Loads and Supports

Structural analysis begins by defining the external actions and restraints. Loads and supports are transferred to a calculation model that preserves the mechanically important features of the real structure.

Main load types

• Concentrated force — an idealized force acting at a point or over a region whose dimensions are negligible at the scale of the model.
• Concentrated moment — an idealized couple producing a moment without a resultant force.
• Distributed load — an action distributed along a length, over a surface, or another geometric region and described by an intensity.
• Body forces — forces acting throughout the material volume, such as gravity or inertia forces.

Variation with time

Loads may be static or time-dependent. When inertia effects are negligible, a quasi-static model may be used. Impact, vibration, and other rapidly varying actions can require dynamic analysis.

Supports and reactions

A support models a connection between a structural element and another part of the structure or its foundation. It prevents selected translations or rotations. Each independent restrained motion is associated with a corresponding unknown reaction component.

In a planar problem, a rigid body has three independent possible motions: translation along $x$, translation along $y$, and rotation in the plane. The support type determines which of these degrees of freedom remain possible.

Roller support

A roller support restrains translation in one direction while allowing motion along the supporting surface and allowing rotation. For an ideal smooth surface it produces one reaction normal to that surface.

This model is commonly used for movable beam supports. An important purpose is to avoid unnecessary restraint, for example by permitting longitudinal movement caused by deformation or thermal expansion.

Pin support

A pin support restrains translation of the supported point in two independent planar directions but allows rotation about the pin. It therefore produces two reaction components, commonly written $R_x$ and $R_y$ or $A_x$ and $A_y$.

An ideal pin does not transmit a reaction moment. The direction of the resultant reaction is not known in advance and follows from its components after solving the equilibrium equations.

Fixed support

A fixed support in a planar model restrains both translations and the rotation of the attached section. It therefore produces three reaction quantities: two force components $R_x$, $R_y$, and a reaction moment $M$.

The fixed end of a cantilever beam is modeled this way when the connection to the foundation is sufficiently rigid relative to deformation of the beam.

Two-force link

An ideal straight link pinned at both ends and carrying no intermediate loads transmits a force along its own axis. The reaction direction is therefore known in advance, while its magnitude and actual sense are determined from equilibrium.

Flexible cable or rope

An ideal flexible cable can transmit only tension along its axis. It cannot provide a compressive reaction; if the geometry and loading would require compression, the cable becomes slack and that restraint is no longer active.

Contact with a smooth surface

Without friction, a smooth surface produces only a normal contact reaction. It prevents penetration into the surface but cannot transmit tangential force. A frictional contact model may additionally include a tangential component.

Supports in three dimensions

A rigid body in space has six independent possible motions: three translations and three rotations. A fully fixed spatial support can therefore develop three force components and three moment components. Spatial pins, guides, bearings, and other restraints remove only the degrees of freedom prohibited by their mechanical construction.

Real connection versus ideal support

The name of a real connection does not by itself determine its mathematical model. Bolted, welded, bearing, and other connections may behave differently depending on geometry and stiffness. The engineer must determine which motions are effectively restrained and which forces or moments the connection can transmit.

Why the support model matters

An incorrect load direction, application point, distribution, or support model changes reactions and internal force resultants. Excessive restraints may make the model statically indeterminate, while insufficient restraints may leave it kinematically unstable. Selecting supports is therefore part of the physical problem definition, not merely a graphical convention.