Overview

EN 1993-1-1: Design of Steel Structures (Eurocode 3) outlines design guidelines for structural steel members for use in buildings using the limit state method. Limit state design entails comparing factored design loads against reduced section and member capacities. These factors are intended to account for variability in loading conditions and material properties. For the ultimate limit state (ULS) design to be satisfied, the following relationship must be true:

\(ULS \;Factor * Load ≤ Reduction \;Factor * Capacity\)

This document outlines the procedure for designing a structural steel member in accordance with EN 1993-1-1 using the EN 1993-1-1 Steel Member Design module.

Contents

• Material Properties
  • Fabrication
  • Steel Grade
  • Yield Strength
• Section Capacity
  • Bending
  • Shear
  • Compression
  • Tension
• Member Capacity
  • Bending
  • Compression

Material Properties

Fabrication

EN 1993-1-1 provides design guidance for four types of structural steel fabrication:

• Hot Rolled Sections: Hot rolled sections are manufactured by heating and rolling steel billet through a mill to achieve a required shape. Examples include UB/UC/UBP I-Sections, T-Sections, Channels and Angle sections.
• Welded Sections: Welded (or fabricated) sections are made up of several hot-rolled flat plates welded together longitudinally to form a steel shape. Custom fabricated sections are typically welded.
• Hot Finished Sections: Hot finished sections are produced by heating steel beyond its recrystallisation temperature before rolling to improve the strength of the end product. These sections are almost always structural hollow sections (RHS/SHS/CHS)
• Cold Formed Sections: Cold formed sections are fabricated by pressing steel billet through a mill at room temperature. Cold forming can be used to produce structural hollow sections and thinner open sections. Note EN 1993-1-1 only provides guidance for hollow cold-formed sections.

Steel Grade

Europe and the United Kingdom has numerous steel grades (strengths) that can be used for design in accordance with EN 1993-1-1. There are several European material standards for different types of steel fabrication:

• EN 10025: Hot rolled products.
• EN 100210: Hot finished structural hollow sections.
• EN 10219: Cold formed welded structural hollow sections.

Common grade availabilities and indicative yield strengths for different steel shapes are outlined below.

Hot Rolled Sections (EN 10025)

• S 235 (f_y = 235 MPa)
• S 275 (f_y = 275 MPa)
• S 355 (f_y = 355 MPa)
• S450 (f_y = 440 MPa)

Structural Hollow Sections (EN 100210 / EN 10219)

• S 235 H (f_y = 235 MPa)
• S 275 H (f_y = 275 MPa)
• S 355 H (f_y = 355 MPa)
• S420 H (f_y = 420 MPa)
• S460 H (f_y = 460 MPa)

Yield Strength

The yield strength of a steel section is dependent on its Grade, with higher grades having higher yield stresses. The yield strength of Hot Rolled and Fabricated sections vary depending on the thickness of the section. Thicker steel sections typically have lower yield strengths than thinner sections of the same Grade.

Cold Formed Sections are the exception to this rule and have a consistent yield strength for each Steel Grade, regardless of section thickness. Section yield strength and ultimate (tensile) strength values can be calculated using Table 2.1 in AS 4100:2020.

Selecting a Section in SkyCiv AS 4100 Steel Member Design

The SkyCiv AS 4100:2020 Steel Member Design tool allows users to select a Standard section from the SkyCiv database or design a completely Custom section. When a Standard section is selected, flange and web yield strengths are automatically calculated based on the steel grade using AS 4100 Table 2.1. When a Custom section is selected, the user must input values for flange and web yield strength. Standard sections can also be used with a Custom steel grade if specified by the user.

 

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Section Capacity

Bending

Section Bending Moment Capacity

AS 4100:2020 calculates the bending moment capacity of a steel section as follows:

\(M_s = f_y*Z_e\)

Where f_y is the yield stress of the material, and Z_e is the effective section modulus. The section modulus of a shape is a geometric property which quantifies the bending resistance of a shape. In structural engineering we use two section modulus values, the elastic (Z) and plastic (S) section modulus. Note, design standards in other regions sometimes interchange the symbols for elastic and plastic section modulus.

The elastic section modulus assumes the entire section (shape) remains elastic under bending, i.e. no part of the section exceeds the yield strength (f_y) of the material. This generally occurs when the extreme fibers in the section (top/btm) reach yielding. The elastic section modulus of a section is calculated as follows:

\(Z = \frac{I}{y}\)

Where I is the second moment of area and y is the geometric centroid of the shape.

