According to the PN-EN 1993-1-1 standard, the load-bearing capacity of compressed sections is calculated using the following formulas:
The load-bearing condition for a section uniformly compressed by a design axial force (NEd) according to the PN-EN 1993-1-1 standard:
\(\frac {N_{Ed}}{N_{c,Rd}} ≤ 1,0
\)
where:
- NEd – design axial force,
- Nc,Rd – design load-bearing capacity of the compressed section for class 1, 2, and 3 sections, calculated using the formula:
N_{c,Rd} = \frac { A \cdot f_y }{Ү_{M0}}
\)
In the case of class 4 sections, the design load-bearing capacity of the compressed section is determined according to the following formula:
\(N_{c,Rd} = \frac { A_{eff} \cdot f_y }{Ү_{M0}}
\)
where:
- A, Aeff – gross cross-sectional area and effective cross-sectional area (working),
- fy – yield strength of the steel,
- ҮM0 – partial safety factor ҮM0 = 1.0.
The load-bearing capacity of the compressed section according to the above formula should be calculated when the centroid of the effective cross-section – Aeff coincides with the centroid of the gross cross-section – A. In this case, the axially compressed section is a bisymmetric class 4 section. Otherwise, in the case of a monosymmetric or asymmetric class 4 section, it should be treated as a compressed section subjected to additional bending, with the moment calculated according to the following formula:
\(∆M_{Ed} = N_{Ed} \cdot e_N
\)
The above formula results from the displacement of the centroid of the effective cross-section by a value of eN relative to the centroid of the gross cross-section.
Literature:
[1] PN-EN 1993-1-1 Eurokod 3: Projektowanie konstrukcji stalowych – Część 1-1: Reguły ogólne i reguły dla budynków.
[2] A.Biegus “Projektowanie konstrukcji stalowych według Eurokodu 3.
