This article presents an overview on classification of steel cross-sections according to EN 1993-1-1:2005. At the end of the article there is a worked example on classification of a Universal Beam (UB) section under bending, axial compression, and combined bending and axial compression.
Why Classification of Steel Cross-Sections?
Steel sections are formed by assembling plate elements to form desired shapes. Any slender plate in this assemblage is susceptible to buckling when under compressive stress such that the resistance of the whole cross-section becomes compromised, even though just only a part of it has failed (buckled). To avoid this localized failure, steel cross-sections are classified into four groups to determine the susceptibility of the cross-section to local buckling. In summary, the role of cross section classification is to identify the extent to which the resistance and rotation capacity of cross sections is limited by its local buckling resistance.
The Classes of Steel Cross-Sections
According to clause 5.5.2(1) of the standard, steel cross-sections can be classified into four classes as follows:
Class 1: These cross-sections are those which can form a plastic hinge with the rotation capacity required from plastic analysis without reduction of the resistance. This cross-section is also referred to as plastic in UK practice
Class 2: These cross-sections are those which can develop their plastic moment resistance but have limited rotation capacity because of local buckling. This cross-section is also referred to as compact in UK practice
Class 3: These cross-sections are those in which the stress in the extreme compression fibre of the steel member assuming an elastic distribution of stresses can reach the yield strength, but local buckling is liable to prevent development of the plastic moment resistance. This cross-section is also referred to as semi-compact in UK practice
Class 4: These cross-sections are those in which local buckling will occur before the attainment of yield stress in one or more parts of the cross-section. This cross-section is also referred to as slender in UK practice
Guide to classification of Cross-section
The classification into the classes above is only necessary for parts of a cross-section that are in compression. These compression parts include every part of a cross-section which is either totally or partially in compression under the load combination considered. The various compression parts in a cross-section (such as a web or flange) can, in general, be in different classes. Each part of a steel section is classified according to its slenderness (width to thickness ratio) to determine its capacity under compressive stress. The least favourable classification of any of the parts is adopted as the class of the entire section.
The limiting proportions for Class 1, 2, and 3 compression parts should be obtained from Table 5.2 of EN 1993-1-1:2005. Any part which fails to satisfy the limits for Class 3 should be automatically taken as Class 4. Class 4 sections are treated in detail in EN 1993-1-5.
Also, for proper usage of Table 5.2 of the standard, a user should be able to distinguish between internal compression parts, and outstand flanges/parts of a cross-section. The definitions for the two types of elements are given below:
Internal compression parts: These are parts of a cross-section that are supported along two edges parallel to the direction of the compression stress. An example of such parts is the web of an I-section or H-section. The limiting ratio for these types of elements can be found in sheet 1 of 3 of Table 5.2.
Outstand flanges: These are parts of a cross-section that are supported along one edge and free on the other edge, parallel to the direction of the compression stress. An example of such parts is the flange of an I-section or H-section. The limiting ratio for these types of elements can be found in sheet 2 of 3 of Table 5.2.
To apply the classification limits from Table 5.2 of EN 1993-1-1:2005 to a cross-section subjected to combined bending and axial compression, the value of plastic stress distribution (α) has to be calculated for class 1, and 2 and the value of elastic stress distribution (ψ) for class 3. For I-section and H-section subjected to combined axial compression and bending and where its neutral axis is located within the web of the cross-section, α can be calculated using the expression given in “Handbook of Structural Steelwork” which is provided below:
$
\alpha \,\,=\,\,\frac{1}{c}\left( \frac{h}{2}\,\,+\,\,\frac{1}{2}\frac{N_{Ed}}{t_wf_y}\,\,-\,\,\left( t_{f\,\,}+\,\,r \right) \right) \,\,\leqslant \,\,1
$
Worked Example
A 457 x 152 x 82 UB in steel grade S355 is to be used under:
- Bending
- Axial compression
- Bending about the major axis and axial compression of 200KN
Classify the cross-section under each case above. The properties of the cross-section are given below.
h = 465.8mm | b = 155.3mm | tw = 10.5mm | tf = 18.9mm | r = 10.2mm | d = 407.6mm
Ratios for Local buckling
For flange: c = (b – tw -2r)/2
For web: c = d
Flange: cf/tf = 3.29
Web: cw/tw = 38.8
Note: These properties of the Universal Beam (UB) are taken from SCI P363: Steel Building Design Data.