The plastic section modulus assumes that the entire section reaches the yield strength of the material under bending, which means parts of the section will exceed the yield strength and experience plastic deformation.  The plastic section modulus of a section is calculated as follows:

\(S = A_C*y_C + A_T*y_T \)

Where A_C and A_T are the areas on either side of the Plastic Neutral Axis (PNA), and y_c / y_t are the distance from the PNA to the centroid of those areas. Note, the PNA location is equal to the geometric centroid location for symmetric shapes but will not equal the geometric centroid location for asymmetric shapes.

Section Classification

Some steel shapes may have elements of the shape locally buckle before reaching their yield strength, meaning the full capacity of the elastic/plastic section modulus cannot be achieved. This typically occurs in larger, thinner shapes, which are more susceptible to local buckling. AS 4100 uses the effective section modulus (Ze) value to account for the possibility of local buckling and reduce the bending capacity of the section accordingly. AS 4100 classifies sections into three categories:

• Compact: Compact sections are not susceptible to local buckling and can achieve their full plastic moment capacity, meaning the entire section can reach its yield strength under bending.
• Non-Compact: Non-compact sections can reach yield strength in the extreme fibres of the section (elastic moment capacity) but cannot achieve their plastic moment capacity before local buckling occurs.
• Slender: Slender sections cannot achieve their elastic moment capacity before local buckling occurs.

Section Slenderness

AS 4100 determines the section classification by calculating the slenderness of each element within a section and finding the “critical element” that will buckle in compression first. For an I-section, the elements are broken down as shown below. Slenderness values are only calculated for outstand elements, i.e. elements which are not restrained in both directions. The area of connection between a flange and web (shown in white below) is restrained in both directions and hence is not susceptible to local buckling.

The slenderness of a flat element is calculated as follows:

\(λ_e = \frac{b}{t}\sqrt{\frac{f_y}{250}}\)

AS 4100 Table 5.2 contains values for plasticity and yield slenderness limits (λ_ep & λ_ey) for compression plate elements based on stress distribution, edge support and residual stresses. The critical element of a section is the element with the highest λ_e / λ_ey ratio. The slenderness values of this element (λ_e) are used to classify the entire section (referred to as λ_s).

If λ_s ≤ λ_sp the section is compact. For compact sections, the effective section modulus is calculated as follows:

\(Z_e = Z_c = min(S,1.5*Z)\)

Where S is the plastic section modulus, and Z is the elastic section modulus of the section. The term Z_c is used interchangeably for the effective section modulus of a compact section.

If λ_sp ≤ λ_s  ≤ λ_sy the section is non-compact. For non-compact sections, the effective section modulus is calculated as follows:

\(Z_e = [(\frac{λ_{sy} – λ_{s}}{λ_{sy} – λ_{sp}})(Z_c-Z)]\)

Where Z_c is the effective section modulus for a compact section.

If λ_s  > λ_sy the section is slender. For a slender section with flat plate elements in uniform compression, the effective section modulus is calculated as follows:

\(Z_e = Z(\frac{λ_{sy}}{λ_s})\)

Note, the effective section modulus for circular hollow sections or flat plat elements with tension at the unsupported edge is calculated differently. Refer AS 4100 Clause 5.2.5 for further information.

Calculating Section Bending Capacity in SkyCiv AS 4100 Steel Member Design

The SkyCiv AS 4100:2020 Steel Member Design tool calculates slenderness classifications and section bending capacities for positive and negative bending about both principal axes. The results of the slenderness classification check for a 230 PFC are detailed below.

It’s apparent that the slenderness values and section classification are different depending on the direction of bending. This is because the stress distributions and edge support values change depending on which elements are in compression or tension, resulting in different slenderness limit values.

Once section slenderness is known, the module calculates the section bending moment capacity (Ms) about each principal axis for positive and negative bending. For symmetric shapes (such as I-Sections), this value will be the same in the positive and negative direction. Asymmetric shapes will have different section bending capacities in the positive and negative bending direction, such as the 230 PFC shown in the example below.

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Shear

Section Shear Capacity

AS 4100 only considers the web of a section to contribute to its shear capacity. Hence the shear capacity of a section (Vv) is equal to the web shear capacity. Vertical stiffeners can be added to a section to increase its shear capacity if required. The capacity of an unstiffened web is calculated differently depending on whether the shear stress distribution across the web is uniform or non-uniform. The following shear stress distributions are assumed for standard section shapes:

Uniform Shear Stress Distribution

The shear capacity of a section with uniform shear stress distribution (V_u) is calculated differently depending on the slenderness of the web panel. For a non-slender web, capacity is calculated as follows:

\(\frac{d_p}{t_w} ≤  \frac{82}{\sqrt{\frac{f_y}{250}}}\rightarrow V_u = V_w = 0.6*f_y*A_w\)

For a Circular Hollow Section Vv = V_w = 0.36*f_y*A (not impacted by section slenderness).

