This simulator places two identical round members side by side, one pulled as a tie and one pushed as a pinned column, and ramps the same axial load into both. It shows that equal and opposite loads do not have equal consequences: the tie simply stretches, while the column can go unstable.
• A 3D tension tie and pinned-pinned compression column with end fixtures and an explanatory first buckling mode. • Four sliders: target axial load (1-80 kN), member length (0.5-3 m), solid diameter (15-60 mm) and Young's modulus (50-220 GPa). • Six live readouts: current load, axial stress magnitude, tie elongation, Euler critical load, P/Pcr and slenderness (L over radius of gyration). • Two presets: Long slender column (compression passes the Euler threshold early) and Diameter effect (doubling diameter raises I and the Euler load 16 times).
For a circular section A = pi d2 / 4 and I = pi d4 / 64. Axial stress is sigma = P / A and elongation is delta = P L / (A E), and these apply to both members. For the pinned-pinned column the Euler load is Pcr = pi2 E I / L2, and slenderness is L / sqrt(I / A). When P/Pcr approaches 1 the column becomes laterally unstable long before the material stress is high, which is the central contrast with the tie.
Loads ramp over 5 s under a small-strain linear axial response with ideal Euler buckling; there is no yielding and no post-buckling equilibrium. Euler is most meaningful for slender elastic columns, so short-column results are only formal comparisons. The bow amplitude and deformations are magnified for visibility and are not predicted by Euler theory. Sweep length at fixed diameter and watch P/Pcr climb as L grows.
Because a slender member can buckle sideways. Buckling is an instability governed by stiffness, length and end conditions, not by the stress reaching yield.
It compares the applied compressive load with the Euler critical load. Values well below 1 mean the ideal column is stable; values approaching 1 mean it is near its buckling threshold.
The second moment of area scales with diameter to the fourth power, so doubling the diameter multiplies I and the Euler load by 16 at the same length and modulus.
No. Euler buckling gives the critical load and mode shape, not the deflection amplitude. The bow in the drawing is an explanatory visual only.