Method of sectionsOne member, one equation — Ritter cut

Why is it so fast? (30 seconds)

• Half a truss is a body in equilibrium — 3 equations: ΣFx, ΣFy, ΣM.
• 3 cut members = 3 unknowns. An exact fit.
• The magic: a moment about the Ritter point. The two other members pass through it — their lever arm is 0 and they vanish from the equation.
• In every cut member assume tension — the arrow leaves the part. Clockwise is +.
• The Ritter point can be outside the part you chose — a moment is taken about any point.
• A horizontal force: the lever arm = the vertical distance to the point. N4 above E pulls to the right → rotates about E clockwise → +N4·2.

3 members from the middle of the truss — 3 equations

The same truss as in the method of joints. Cut through N4, N5 and N6, and solve the left part: AY = 3 t and 4 t at D.

• N6
  N4 and N5 meet at D → ΣMD: 3·2 − N6·2 = 0 (the 4 t passes through D — lever arm 0) → N6 = 3 tension
• N4
  N5 and N6 meet at E → ΣME: 3·4 − 4·2 + N4·2 = 0 → N4 = −2 compression
• N5
  N4 and N6 are parallel (horizontal) — no Ritter point → sum of forces along the axis perpendicular to them: ΣFy: 3 − 4 − N5·0.707 = 0 → N5 = −1.414 compression

That's it. 3 members from the middle of the truss without going through a single joint — and exactly the same results as in the method of joints ✓

4 pitfalls everyone falls into

• Cutting 4 members. 4 unknowns, 3 equations — no solution.
• A cut that leaves one joint alone. That is the method of joints in disguise — it works, but saves nothing.
• Forgetting a force on the part. Every load and every reaction on the part you chose goes into the equation — and only they.
• Guessing a direction. Tension in every cut member, and the sign decides.

Bonus: Choose the part with fewer forces — fewer terms, fewer mistakes.