dreiemomentbehov

Dreiemomentbehoev is a term used in structural engineering to denote the requirement to account for three bending moments at consecutive supports in the analysis of a statically indeterminate continuous beam. The word is a composite from elements meaning three, moment, and need or requirement, and appears in some German- and Dutch-language texts to describe the same concept as the three-moment theorem.

The theoretical basis is Clapeyron's theorem of the three moments, which establishes a linear relation among the bending moments at three successive supports of two adjacent spans for a prismatic beam. Given the spans’ lengths, the flexural rigidity EI, and the loads on the spans, the equation links the unknown moments M1, M2 and M3. Solving the three-moment equation with appropriate boundary conditions yields the support moments and the internal moment distribution along the beam.

In practice, the dreiemomentbehoev concept is used to address redundancy in continuous-beam analysis, where simple support reactions are insufficient to satisfy deformation compatibility. It emphasizes incorporating the continuity of moment distribution at internal supports and the overall compatibility of the structure, rather than treating spans in isolation.

Terminology: in English-language literature the standard terms are “three-moment theorem” or “Clapeyron’s theorem of the three moments.” The hyphenated term dreiemomentbehov is uncommon outside some German- or Dutch-language references, and readers may encounter the more widely used English terminology in many texts.

See also: Clapeyron's theorem of the three moments; Three-moment equation; Continuous beam; Structural analysis.