Buigmomentdiagram

Buigmomentdiagram, literally bending moment diagram in Dutch, is a graphical representation of the internal bending moments along a beam under a given set of loads and boundary conditions. It plots the bending moment M as a function of position x along the member, and is commonly used in structural analysis and design. The diagram is typically drawn for a beam with the origin at one end; units are kN·m or N·m.

Construction: For statically determinate beams, reactions are found by equilibrium, then the shear force diagram V(x) is drawn and the bending moment diagram M(x) is obtained from dM/dx = V(x). M is zero at simply supported ends; maxima occur where V(x) crosses zero. Point loads yield piecewise linear V(x) and piecewise quadratic M(x); distributed loads yield curved segments.

Sign convention: In many civil engineering texts, a positive bending moment indicates sagging (beam concave up, top fibers in compression, bottom fibers in tension). Negative moment indicates hogging (concave down). Some documents use alternate conventions, so the sign should be checked against the local standard.

Interpretation and use: The maximum M is used to check strength with the section modulus and material properties. M relates to curvature κ ≈ M/(EI). Inflection points occur where M = 0. For indeterminate beams, M is found with methods such as Clapeyron's theorem of three moments, slope-deflection, force method, or finite element analysis, then plotted.

Practical notes: The diagram shows supports, spans, loads, and units, with indications of positive/negative moments. It is essential for sizing sections and code compliance in beam design.

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