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The BST binders · Beams binder · S and M diagrams · updated 27.9.2026

M diagramThe area method, and Mmax at Z

M = the area under S, accumulated from left to right.

  • Rectangle b · h → diagonal line
  • Triangle b · h / 2 → parabola
  • Trapezoid (a + b) · h / 2 → parabola

In the rectangle and the triangle: b — the segment length, h — the height in S. In the trapezoid: a and b — the two heights in S, h — the segment length.

Mmax sits where S changes sign: at Z (when the crossing is on a diagonal line), or under a point force (when the crossing is at a jump).

  1. 01

    Why does it work? (30 seconds)

    • Every segment in S is an area. The area = how much M changed in that segment.
    • Area above the axis → M grows. Below → it drops.
    • S changes sign → the areas change sign → M stops growing → that is where the maximum is.
    • In BST, positive M is drawn below the axis.
  2. 02

    The same beam — 4 areas

    2 t/m6 tAY = 6.5 tBY = 7.5 t2 m2 m4 mSZ6.50.5−7.5MZ13Mmax = 14.06
    Beam, S and M — the same x axis. Positive M is drawn below the axis, as in BST · scroll the drawing sideways
    • 0–2
      Rectangle 6.5 · 2 = 13 → M = 13 (diagonal line)
    • 2–4
      Rectangle 0.5 · 2 = 1 → M = 14 (diagonal line)
    • 4–Z
      Z = S / Q = 0.5 / 2 = 0.25 m → x = 4.25 · triangle 0.25 · 0.5 / 2 = 0.06 → Mmax = 14.06 t·m (parabola)
    • Z–8
      Triangle below the axis 3.75 · 7.5 / 2 = 14.06 → 14.06 − 14.06 = 0 closes ✓

    That's it. Four areas, and M closes at 0 at the support — exactly as it should.

    A concentrated moment? M₀ → a jump in M of size M₀, at the point where it acts: clockwise +M₀, counter-clockwise −M₀. In S it changes nothing.

    And if there is no Z? When S crosses 0 at a jump — under a point force — there is no diagonal line to cross. Mmax sits exactly at the point of the force.

  3. 03

    4 pitfalls everyone falls into

    • A diagonal line under a trapezoid. Trapezoid = parabola.
    • Calculating M only at the load points. The positive Mmax can sit at Z — in the middle of a segment. Calculate there too.
    • Forgetting the sign. An area below the axis lowers M.
    • M does not close at 0 — and carrying on. The mistake is in S or in the reactions. Go back.

Beams binder · BST · beamsolvertool.com/en/learn/beams/moment-diagram/

Draw M in BST BST builds the M diagram by the area method and finds Mmax

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