Buckling

Why a slender member in compression can fail before it ever runs out of strength, and how to check for it in Truzme.

Quickstart

1. Open a truss and calculate it as usual.
2. In the Utilisation panel, find the Max buckling chip and turn its switch on.
3. Any member close to buckling shows up there, with a percentage and a red/amber/teal bar — 100% means it would buckle under the current load.
4. Click DETAILS on the chip to see the numbers behind the check for that member, or hover the ⓘ next to a value for its formula.
5. Switch the canvas to the Buckling diagram mode to see every member's percentage at once, not just the worst one.

What it is

A member doesn't only fail by running out of material strength. A long, slender member in compression — being pushed together from both ends — can suddenly bow sideways and give way well before the material itself would tear or crush. That's buckling, and it's a different failure mode from the strength check: a short, stocky member can carry a compression force all the way up to its material limit, while a long, thin member carrying the exact same force can buckle long before it gets there.

Buckling only applies to members in compression. A member in tension — being pulled apart — is being straightened out, not pushed sideways, so it can't buckle.

The formula

Truzme checks buckling with the classic Euler formula for the compression force a member can carry before it buckles, its critical load:

Ncr = π² · E · I_min / (K · L)²

• E — the material's stiffness (modulus of elasticity). A stiffer material resists buckling better.
• I_min — the cross-section's smallest moment of inertia. A member buckles about its weakest axis, so the smallest one is what matters, not the average. For the built-in shapes (round, tube, rectangle, hollow rectangle), Truzme computes it automatically from the dimensions you enter in the section editor. For a custom section, there are no dimensions to compute it from, so you enter I_min yourself.
• L — the member's length. Buckling resistance drops off sharply as a member gets longer — doubling the length cuts the critical load to a quarter.
• K — the effective length factor, which accounts for how the member's ends are held (pinned, fixed, free, …). Truzme currently fixes K at 1, the value for a member pinned at both ends.

The check itself is a simple ratio of the actual compression force to that critical load:

u = |Nx| / Ncr

Nx is the member's internal axial force (negative in compression); Ncr is always positive, so the absolute value is what's compared. u ≥ 1 means the compression force has reached the critical load — the member could buckle.

Behavior notes

Opt-in, like strength. Buckling and strength are two separate checks, each with its own switch in the Utilisation panel, both off by default. Turning one on doesn't affect the other.

Two checks, one governing member. With both switches on, a Governing badge shows which check is currently closer to failing — strength and buckling can easily point at different members, since a member can be strong but slender, or thick but overstressed.

Compression-only. A member in tension always shows as fine on the Buckling chip and diagram — buckling has nothing to say about it.

K is fixed for now. Truzme doesn't yet let you set the effective length factor per member — every member is treated as pinned at both ends (K = 1), which is the conservative, typical assumption for a truss.