Class 4 Steel Sections, Theoretical Aspects and Practical Example with PRO_CL4

The classification of cross-sections, in fact, makes it possible to determine to what extent strength and rotational capacity are limited by the tendency to local buckling.

Reference standards

The references for the classification of steel profiles used in PRO_CL4 are as follows:

• [1] Ministerial Decree 2018 §4.2.3.1 Classification of sections;
• [2] Circular no. 7 of 21/01/2019 §C.4.2.3.1 Classification of sections and §C4.2.4.1.3.4.2 Stability of panels subject to compression;
• [3] UNI EN 1993-1:1 2022 §7.5 Classification of sections and § 8.2.9.3 Verification of sections in class 4;
• [4] UNI EN 1993-1:2 2005 §4.2.2 Classification of sections exposed to fire;
• [5] UNI EN 1993-1:5 2019 §4.4 Calculation of effective widths.

Classification of steel sections

Following the indications of the reference standards [1] and [3], four section classes are distinguished:

• class 1 (ductile) if the section is able to develop a plastic hinge having the rotational capacity required for the structural analysis conducted with the plastic method without undergoing reductions in strength;
• class 2 (compact) if the section is able to develop its own plastic resistant moment, but with limited rotational capacity;
• class 3 (semi-compact) if in the section the stresses calculated in the compressed extreme fibers can reach the yield stress, but the local buckling prevents the development of the plastic resisting moment;
• class 4 (slender) if, in order to determine the strength of the section, it is necessary to take into account the effects of local buckling in the elastic phase in the compressed parts. In this case, instead of the geometric section, it is necessary to consider the effective section.

For the most common cases of section shape and stress, the tables in [1] and [3] provide guidance for classification. In detail, using tables, the classification of the section is a function of:

• yield strength of the material;
• ratio between the width and thickness of the individual compressed parts;
• constraint conditions at the ends distinguishing between internal elements connected to other parts of the section (cores) and external elements having a free end (flanges);
• distribution of stresses on the individual compressed parts.

The limits of the width and thickness ratios (for both internal and external elements) are influenced by a factor and that depends on the yield stress of the material and is defined as

The class of a section with multiple compressed components is the highest of the identified class values. Sections that do not meet the requirements imposed for class 3 are class 4. In this case, it is necessary to evaluate the width of the areas which, by becoming unstable, do not contribute to the resistance and must therefore be neglected in order to replace the gross geometric section with the effective section.

Finally, both [2] and [3] provide that the slenderness limits provided for class 3 can be increased by a factor

thus considering the maximum compressive stress actually acting in the element. It should be noted that this increase is allowed only for the purposes of resistance checks.

Effective Section

In class 4 sections, due to the effect of local instability in the elastic phase, part of the compressed components must be considered as not present in the effective section (e.g. the part closest to the freeboard for the flanges, the barycentric strip for the web) as in the figure.

In [2] and [5] we find the indications to determine the reduction ρ to be applied for each compressed component: the value of this coefficient depends on the yield stress f_y, the ψ stress distribution and the buckling factor k_σ function of the stress distribution and the boundary conditions of the compressed element:

In [5] it is foreseen, also in this context, the possibility of considering the maximum compressive stress actually acting in the element, obtaining a reduction of the slenderness λ_p of the same, through a factor

It should be noted that, even in this case, this reduction is allowed only for the purposes of resistance checks.

It is important to point out that since geometric characteristics that are a function of the stresses themselves are used in the calculation of stresses (and their ratios), it is necessary to use an iterative procedure as shown below

Verification of the sections in class 4

As far as we have seen, in general, the classification of the section must be carried out according to the stress regime (i.e. by load combination), possibly considering the maximum compressive stress acting to increase the slenderness limit provided for class 3, and finally iterating to identify its effective characteristics. Standards [2] and [3] also provide that the verification is also carried out considering the transport moments due to the displacement (eccentricity and_Ny and it is_Nz) of the center of gravity of the effective section with respect to that of the gross section.

The verification process can become very challenging and inevitably requires special software.

[2] and [3] also allow, as an alternative to the evaluation of the effective characteristics corresponding to the real stress regime, the evaluation of these characteristics by considering only one stress component at a time, namely:

• Effective area, and_Ny and_Nz evaluated considering the section subject to simple compression;
• W effective values evaluated considering the section subject to pure bending: in general, the deflections acting on both axes of the section with both positive and negative signs must be considered, for a total of 4 bends.

