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Analyse a steel beam or column in accordance with Eurocode 3.

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Result
Pass ✅
Utilisation
12%
Section Depth mm
Section Width mm
Plate thickness mm
Total Area cm2
Y-Y Axis:
1st moment of area cm4
2nd moment of area cm4
Wpl,y cm3
Wel,y cm3
Z-Z Axis:
1st moment of area cm4
2nd moment of area cm4
Wpl,z cm3
Wel,z cm3
Steel analysis summary
251/313 sections in our database pass. ✅
Section:
Enter beam or column length:
Length m
Enter length more than 0 & less than 50m.
Apply loads about y-y axis:
Bending Med,y kNm
Enter value greater than 0.
Shear Ved,y kN
Enter value greater than 0.
Axial Ned kN
Apply loads about z-z axis:
Bending Med,z kNm
Enter value greater than 0.
Shear Ved,z kN
Enter value greater than 0.
Support conditions
Support types
Connection
results

The classification of the cross-section parts is specified in EN1993-1-1 Table 5.2
Plate classification:
  • For the Plate: c / t = (h - 2⋅tf - 2⋅r) / tw See table 5.2 for element subject to bending and shear (α = ) c / t = 12.08
  • Plate classification: Class 1 (c/t <= 72ε)
Section classification: Class 1

The critical cross-section is verified for tensile axial force in accordance with EN1993-1-1 §6.2.3:
  • NEd / Nt,Rd ≤ 1.0
  • Where NEd = 0 kN is the design tensile axial force. The tension resistance Nt,Rd is estimated as the plastic tension resistance Npl,Rd on the basis of the gross cross-section area A and the steel yield stress fy.
  • Npl,Rd = 2453kN
Result: Pass ✅
Utilisation: 0
According to EN1993-1-1 §6.2.3(2)b) for the case where holes for fasteners or other openings are present the tension verification must also be performed on the basis of the net cross-section area Anet and the steel ultimate stress fu>: Nu,Rd = 0.9 ⋅ Anet ⋅ fu / γM2

The critical cross-section is verified for compressive axial force in accordance with EN1993-1-1 §6.2.4:
  • NEd / Nc,Rd ≤ 1.0
  • Where NEd = 10 kN is the design compressive axial force. For the case of class 1, 2, or 3 cross-section the compression resistance Nc,Rd is estimated as:
  • Nc,Rd = 2453kN
Result: Pass ✅
Utilisation: 0
Verification is sufficient for steel members without holes or with fastener holes filled with fasteners with the exception of oversize and slotted holes.

The critical cross-section is verified for bending moment in accordance with EN1993-1-1 §6.2.5:
MEd / Mc,Rd ≤ 1.0
  • For class 1 or 2 cross-sections the design resistance Mc,Rd for bending about one principal axis is estimated as the corresponding plastic bending resistance Mpl,Rd on the basis of the corresponding plastic section modulus Wpl:
  • For the major axis y-y: Mc,y,Rd = Wpl,y ⋅ fy / γM0 = 160.05kNm (>20.0kNm)
  • For the minor axis z-z: Mc,z,Rd = Wpl,z ⋅ fy / γM0 = 130.075kNm (>0.0kNm)
  • For bending about the major axis y-y utilisation: 0.12
  • For bending about the minor axis z-z utilisation: 0
Bending result: Pass ✅
Utilisation: 0.12

The critical cross-section is verified for shear force in accordance with EN1993-1-1 §6.2.6:
VEd> / Vc,Rd ≤ 1.0
  • For class 1 or 2 cross-sections the design shear resistance Vc,Rd for shear force along one principal axis is estimated as the plastic shear resistance Vpl,Rd on the basis of the corresponding shear area Av:
  • For the shear force along z-z: Vpl,Rd,z = Av,z ⋅ (fy / √3 ) / γM0 = 607kN (>10.0kN)
  • For the shear force along y-y: Vpl,Rd,y = Av,y ⋅ (fy / √3 ) / γM0 = 809kN (>0.0kN)
  • For shear about the major axis y-y utilisation: 0.02
  • For shear about the minor axis z-z utilisation: 0
Shear result: Pass ✅
Utilisation: 0.02

The effect of the shear force on the moment resistance is examined in accordance with EN1993-1-1 §6.2.8.
  • According to EN1993-1-1 §6.2.8(3) the bending resistance of the cross-section is reduced when the applied shear force VEd is larger than one-half of the corresponding plastic shear resistance Vpl,Rd.
  • Shear utilisation along axis z-z: Vz,Ed / Vpl,Rd,z = 0.02 < 0.5 ✅ No additional checks required for bending and shear
  • Shear utilisation along axis y-y: Vy,Ed / Vpl,Rd,y = 0 < 0.5 ✅ No additional checks required for bending and shear

