Apply loads about z-z axis:

Bending M_{ed,z}
kNm

Enter value greater than 0.

Shear V_{ed,z}
kN

Enter value greater than 0.

Support conditions

Support types

Connection

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Section Depth
mm

Section Width
mm

Web thickness
mm

Flange thickness
mm

Total Area
cm^{2}

Root
mm

Y-Y Axis:

1st moment of area
cm^{4}

2nd moment of area
cm^{4}

W_{pl,y}
cm^{3}

W_{el,y}
cm^{3}

Z-Z Axis:

1st moment of area
cm^{4}

2nd moment of area
cm^{4}

W_{pl,z}
cm^{3}

W_{el,z}
cm^{3}

Overall result:

Section utilisation: **%**

Click any section to expand

The classification of the cross-section parts (flanges and web) is specified in EN1993-1-1 Table 5.2. In this calculation cross-section classification is carried out for the case of predominant axial force NEd and bending moment My,Ed about the major axis y-y. For this case the web is classified for the combination of bending and compression and the compressive flange is classified for pure compression. The class of the compression part depends on its width c to thickness t ratio, adjusted by the factor ε = 1.000. The classification of the total cross-section is determined by the class of its most unfavorable compression part, web or flange.

- For the compression flange: c / t = (b / 2 - tw / 2 - r) / tf =
- Flange classification: Class

The classification of the cross-section parts is specified in EN1993-1-1 Table 5.2

- For the Web: c / t = (h - 2⋅tf - 2⋅r) / tw See table 5.2 for element subject to bending and shear (α = ) c / t =
- Web classification: Class

Section classification: **Class **

The shear buckling resistance of the web is verified in accordance with EN1993-1-1 §6.2.6(6):

- Shear buckling resistance without additional measures is proven when: h
_{w}/t_{w}≤ 72 ⋅ ε / η - 72 ⋅ ε / η =
- h
_{w}/t_{w}=

Result:

The critical cross-section is verified for tensile axial force in accordance with EN1993-1-1 §6.2.3:

- N
_{Ed}/ N_{t,Rd}≤ 1.0 - Where N
_{Ed}= kN is the design tensile axial force. The tension resistance N_{t,Rd}is estimated as the plastic tension resistance N_{pl,Rd}on the basis of the gross cross-section area A and the steel yield stress f_{y}. - N
_{pl,Rd}= kN

Result:

Utilisation:

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 f_{u}>: N_{u,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:

- N
_{Ed}/ N_{c,Rd}≤ 1.0 - Where N
_{Ed}= kN is the design compressive axial force. For the case of class 1, 2, or 3 cross-section the compression resistance N_{c,Rd}is estimated as: - N
_{c,Rd}= kN

Result:

Utilisation:

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:

M_{Ed} / M_{c,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 W
_{pl}: - For the major axis y-y: M
_{c,y,Rd}= W_{pl,y }⋅ f_{y}/ γ_{M0}= kNm - For the minor axis z-z: M
_{c,z,Rd}= W_{pl,z}⋅ f_{y}/ γ_{M0}= kNm - For bending about the major axis y-y utilisation:
- For bending about the minor axis z-z utilisation:

Bending result:

Utilisation:

The critical cross-section is verified for shear force in accordance with EN1993-1-1 §6.2.6:

V_{Ed}> / V_{c,Rd} ≤ 1.0

- For class 1 or 2 cross-sections the design shear resistance V
_{c,Rd}for shear force along one principal axis is estimated as the plastic shear resistance V_{pl,Rd}on the basis of the corresponding shear area A_{v}: - For the shear force along z-z: V
_{pl,Rd,z }= A_{v,z}⋅ (f_{y}/ √3 ) / γ_{M0}= kN - For the shear force along y-y: Vpl,Rd,y = Av,y ⋅ (fy / √3 ) / γM0 = kN
- For shear about the major axis y-y utilisation:
- For shear about the minor axis z-z utilisation:

Shear result:

Utilisation:

