Buckling reduction factor φ (χ)

A long compressed member — a truss leg or brace — buckles before its stresses reach yield. So its resistance is multiplied by a factor below one that depends on the relative slenderness λ̄ (length, section and steel).

For tubes under DBN V.2.6-198:2014 the factor φ comes from formulas (8.4)–(8.5). Solispec puts a closed bent-and-welded tube on curve b (α = 0.04, β = 0.09, Table 8.1):

At λ̄ ≤ 0.4, φ = 1, so a short member works at full strength; for curve b at λ̄ > 4.4, φ is at most 7.6/λ̄². For compression with bending the DBN gives a separate factor φ_e from Table Ж.3.

For a C-profile the same idea is χ under EN 1993-1-1:2005 (cl. 6.3.1.2, eq. 6.49), with curve b (α = 0.34, Table 6.1), but computed for the effective section. The simplest way to reduce slenderness is a shorter free length: an extra brace or tie.

How this applies to a PV truss. The compressed members of a ground truss are the legs and braces under snow, and under wind from below some members change the sign of their force. The buckling lengths in and out of the truss plane differ, since trusses are tied to each other only by the rails, so the engine checks both. An extra brace or tie shortens the free length, which directly raises φ. The Solispec constructor shows each member's utilisation and the governing check, so you can see where the truss lacks stability.

The Solispec engine computes φ and φ_e for every tube member of the truss (phiDbn, phiE) with in-plane and out-of-plane lengths. For the C-profile it computes χ per EN 1993-1-1:2005 on the effective section, for flexural, torsional and flexural-torsional modes, and shows each member’s utilisation in the report.

Solispec constructor