The effect of axial force on the plastic bending moment resistance of class 1 or class 2 cross-sections is specified in EN1991-1-4 §6.2.9.1.
Consideration of the effect of axial force on bending moment resistance
  • The normalized axial force n is:
  • n = NEd / Npl,Rd = 0.004
  • The ratio a is defined as: a = min[0.5, (A' - 2⋅b⋅t'f) / A' = 0.5
  • The reduced bending moment resistance about major axis y-y is given as:
  • My,Rd = min[Mpl,y,Rd, Mpl,y,Rd(1 - [(n - a) / (1 - a)]2) ] = 160.05kNm
  • The reduced bending moment resistance about minor axis z-z is given as:
  • Mz,Rd = Mpl,z,Rd(1 - [(n - a) / (1 - a)]2) = 130.075kNm
  • Therefore the utilization for the reduced bending resistance due to axial force is:
  • For bending about the major axis y-y: My,Ed / MN,y,Rd = 0.12
  • For bending about the major axis z-z: Mz,Ed / MN,z,Rd = 0
  • The effect of biaxial bending is examined in accordance with the criterion specified in EN1991-1-4 §6.2.9.1(6):
  • [My,Ed / MN,y,Rd]α + [Mz,Ed / MN,z,Rd]β ≤ 1
  • where the exponents α and β are defined as follows:
  • α = 1; β = 1
  • Therefore the utilization factor for biaxial bending including the effect of the axial force is:
  • Biaxial bending: u = [My,Ed / MN,y,Rd]α + [Mz,Ed / MN,z,Rd]β = 0.12
Result: Pass ✅
Utilisation: 0.12

The effect of the shear force and axial force on the moment resistance is examined in accordance with EN1993-1-1 §6.2.10.
  • According to EN1993-1-1 §6.2.10(2) the resistance of the cross-section for bending and axial force is reduced when the applied shear force VEd is larger than one-half of the corresponding plastic shear resistance Vpl,Rd.
  • Worst case shear force utilisation: VEd / Vpl,Rd = 0.02
  • Result: Pass ✅ applied shear less than 50% of the corresponding plastic shear resistance. Therefore the effect of shear forces on the bending moment resistance may be ignored.

The compression member is verified against flexural buckling in accordance with EN1993-1-1 §6.3.1 as follows: NEd / Nb,Rd ≤ 1.0
Nb,Rd is the design buckling resistance of the compression member given in EN1993-1-1 §6.3.1.1(3) for class 1, 2 and 3 cross-sections: Nb,Rd = χ⋅A⋅fy / γM1
The reduction factor χ due to flexural buckling is calculated for both the major and the minor bending axes.
Flexural buckling about major axis y-y:
  • The appropriate buckling curve is determined from EN1993-1-1 Table 6.2 as Curve "a".
  • The imperfection factor α corresponding to the buckling curve is determined from EN1993-1-1 Table 6.1 as α = 0.21.
  • The critical buckling length Lcr,y for flexural buckling about the major axis y-y is considered as Lcr,y = 1⋅L = 5 m.
  • According to the theory of elasticity the elastic critical buckling load for flexural buckling is:
  • Ncr,y = π2⋅E⋅Iy / Lcr,y2 = 3846.78kN
  • The ratio of the compression load to the elastic critical buckling load is NEd/Ncr,y = 0.0026
  • For class 1, 2 and 3 cross-section the non-dimensional slenderness λy for flexural buckling is given in EN1993-1-1 §6.3.1.3(1):
  • λy = (A⋅fy / Ncr,y)0.5 = 0.8
  • According to EN1993-1-1 §6.3.1.2(4) flexural buckling effects may be ignored when NEd/Ncr,y ≤ 0.04 or λy ≤ 0.20.
  • Result: Pass ✅ no further verification of flexural buckling is required.
Flexural buckling about minor axis z-z:
  • The appropriate buckling curve is determined from EN1993-1-1 Table 6.2 as Curve "a".
  • The imperfection factor α corresponding to the buckling curve is determined from EN1993-1-1 Table 6.1 as α = 0.21.
  • The critical buckling length Lcr,y for flexural buckling about the minor axis z-z is considered as Lcr,z = 1⋅L = 5 m.
  • According to the theory of elasticity the elastic critical buckling load for flexural buckling is:
  • Ncr,z = πcr,z>⋅E⋅Iz / Lcr,z2 = 2420.82kN
  • The ratio of the compression load to the elastic critical buckling load is NEd/Ncr,z = 0.0041
  • For class 1, 2 and 3 cross-section the non-dimensional slenderness λz for flexural buckling is given in EN1993-1-1 §6.3.1.3(1):
  • λz = (A⋅fy / Ncr,z)0.5 = 1.01
  • According to EN1993-1-1 §6.3.1.2(4) flexural buckling effects may be ignored when NEd/Ncr,z ≤ 0.04 or λy ≤ 0.20.
  • Result: Pass ✅ no further verification of flexural buckling is required.
Overall flexural buckling result:
Flexural buckling result: Pass ✅
Utilisation: 0.01

What are steel beams used for in construction?