- For class 3 cross-sections the design elastic shear resistance is verified in accordance with EN1993-1-1 §6.2.6(4).
- Shear resistance: [ fy / (√3 ⋅ γM0) ] = N/mm
^{2} - The maximum shear stress τEd for the critical point of the cross-section is verified on the basis of the Von Mises yield criterion: τEd / [ fy / (√3 ⋅ γM0) ] ≤ 1.0
- The shear stress τEd is evaluated on the basis of elastic theory as specified in EN1993-1-1 §6.2.6: τEd = VEd ⋅ S / ( I ⋅ t )
- where S is the first moment of area about the centroidal axis of the part of the cross-section between the examined point and the boundary of the cross-section, I is the corresponding second moment of area of the whole cross-section, and t is the thickness at the examined point.
**For shear stress along axis z-z:**- First moment of area S
_{y}: mm^{3} - Second moment of area I
_{y}: mm^{4} - Shear stress z-z: N/mm
^{2} - Shear utilisation z-z:
**For shear stress along axis y-y:**- First moment of area S
_{z}: mm^{3} - Second moment of area I
_{z}: mm^{4} - Shear stress y-y: N/mm
^{2} - Shear utilisation y-y:
- Result:

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 V
_{Ed}is larger than one-half of the corresponding plastic shear resistance V_{pl,Rd}. - Shear utilisation along axis z-z: V
_{z,Ed}/ V_{pl,Rd,z}= - Shear utilisation along axis y-y: V
_{y,Ed }/ V_{pl,Rd,y}=

- The effect of shear force V
_{z,Ed}on the bending moment resistance should be considered. - The corresponding reduction factors ρ is calculated in accordance with EN1993-1-1 § 6.2.8(3):
- For z-z: ρ = (2⋅V
_{z,Ed}/ V_{pl,Rd,z}- 1)^{2}> = - For y-y: ρ = (2⋅V
_{y,Ed}/ V_{pl,Rd,y}- 1)^{2}= - Worst case yield strength reduction:
- Reduced yield strength: N/mm
^{2} - For z-z: Reduced bending resistance kNm
- Bending utilisation z-z:
- For y-y: Reduced bending resistance kNm
- Bending utilisation y-y:

Bending with shear result:

Utilisation:

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.

- For doubly symmetrical I- and H-sections allowance for the effect of axial force on the bending moment resistance need not be made when the following conditions are satisfied.
- For bending about major axis y-y:
- Check that N
_{Ed}≤ 0.25⋅N_{pl,Rd}= kN - and N
_{Ed}≤ 0.50⋅h_{w}⋅t_{w}⋅f_{y}/ γ_{M0}= kN - For bending about minor axis z-z:
- Check that N
_{Ed}≤ h_{w}⋅t_{w}⋅f_{y}/ γ_{M0 }= kN - N
_{Ed}= kN - Result:

- The normalized axial force n is:
- n = N
_{Ed}/ N_{pl,Rd}= - The ratio a is defined as: a = min[0.5, (A - 2⋅b⋅t
_{f}) / A ] = - The reduced bending moment resistance about major axis y-y is given as:
- M
_{y,Rd}= min[M_{pl,y,Rd}, M_{pl,y,Rd}⋅(1 - n) / (1 - 0.5⋅a) ] = kNm - The reduced bending moment resistance about minor axis z-z is given as:
- M
_{z,Rd}= M_{pl,z,Rd}⋅(1 - [(n - a) / (1 - a)]^{2}>) = kNm - Therefore the utilization for the reduced bending resistance due to axial force is:
- For bending about the major axis y-y: M
_{y,Ed}/ M_{N,y,Rd}= - For bending about the major axis z-z: M
_{z,Ed}/ M_{N,z,Rd}= - The effect of biaxial bending is examined in accordance with the criterion specified in EN1991-1-4 §6.2.9.1(6):
- [M
_{y,Ed}/ M_{N,y,Rd}]α + [M_{z,Ed}/ M_{N,z,Rd]}β ≤ 1 - where the exponents α and β are defined as follows:
- α = 1; β =
- Therefore the utilization factor for biaxial bending including the effect of the axial force is:
- Biaxial bending: u = [M
_{y,Ed}/ M_{N,y,Rd}]^{α}+ [M_{z,Ed}/ M_{N,z,Rd}]^{β}=

