

A structural element which has one dimension (length) considerably larger than the other two dimensions in its cross-section, is supported at a few points, and is subjected to lateral loads.

Statically Determinate Beam

A beam in which all support reaction components can be found using the equations of equilibrium only.

Statically Indeterminate Beam

A beam in which the number of unknown support reaction components is greater than the number of available independent equations of equilibrium.

Simple Support

A support condition where the end of the beam rests simply on a rigid support, offering zero restraint to rotation and yielding a reaction always normal to the support.

Roller Support

A support condition where the beam end rests on rollers, offering no resistance to motion along the line of support or to rotation, resulting in a reaction always normal to the support.

Hinged Support

A support where the position of the beam end is fixed but free to rotate, represented by reaction components in two mutually perpendicular directions and offering zero moment resistance.

Fixed Support

A support condition where the beam end is prevented from both translation and rotation, developing reaction forces in mutually perpendicular directions alongside a resisting moment.

Cantilever Beam

A beam fixed at one end and free at the other end, having three reaction components ($V_A$, $H_A$, and $M_A$) at the fixed end and none at the free end.

Simply Supported Beam

A beam supported simply at both ends, developing one reaction component at each end acting normal to the beam axis.

Overhanging Beam

A beam that projects beyond its support or supports on one side or on both sides.

Propped Cantilever

A beam fixed at one end and simply supported or supported on rollers at the other end, possessing four total reaction components ($V_A$, $H_A$, $M_A$, and $R_B$).

Continuous Beam

A beam having three or more supports, resulting in three or more reaction components.

Concentrated Load

A load acting over a very small length compared to the span of the beam, approximated and represented as a point load.

Uniformly Distributed Load (UDL)

A load having constant intensity over a considerable length, which can be modeled for overall equilibrium as a single load acting at its midpoint.

Uniformly Varying Load

A load whose intensity increases linearly along the beam length, often taking a triangular shape when starting from zero intensity.

Moment of a Force

The measure of the rotational effect of a force about a point, calculated as the product of the magnitude of the force and the perpendicular distance from the point to the line of action.

Varignon's Theorem

A theorem stating that the sum of moments of a system of coplanar forces about a moment centre is equal to the moment of their resultant about the same moment centre.

Couple

Two parallel forces equal in magnitude but opposite in direction separated by a definite distance $d$, producing a moment $M = Fd$ about any point.