Learning topic
Hinged Multispan Beams
Analyze statically determinate Gerber beams using the structural hierarchy, sequential equilibrium, support reactions, and shear-force and bending-moment diagrams.
A hinged multispan beam consists of several beam segments connected by internal hinges. A suitable arrangement of hinges produces a geometrically stable, statically determinate structure spanning several bays.
Internal hinge
An internal hinge transfers forces between adjacent parts but does not transfer bending moment. Therefore, unless an external couple is applied directly at the hinge, $M=0$ there. This condition allows the compound structure to be separated into individual free bodies.
Structural hierarchy
It is useful to identify which beam segments are supporting components and which are suspended from them. This relationship is often represented by a hierarchy or storey diagram. Analysis begins with the suspended components, whose reactions are then applied as loads to the supporting components.
Analysis sequence
Equilibrium is applied to each component to determine reactions, after which shear and bending-moment diagrams are constructed. Interaction forces at an internal hinge are equal in magnitude and opposite in direction on the two connected parts.
Checks
In addition to equilibrium of individual components, verify equilibrium of the complete beam. The bending-moment diagram must pass through zero at unloaded internal hinges, and force transfer between structural levels must satisfy action and reaction.
About this topic
This topic covers hinged multispan or Gerber beams, static determinacy, structural hierarchy diagrams, sequential support-reaction calculations, and internal-force diagrams.