Concentrated momentS does not jump, M jumps

Why? (30 seconds)

• M₀ does not push the beam up or down — it only rotates it → it has no place in ΣFy or in the S diagram.
• It is already 'force × lever arm' → it enters ΣM as it is, about any point you choose.
• Whoever passes the point in the M diagram 'feels' the whole rotation at once → a jump.

A 6 m beam — with only a moment on it

• ΣMA
  6 − BY·6 = 0 → BY = 1 t upward
• ΣMB
  AY·6 + 6 = 0 → AY = −1 t — the minus: AY acts downward
• Check
  −1 + 1 = 0 ✓
• S
  AY downward → −1, a straight line to the end — M₀ does not move S → BY closes to 0
• 0–2
  Rectangle −1 · 2 = −2 → M = −2
• x = 2
  M₀ clockwise → −2 + 6 = +4 jump
• 2–6
  Rectangle −1 · 4 = −4 → 4 − 4 = 0 closes ✓

That's it. A reaction that pulls down, a completely flat S — and one jump in M.

And where is Mmax? There is no Z — S does not cross 0. The extreme values sit on both sides of the jump: −2 on the left, +4 on the right. The largest in magnitude: 4 t·m.

4 pitfalls

• M₀ times a distance in ΣM. It is already a moment — it goes in as it is.
• A jump in S. M₀ does not change S at all.
• 'Fixing' the minus of AY. The minus tells the direction — flip the arrow and keep the magnitude.
• A jump in the opposite direction. Clockwise = +M₀.