In this case (simplified classification) the resulting stress state is not the actual one and cannot be considered either to increase the slenderness limits provided for class 3, or to reduce the slenderness of the elements in the assessment of instabilizations.

PRO_CL4

The PRO_CL4 application, developed by 2SI, represents an important innovation in the field of design and verification of steel structures. This instrument is designed for the classification of steel sections and for the verification of sections belonging to class 4, offering a wide range of practical applications, including:

• simplified classification of sections or on the basis of load combinations;
• classification of sections exposed to fire (simplified or based on load combinations);
• calculation of effective parameters for sections in class 4;
• calculation of the cutting center, shear resistant areas and torsional stiffness factor.

The versatility of the program in defining the section should be emphasized: in addition to access to the most common profiles, it allows you to insert sections of custom dimensions starting from those of the profile or to draw generic sections and stiffeners with the internal CAD or by importing an external file.

In the following image you can see a practical example with PRO_CL4 of the classification just illustrated, in which the traits subject to local instability are highlighted in red and therefore will not be considered in the calculation of the effective characteristics:

In this dialog box, the possibility of opting for

1. Simplified classification: with a preliminary assessment based on individual elastic limit stresses and with the comparison of the requirements indicated in the tables above.
2. Classification by combination: considering actual load combinations, allowing for more detailed verification and optimized design.

Both methods are based on the determination of the effective parameters described in the previous paragraphs.

In addition, the options for the classification of the sections exposed to fire and for the use of the effective stress regime both for the classification and for the calculation of the effective characteristics can be activated.

Practical example with structural calculation PRO_CL4 integrated into PRO_SAP

An example of a calculation of a steel structure is shown, for which the 100*30*15*2.0 omega section in S235 steel provided for purlins is studied.

The section has been defined and classified within the new PRO_CL4 module.

The comparisons in terms of classification and exploitation obtained by adopting the methods implemented in the software are shown below.

Simplified classification

The simplified classification considers the stress components taken individually, then the classification is performed for normal stress only, and for the individual bending moments M2+, M2-, M3+, M3-. Simplified classification can be performed before performing structure analyses because it is based on the stress distributions of the individual stress components.

As shown in the table, all types of stress have been considered with the simplified classification: normal stress and moments with a vertical axis (M2) indicate class 4, moments with a horizontal axis (M3) indicate class 1. The verification of this section will be conducted using the highest classification, i.e., class 4, using the effective parameters of section (A_eff, W_{eff_y} and W_{eff_z}) and applying the transport moments due to the displacement of the center of gravity of the effective section with respect to the gross section.

Classification by combination

Classification by combination considers the stresses of the analysis, so it is only available downstream of the structure calculation. Effective parameters are obtained by evaluating the stress distribution resulting from pressure bending regimes and accurately identifying the parts of the section that may become ineffective.

It should be noted that the load combinations, having only M3 other than 0, induce a stress regime that is detected by the program similar to that used for the classification by simple bending M3, therefore the section is in class 1.

By using the combination classification function, the cross-section utilization is reduced by more than 30%.

It is also interesting to observe what happens in the event that purlins are subject to deflected bending, i.e. also with bending around the vertical plane.

In this case, the program detects the compressive stress state in the cores and, therefore, returns the section to class 4, but considering the possibility of evaluating the increase in the limits of the classification requirements as a function of the actual exploitation of the section, it can be traced back to class 3.

In summary, the simplified method is always in favor of safety because it considers all possible stress components, regardless of the effects that the actual intensity of the individual components or the interaction between them may have, consequently it is very likely to obtain an oversizing of the structure. The combination method considers the stress state that results from the analyses, allowing you to accurately identify the parts of the section that may become ineffective.

It is evident that an accurate analysis of these aspects during the sizing phase is essential to optimize structural performance and achieve cost reduction.

Conclusion

The PRO_CL4 application is a versatile and advanced tool for the design of steel profiles. Thanks to the load combination method and the options available to take into account the actual distribution of the stress state, it allows a considerable optimization of the dimensioning.

The main features are as follows:

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