[ehcrea]

Summary

Eren found the buckling animation odd. The sketch now follows the usual Euler-case figures:

• The column itself bends. It is drawn as a solid bar in the buckling mode, over a dashed straight reference axis. Before, a straight bar had a separate dashed curve next to it.

• End conditions are physically consistent.

  • The top support moves with the end when the end can slide sideways (free or guided).
  • The load acts on the top end itself, not on a fixed hatched ground.
  • A pinned or clamped top end is held sideways between two walls, and a guided end is a block that stays horizontal.

• Buckling length is marked. L_b = k·L is drawn as the half sine wave in the mode shape: the whole column for k = 1, the segment between the inflection points for k = 0.7 and 0.5, and "½·L_b, L_b = 2·L" for k = 2.

• The animation follows the physics.

  1. The load ramps up to F_b while the column stays straight.
  2. At F_b the column buckles smoothly.
  3. The load is removed and the column springs back.

  A caption names each stage and shows F as a percentage of F_b.

I couldn't load the illustrations on JPE's page from this environment (the image requests fail), so the depiction follows the standard Euler cases and the JPE table of buckling lengths.

Test plan

• npm test: 709 checks pass, including every animation phase for each end condition.
• Rendered all six end conditions in the browser, static and at the "straight" and "buckled" stages; no console errors.

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Generated by Claude Code