Influence of Material Strength
The UK National Annex recommends that EN 10025-2:2004 should replace Table 3 of EN 1993-1-1:2005 for yield strength (fy) and ultimate strength (fu) of the steel
For Thickness of 18.9mm for grade S355, fy = 345 | fu = 510 (Table 7, EN 10025-2)
$$
\varepsilon \,\,=\,\,\sqrt{\frac{235}{345}}\,\,=\,\,0.83
$$
Cross-section in Bending
Flanges (Outstand Element)
(Using Table 5.2 (Sheet 2 of 3) of EN 1993-1-1-2005)
cf/tf = 3.29
from the table, limiting value for class 1 is 9 ℇ = 9 x 0.83 = 7.47
since 3.29 < 7.47, the flanges are class 1
Web (Internal Element)
(Using Table 5.2 (Sheet 1 of 3) of EN 1993-1-1-2005)
cw/tw = 38.8
from the table, limiting value for class 1 is 72ℇ = 72 x 0.83 = 59.76
since 38.8 < 59.76, the web is class 1
The entire cross-section is class 1 in bending.
Cross-section in Axial Compression
Flanges (Outstand Element)
(Using Table 5.2 (Sheet 2 of 3) of EN 1993-1-1-2005)
cf/tf = 3.29
from the table, limiting value for class 1 is 9 ℇ = 9 x 0.83 = 7.47
since 3.29 < 7.47, the flanges are class 1
(Note: it should be noted that for the flange (outstand element), the classification is the same as when in bending as its under compression under both loading).
Web (Internal Element)
(Using Table 5.2 (Sheet 1 of 3) of EN 1993-1-1-2005)
cw/tw = 38.8
from the table, limiting value for class 1 is 33ℇ = 33 x 0.83 = 27.39
The aspect ratio is greater than the limiting ratio for class 1, let’s check the limiting ratio for class 2.
Limiting ratio for class 2 is 38ℇ = 38 x 0.83 = 31.54.
It is still greater than the limiting ratio, let’s check for class 3
Limiting ratio for class 3 is 42ℇ = 42 x 0.83 = 34.86.
Since the aspect ratio is greater than the limiting ratio for Class 3, the web is Class 4
The entire cross-section is class 4 under pure axial compression.
Cross-section in Bending about the major axis and axial compression of 200KN
Flanges (Outstand Element)
Since the neutral axis of the section is assumed to be within the web, the flange is in compression and is a Class 1 section as evaluated previously.
Web (Internal Element)
(Using Table 5.2 (Sheet 1 of 3) of EN 1993-1-1-2005)
cw/tw = 38.8
from the table, limiting value for class 1 is:
397ℇ/(13∝ – 1) (f0r ∝ > 0.5)
36ℇ/∝ (for ∝ ≤ 0.5)
$
\alpha \,\,=\,\,\frac{1}{c}\left( \frac{h}{2}\,\,+\,\,\frac{1}{2}\frac{N_{Ed}}{t_wf_y}\,\,-\,\,\left( t_{f\,\,}+\,\,r \right) \right) \,\,\leqslant \,\,1
$
c = d = 407.6mm
$
\alpha \,\,=\,\,\frac{1}{407.6}\left( \frac{465.8}{2}\,\,+\,\,\frac{1}{2}\frac{200 x 10^3}{10.5 x 345}\,\,-\,\,\left( 18.9{\,\,}+\,\,10.2 \right) \right) = 0.57
$
limiting value = 397 x 0.83/(13 x 0.57 – 1) = 51.28
Since the actual value (38.8) < the limiting value (51.28), the web is Class 1
References
EN 1993-1-1:2005: Eurocode 3, Design of Steel structures – Part 1:1: General rules for buildings.
Handbook of Structural Steelwork: Eurocode Edition
Design of Structural Elements to Eurocode 2 By Mc Kenzie
