A tension member’s capacity is the cross-sectional area times the yield strength. Length never enters the formula. Put the same section under compression, and it fails at a fraction of that value, set by unbraced length, end restraint, and how straight the member came out of the mill. This article covers the path from axial force to verified capacity: slenderness, buckling mode, and cross-section class.
Compression Is Checked on the Whole Member
EN 1993-1-1 writes both checks in nearly the same form. Tension resistance is area times yield strength, divided by a partial factor. Compression resistance is that same product with a buckling reduction factor applied. Everything specific to compression lives in that one factor.
The reduction factor follows from the relative slenderness, which requires the Euler critical force, which depends on the second moment of area and the buckling length. Section properties come out of the shape tables.
Buckling length does not. An engineer assigns it from the end restraint conditions, and because it enters Euler’s formula squared, an error there propagates quadratically into the result.
A given profile therefore has no single compression resistance. It differs between the two principal axes, changes with the support scheme, and differs between rolled and welded sections of identical geometry, whose residual stress patterns are not the same.
Where the Axial Force Comes From
Beam type elements will always return N, which is one of the six components of internal forces per element. Shell or solid models, however, do not carry this value. Instead, they create a stress tensor field, and the axial force needs to be retrieved by integrating normal stresses over the cross section.
Bending affects the value of local stress, which corresponds to N/A at no given location on the cross section. Hence, there is no way to use the peak contour value to conduct a column check.
The definition is geometric in nature: an axial load acts along the axis of the centroid. Thus, the uniform distribution of σ = N/A can only occur if the force is applied directly at the centroid. It is unlikely that this occurs during real detailing.
If you have an angle connected by one leg or a gusset welded along one side of the brace axis, you will introduce eccentricity from the moment of the first load application. It will then act like a beam-column.
Slenderness Governs, Area Does Not
The slenderness ratio is found by taking the buckling length divided by the radius of gyration, which is equal to the square root of the second moment of area divided by the area. Since this ratio is a dimensionless ratio, the buckling charts in the code are based on this ratio, not the absolute dimensions of the sections.
The cross-sectional area has no meaning on its own in relation to compression resistance. For example, a 14 W x 48 section has a strong axis radius of gyration equal to 5.85 inches, and a weak axis radius of gyration, which is almost 3 times less, equal to 1.91 inches.
Thus, the critical buckling force relates to the square of this radius, leading to much lower buckling strength of the member in the weak plane compared with the strong plane, with the ratio of weak to strong plane strengths about equal to 9.
If braces are spaced differently between the two planes, the controlling plane for i.e. the one that must be checked for slenderness is the one with the larger slenderness ratio (not necessarily the one with the smaller second moment of area).
For built-up members there is a question of what constitutes a member. A built-up member acts as one member only to the extent that the lacing and battens forces the individual parts to deform together.
The Royal Commission investigating the collapse of the Quebec Bridge in 1907 found that the immediate cause of the failure was buckling of the lower compression cords which were each made of 4 layers of ribs. Testing done afterwards confirmed the sequence of failure with the lacing rivets shearing first followed subsequently by buckling of the chords as a whole.
Between Yielding and Euler
Stocky members fail by yielding. Very slender ones follow Euler. Most real steel members sit in the inelastic range between the two.
There, parts of the cross-section yield before the member becomes unstable. Residual stress explains it: rolled shapes cool unevenly, and welded sections add shrinkage at the web-to-flange welds.
External compression stacks onto the residual compression already locked into the flange tips, those fibers yield first, and stiffness drops well before the average stress over the section reaches yield. F. R. Shanley showed in 1947 that lateral deflection starts at the tangent modulus, already below the elastic modulus by that stage.
The gap is measurable. At a relative slenderness of 1.0, the Euler critical force equals the squash load exactly. EN 1993-1-1 curve b gives a reduction factor of 0.60 at that point, and AISC 360 gives 0.66. An idealized elastic formula would therefore overstate capacity by 68% and 52%, respectively.
AISC sets the boundary between the inelastic and elastic branches at a slenderness of 4.71√(E/Fy), which is KL/r of about 113 for A992 steel. Sensitivity to initial out-of-straightness peaks in this transition zone, falling off toward both ends of the range. An initial bow on the order of L/1000 is built into the code curves from the outset.
Flexural Buckling Is Not the Only Mode
The standard EN 1993-1-1 defines three possible buckling modes for compression members. The first system consists of the flexural buckling phenomenon of all types of cross-sections.
The second buckling failure mode upward secures a greater critical buckling load in those beams whose path is determined by the shear center, not by the location of the mass center, as well as in sections that have very little torsional rigidity.
In practice, this system includes mono-symmetric or asymmetric open sections; for example, angles, tees, and C and Z channels made in cold-formed design. Closed sections, however, are not considered in the method, because of their greater torsional stiffness. Therefore, closed sections cannot fail under the torsional-flexural buckling criterion.
A misunderstanding of what buckling system controls has led to several collapses in structures. The roof of Hartford Civic Center collapsed due to snow load in 1978. The official report claimed that the collapse resulted from straight overload on some top chord compression members; for example, the maximum overload reached 852% and 213%.
What the Analysis Model Can See
Beam (1D) elements carry axial force correctly and capture the global buckling mode. Local buckling of a web or flange they cannot represent by the formulation: a one-dimensional element has no degrees of freedom that describe a plate bulging out of plane.
Because the uniform load classification applies in regard to the c/t value of all plate elements, not just those in compression, unlike in bending. Class 4 sections have effective properties under EN 1993-1-5.
The second generation of Eurocode 3 tightens the class 4 line between class 3 and 4 forms of buckling for uniform compression from 42 Js to 38 J/s, which is consistent with the plate slenderness limit of 0.673. At S355, this takes the limit from 34.2 to 30.9, bringing more profiles into class 4 classifications with no change in dimension.
Shell models can capture local modes; however, the classical linear eigenvalue analysis cannot evaluate anything but perfect conditions. A realistic capacity assumption requires two runs to pull out the first run to get the buckling shape modified by code-required imperfections, then taking the distortion into account with a GMNIA solution on the distorted model.
Since 2025, this has had a separate guideline in EN 1993-1 14 taking over the informative annex that previously existed in EN 1993-1-5.
Compression Rarely Arrives Alone
Clause 6.3.3 in EN 1993-1-1 indicates that it is essential to check beam-columns for both axes and use the interaction factors as prescribed in Annex A or Annex B, using Method 1 or Method 2.
The above equations also have the lateral-torsional buckling factor and the flexural buckling reduction factors built into them, while the applied moments have to consider second-order effects of frame sway.
This means the amount of work will multiply: member numbers multiplied by loading combinations multiplied by buckling modes multiplied by lifting planes. Any modification to a section will invalidate everything previously completed because stiffness changes, internal forces redistribute, a section’s classification may change, and slenderness is reshuffled.
Here, automated code-checking modules within FEA software will ensure that the various checks are within the model entities, along with a complete reevaluation; therefore, leaving the engineer with necessary input that none of the solvers will obtain: assignments of the end restraints, selection of the buckling curve, and the discretion determining how much a particular joint genuinely restrains the buckling process.