Learning topic
Kinematic Analysis and Geometric Stability
Learn how to assess geometric stability of framed structures using degrees of freedom, constraints, mechanisms, instantaneous instability, and kinematic analysis.
Kinematic analysis determines whether a framed system can preserve its geometric configuration without deformation of its members. A structural model needs not only enough constraints but also a suitable geometric arrangement of those constraints.
Degrees of freedom and constraints
A free rigid body in a plane has three independent motions: two translations and one rotation. Constraints remove selected degrees of freedom. For structures made of several members or rigid parts, both external supports and internal connections must be considered.
Geometric stability
A geometrically stable structure cannot change its configuration without deformation of its members. A triangle is the simplest stable planar pin-jointed form, which is why triangulation plays a fundamental role in truss stability.
Mechanisms and instantaneous instability
A system that can undergo finite motion without member deformation is a mechanism. An instantaneously unstable configuration is a special case in which an infinitesimal motion is possible because of a singular geometric arrangement of constraints.
Why counting is not enough
A model can contain the nominally required number of constraints and still be unstable if some constraints are dependent or improperly arranged. Numerical counting must therefore be supplemented by geometric inspection.
About this topic
This topic covers degrees of freedom and constraints, geometric stability of framed systems, mechanisms and instantaneously unstable configurations, and basic kinematic analysis.