When the web of the section is slender capacity is calculated as follows:

\(\frac{d_p}{t_w} >  \frac{82}{\sqrt{\frac{f_y}{250}}}\rightarrow V_u = V_b = α_v*V_w\)

\(α_v = \left[\frac{82}{(\frac{d_p}{t_w})\sqrt{\frac{f_y}{250}}}\right]^2\)

Where d_p is the clear depth of the web panel (i.e. depth excluding flanges), t_w is the thickness of the web panel, f_y is the web yield strength and A_w is the gross sectional area of the web. Note A_w is calculated differently for welded and hot rolled sections. For hot rolled sections, A_w takes the web depth as the entire section depth (d). For welded sections, A_w only takes the clear web depth between the flanges (d_p). Rectangular Hollow Sections also use d_p for calculation of A_w.

Non-Uniform Shear Stress Distribution

The shear capacity of a section with uniform shear stress distribution (V_v) is calculated as follows:

\(V_v = \frac{2*V_u}{0.9+\left(\frac{f*_{vm}}{f*_{va}}\right)} ≤  V_u\)

Where V_u is the section shear capacity with a uniform shear stress distribution and f*_vm /f*_va is the ratio of maximum and average design shear stresses in the web.

Calculating Shear Capacity in SkyCiv AS 4100 Steel Member Design

The SkyCiv AS 4100:2020 Steel Member Design tool calculates the shear capacity of a section in both principal axes. Minor axis (Z) shear capacity is calculated using the contribution of the section flanges, excluding any contribution from the section web. Results from the shear capacity calculations for a 200 UB 22.3 are detailed below.

Compression

Section Compression Capacity

AS 4100 calculates the compression capacity (N_s) of a concentrically loaded section as follows:

\(N_s = k_f*A_n*f_y\)

Where k_f is the form factor of the section, A_n is the net area of the cross section (gross area excluding penetrations/holes) and f_y is the yield strength of the section. The form factor of a section represents how much of a section can contribute to its compression capacity before local buckling occurs. The form factor is calculated as follows:

\(k_f = \frac{A_e}{A_g}\)

Where A_g is the gross area of the section, and A_e is the “effective area” of the section, i.e. the gross area of the section minus any “ineffective” areas under compression. An ineffective area is part of the section that will buckle before it reaches its yield capacity under compression. Effective areas are calculated by finding the “effective width” of each flat plate element within a section and recalculating the section area using these adjusted width values. The effective width of a flat plate element is calculated as follows:

\(b_e = b\left(\frac{λ_{ey}}{λ_{e}}\right) ≤ b\)

Where:

\(λ_e = \frac{b}{t}\sqrt{\frac{f_y}{250}}\)

Note, most design software (including SkyCiv AS 4100:2020 Steel Member Design) uses the section yield strength for element slenderness calculations, rather than the specific yield strength of the web/flange. This will always provide a conservative result. The b values used for λ_e calculation are identical to the dimensions used for bending section slenderness checks (with the flange split about the web), but the b used for b_e calculation is the total flange/web width. λ_ey is taken from AS 4100 Table 6.2.4, depending on the edge support and residual stresses of that element.

The effective width of a circular hollow section is calculated as follows:

\(d_e = min(d_{o}\sqrt{\left(\frac{λ_{ey}}{λ_{e}}\right)},  d_{o}\left(\frac{3*λ_{ey}}{λ_{e}}\right)^2) ≤ d_{o}\)

Where:

\(λ_e = \left(\frac{d_o}{t}\right)\left(\frac{f_y}{250}\right)\)

Calculating Section Compression Capacity in SkyCiv AS 4100 Steel Member Design

The SkyCiv AS 4100:2020 Steel Member Design tool calculates the form factor and section compression capacity (N_s) for standard Australian sections and custom user-defined sections. Results from the section compression capacity calculations for a 610UB 125 are detailed below.

Tension

Section Tension Capacity

AS 4100 calculates the capacity of a tension member (Nt) as follows:

\(N_t = min(A_{g}*f_{y}\; ,\; 0.85*k_t*A_n*f_u)\)

Where A_g is the gross area of the section, A_n is the net area of the cross section (gross area excluding penetrations/holes), f_y is the yield strength of the section, f_u is the tensile (ultimate) strength of the section and k_t is the tensile force distribution correction factor. The k_t used in design varies depending on the section shape and connection type. Connections which provide uniform force distribution result in a k_t factor of 1.0, connections with unequal force distribution result in a k_t factor between 0.75-1.0.

