Influence Lines in Hinged Multispan Beams

In hinged multispan beams, a moving load may act on one component while the response of interest occurs in another. Influence-line construction therefore relies on the structural hierarchy and on force transfer through internal hinges.

Structural hierarchy

First identify supporting and suspended beam components. When the unit load is on a suspended member, that member's reactions are transmitted to lower supporting members as concentrated forces. The effect of the moving load therefore propagates through the structural hierarchy.

Piecewise construction

Within each component of a statically determinate system, influence-line ordinates follow equilibrium relations and are often linear. Values at supports, hinges, and ends of suspended members define the characteristic segments of the complete influence line.

Transfer through a hinge

An internal hinge does not transmit bending moment but does transmit force. A load on one beam segment can therefore influence reactions and internal forces in another through the hinge force. The spans cannot always be analyzed as independent beams.

Verification

Place the unit load at several characteristic positions and calculate the selected response independently from equilibrium. These values should match the ordinates of the constructed influence line.