  • Steel beams are one of the most widely used elements in construction. Steel is an excellent construction material due to its well understood properties, high strength and low manufacturing cost. Steel beams and columns are used in structures for load bearing and provide a to provide a structural frame on which the building (or other structure) is constructed.

How do I design a steel beam?

  • Steel beams can be designed in 6 stages
    1. Choose grade of steel, a lot of steel used today is S275 or S355.
    2. Select a section shape classification, options include I beams, H beams, hollow sections and channels.
    3. Decide your beam span, what is the length of the beam span?
    4. Consider the support conditions, are the beam connections fixed, pinned, roller?
    5. Calculate loading, there is always some form of loading acting on a beam or column.
    6. Design, using your countries accepted codes of practice.

How to calculate a steel section classification?

  • Class 1 cross sections can form a plastic hinge with the rotation capacity required for plastic analysis without reducing the resistance.
  • Class 2 cross sections can develop their plastic moment resistance, but which have limited rotation capacity because of local buckling.
  • Class 3 cross sections assume the stress in the extreme compression fibre of the steel member has an elastic distribution of stresses which can reach the yield strength, but local buckling prevents development of the plastic moment resistance.
  • Class 4 cross sections are those in which local buckling will occur before the attainment of yield stress.
  • The class of the cross section can be determined from Table 5.2 of BS EN 1993-1-1, where a cross section is classified according to the highest (least favourable) class of its parts subject to compression.

How to design of a steel section in accordance with Eurocode 3?

How to calculate the tension resistance of the steel section
  • To calculate the tension resistance of a steel section the equation below can be used:
  • Npl,rd = A x fy / ymo
  • Where A is the area of the steel section, fy is the yield strength of the steel and ymo is the partial factor of safety for the material. Following the Eurocode 3 (EC3) approach
How to calculate the compressive resistance of the steelwork
  • To calculate the compressive resistance of a steel section the equation below can be used:
  • Nc,rd = A x fy / ymo
  • Where A is the area of the steel section, fy is the yield strength of the steel and ymo is the partial factor of safety for the material. Following the Eurocode 3 (EC3) approach
How to calculate the bending resistance of the steel beam
  • To calculate the bending resistance of a steel section the equation below can be used:
  • Mc,rd = Wpl,Rd * fy / ymo
  • Where Wpl is the fibre with the maximum elastic stress, fy is the yield strength of the steel and ymo is the partial factor of safety for the material. Following the Eurocode 3 (EC3) approach. This equation is applicable to section classifications 1 and 2 bending along one plane with no bi-axial bending.
How to calculate the shear resistance of the steel member
  • To calculate the bending resistance of a steel section the equation below can be used:
  • Vpl,rd = Av * (fy / sqrt(3) ) / ymo
  • Where Av is the shear area of the beam, fy is the yield strength of the steel and ymo is the partial factor of safety for the material. Following the Eurocode 3 (EC3) approach.
How to calculate the buckling resistance of a compression member
  • The buckling resistance of a steel section is calculated using reduction values applied to the axial resistance. These buckling values depend upon the buckling failure mode expected and the slenderness of the section. Details of reduction factors can be seen in Table 6.2 of BS EN 1993-1-1.
How to calculate the lateral torsional buckling resistance
  • Lateral torsional buckling can occur when a bending moment is applied to a slender laterally unrestrained steel section. Lateral bracing can be provided in the form of web stiffeners, which are steel plates placed within the web of the beam and welded.
  • The design buckling resistance of a laterally unrestrained beam is given by:
  • Mb,Rd = *χ*LT * Wy * fy / ym1
  • Where Wy is the plastic section modulus for class 1 and 2 steel sections, *χ*LT is the lateral torsion buckling reduction factor and fy is the yield strength of the steel.
What's this calculator used for?

Steel design is one of the most commonly encountered and essential tasks for Structural Engineers, with steel being one of the most commonly used construction materials in the world. Check your steel design proposals against Eurocode 3 with this software.

Search through our steel section tables of supplier steel sizes and steel properties to automate your steel design. Calculate bending moments, shear forces and axial forces for different steel beam sizes, steel columns or cantilevers, including steel hollow sections.

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