Calculating Tension Capacity in SkyCiv AS 4100 Steel Member Design

The SkyCiv AS 4100:2020 Steel Member Design tool allows users to specify the section k_t value for used in design. A lower k_t value will result in a lower section tension capacity. The SkyCiv AS 4100 Member Design calculator assumes no significant holes are present in the section, hence A_n is taken as equal to A_g. Results from the section tension capacity calculations for a 610UB 125 are detailed below.

 

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Member Capacity

Bending

Member Bending Moment Capacity

The bending moment capacity of a steel member may not always be governed by the bending moment capacity of the section (M_s). This is because members can fail by another method before the capacity of the section is reached. Lateral torsional buckling is a common failure method for long/unrestrained steel members, which occurs when the section rotates away from its major axis (towards its minor axis) reducing its moment capacity in the direction of bending.

AS 4100 contains guidance on calculating nominal member capacity (M_b), which factors the section capacity of a steel member (M_s) to account for the impact of member slenderness and restraint conditions.

Members with Full Lateral Restraint

Critical Flange

The critical flange of a cross-section is the flange which would deflect the furthest during buckling, eventually resulting in lateral torsional buckling failure. This is typically the compression flange of a member. Critical flange locations for standard sections under vertical loading are shown below.

Full Lateral Restraint

Shorter members with high rotational/lateral rigidity are less likely to rotate out of plane under loading, reducing the likelihood of lateral torsional buckling failure. If a member is short/rigid enough it will be able to reach its section moment capacity (M_s) before another failure method occurs. Members which satisfy this condition are deemed as having “Full Lateral Restraint”.

\(Full \; Lateral \; Restraint \; \rightarrow M_b = M_s\)

AS 4100 Clause 5.3.2 provides guidance on calculating the Full Lateral Restraint limit for a member. Circular Hollow Sections (CHS) and Square Hollow Sections (SHS) are not susceptible to lateral torsional buckling, as they have high lateral/torsional rigidity and equal section moment capacities about both axes. Hence these sections are generally assumed to achieve Full Lateral Restraint regardless of member length.

Continuous Lateral Restraint

Members which have continuous restraint to the critical flange along their entire length are deemed as having “Continuous Lateral Restraint”.  Continuous Lateral Restraint is considered equivalent to Full Lateral Restraint for the calculation of member bending capacity (M_b).

Members without Full Lateral Restraint

The bending moment capacity of a member that doesn’t achieve full lateral restraint is calculated as follows:

\(M_b = α_m*α_s*M_s ≤ M_s\)

Where α_m is the moment modification factor and α_s is the slenderness reduction factor. AS 4100 Clause 5.6 outlines the procedure for calculating α_m and α_s.

Minor Axis Member Bending Capacity

The bending capacity for a member bent about its minor axis (M_b) is equal to the minor axis section capacity (M_s) about that axis. The minor axis section capacity reflects is the minimum capacity that section can achieve about any axis, hence the member cannot rotate from this axis into a less-favourable orientation.

Calculating Member Bending Capacity in SkyCiv AS 4100 Steel Member Design

The SkyCiv AS 4100:2020 Steel Member Design tool calculates carries out full lateral restraint checks and calculates member bending moment capacities about both principal axes for positive and negative bending. Users also have the option of selecting “Continuous Lateral Restraint” to bypass the Full Lateral Restraint check. Results from the member bending capacity calculations for a 3m long 200UB22.3 are detailed below.

Note, this calculator assumes α_m = 1.0 and β_s = -1.0 in all calculations. Cantilevered members are not supported by this tool.

Compression

Member Compression Capacity

The axial compression capacity of a member is also affected by its length, lateral rigidity and restraint conditions. Unrestrained, longer members are likely to fail due to flexural buckling before the section (squash) capacity is reached. AS 4100 contains guidance on calculating nominal member capacity (N_c), which factors the compression section capacity (N_s) to account for the impact of member slenderness and restraint conditions.

\(N_c = α_c*N_s ≤ N_s\)

Where α_c is the member slenderness reduction factor. Clause 6.3.3 of AS 4100 provides guidance on calculating α_c. Member compression capacity must be checked about both axes to find the governing value.

Calculating Member Compression Capacity in SkyCiv AS 4100 Steel Member Design

The SkyCiv AS 4100:2020 Steel Member Design tool calculates member compression capacity about both principal axes based on restraint lengths and effective length factors specified by the user. Results from the member compression capacity calculations for a 200UB22.3 with an unrestrained length of 4500mm and 1500mm in the Z and Y axis (respectively) are detailed below.

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