Result:

Utilisation:

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 V
_{Ed}is larger than one-half of the corresponding plastic shear resistance V_{pl,Rd}. - Worst case shear force utilisation: V
_{Ed}/ V_{pl,Rd}= - Result:

- For y-y: ρ = (2⋅V
_{y,Ed }/ V_{pl,Rd,y}- 1)^{2}= - Reduced yield strength: N/mm
^{2} - Reduced axial force resistance is N
_{V,pl,Rd}= kN - Normalized axial force n = N
_{Ed}/ N_{V,pl,Rd}= - The ratio a is defined as: a = min[0.5, (A' - 2⋅b⋅t'f) / A'] =
- Moment resistance about major axis y-y: M
_{N,V,y,Rd}= min[M_{V,pl,y,Rd}, M_{V,pl,y,Rd}⋅(1 - n) / (1 - 0.5⋅a) ] = kNm - Moment resistance about major axis y-y: M
_{N,V,z,Rd}= M_{V,pl,z,Rd}⋅(1 - [(n - a) / (1 - a)]2) = kNm - Utilisation for bending about the major axis y-y: M
_{y,Ed}/ M_{N,V,y,Rd}= - Utilisation for bending about the major axis z-z: M
_{z,Ed}/ M_{N,V,z,Rd}= - The effect of biaxial bending is examined in accordance with the criterion specified in EN1991-1-4 §6.2.9.1(6):
- [M
_{y,Ed}/ M_{N,y,Rd}]α + [M_{z,Ed}/ M_{N,z,Rd}]β ≤ 1 - where the exponents α and β are defined as follows:
- α = 1; β =
- Therefore the utilization factor for biaxial bending including the effect of the axial force is:
- Biaxial bending: u = [M
_{y,Ed}/ M_{N,y,Rd}]^{α}+ [M_{z,Ed}/ M_{N,z,Rd}]^{β}=

Result:

Utilisation:

The compression member is verified against flexural buckling in accordance with EN1993-1-1 §6.3.1 as follows: N_{Ed} / N_{b,Rd} ≤ 1.0

N_{b,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: N_{b,Rd} = χ⋅A⋅fy / γ_{M1}

The reduction factor χ due to flexural buckling is calculated for both the major and the minor bending axes.

- The appropriate buckling curve is determined from EN1993-1-1 Table 6.2 as
**Curve ""**. (For rolled I-sections, h/b =, t_{f}= mm, bending about major axis y-y.) - The imperfection factor α corresponding to the buckling curve is determined from EN1993-1-1 Table 6.1 as α = .
- The critical buckling length Lcr,y for flexural buckling about the major axis y-y is considered as Lcr,y = ⋅L = m.
- According to the theory of elasticity the elastic critical buckling load for flexural buckling is:
- N
_{cr,y}= π^{2}⋅E⋅I_{y}/ L_{cr,y2}= kN - The ratio of the compression load to the elastic critical buckling load is N
_{Ed/Ncr,y}= - 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):
- λ
_{y}= (A⋅f_{y}/ N_{cr,y})^{0.5}= - According to EN1993-1-1 §6.3.1.2(4) flexural buckling effects may be ignored when N
_{Ed}/N_{cr,y}≤ 0.04 or λ_{y}≤ 0.20. - Result:

- The factors Φ and χ
_{y}are calculated in accordance with EN1993-1-1 §6.3.1.2: - Φ = 0.5⋅[1 + α⋅(λ
_{y}- 0.20) + λ_{y}^{2}] = - χy = min[1.0, 1 / (Φ + [Φ
^{2}- λ_{y}^{2}]^{0.5})] = - The design buckling resistance of the compression member for flexural buckling about the major axis y-y is calculated as:
- N
_{b,Rd,y}= χ_{y}⋅ A ⋅ f_{y}/ γ_{M1}= kN - Therefore the utilization for the flexural buckling resistance about major axis y-y:
- Flexural buckkling result about major y-y axis:

- The appropriate buckling curve is determined from EN1993-1-1 Table 6.2 as
**Curve ""**. For rolled I-sections, h/b =, t_{f}= mm, bending about minor axis z-z. - The imperfection factor α corresponding to the buckling curve is determined from EN1993-1-1 Table 6.1 as α = .
- The critical buckling length L
_{cr,y}for flexural buckling about the minor axis z-z is considered as L_{cr,z}= ⋅L = m. - According to the theory of elasticity the elastic critical buckling load for flexural buckling is:
- N
_{cr,z}= π_{cr,z}>⋅E⋅I_{z}/ L_{cr,z}^{2}= kN - The ratio of the compression load to the elastic critical buckling load is NEd/Ncr,z =
- 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):
- λ
_{z}= (A⋅f_{y}/ N_{cr,z})^{0.5}= - According to EN1993-1-1 §6.3.1.2(4) flexural buckling effects may be ignored when N
_{Ed}/N_{cr,z}≤ 0.04 or λ_{y}≤ 0.20. - Result:

- The factors Φ and χz are calculated in accordance with EN1993-1-1 §6.3.1.2:
- Φ = 0.5⋅[1 + α⋅(λ
_{z}- 0.20) + λ_{z}^{2}] = - χ
_{y}= min[1.0, 1 / (Φ + [Φ^{2}- λ_{z}^{2}]^{0.5})] = - The design buckling resistance of the compression member for flexural buckling about the minor axis z-z is calculated as:
- N
_{b,Rd,z}= χ_{z}⋅ A ⋅ f_{z}/ γ_{M1}= kN - Therefore the utilization for the flexural buckling resistance about minor axis z-z:
- Flexural buckling result about minor z-z axis:

Flexural buckling result:

Utilisation:

Members with laterally unrestrained compression flange subject to bending about major axis y-y should be verified against lateral-torsional buckling in accordance with EN1993-1-1 §6.3.2 as follows: My,Ed / Mb,Rd ≤ 1.0

Where Mb,Rd is the design buckling resistance moment given in EN1993-1-1 §6.3.2.1(3): Mb,Rd = χLT⋅Wy⋅fy / γM1

- For class 1 or 2 cross-sections: Wy = Wpl,y = cm
^{3} - The reduction factor χLT due to lateral-torsional buckling is calculated for rolled sections or equivalent welded sections in accordance with EN1993-1-1 §6.3.2.3, depending on the elastic critical moment Mcr for lateral-torsional buckling.

- The elastic critical moment Mcr for lateral-torsional buckling may be calculated by the following formula derived from buckling theory:
- Mcr = C1⋅π2⋅E⋅Iz / (k⋅LLT)2 ⋅ ( [ (k /kw)2 ⋅ (Iw /Iz) + (k⋅LLT)2⋅G⋅IT / (π2⋅E⋅Iz) + (C2⋅zg)2]0.5 - C2⋅zg )
- The factors k and kw are effective length factors. The factor k refers to end rotation on plan. It is analogous to the ratio of the buckling length to the system length for a compression member. The factor k should be taken as not less than 1.0 unless the value less than 1.0 can be justified. The factor kw refers to end warping. Unless special provision for warping fixity is made, kw should be taken as 1.0. In the following calculation the effective length factors are considered as k = 1.000 and kw = 1.000.
- The distance between the point of load application and the shear center is denoted as zg. For double symmetric cross-sections the shear center coincides with the centroid of the cross-section. The value of zg is positive for loads acting towards the shear center from their point of application. For loading on the centroid the appropriate value is zg = 0.0 mm.
- The coefficients C1 and C2 depend on the loading and end restraint conditions. It can be shown that the values of C1 and C2 depend on the ratio E⋅Iw / (G⋅Iw⋅LLT2). In the NCCI this ratio is considered equal to 0 which leads to conservative values for the coefficient C1 and the elastic critical moment Mcr. According to the NCCI, for uniform bending moment diagram, corresponding to no internal loading, and ratio of the end moments ψ = 1.0, the corresponding values of the coefficients are:
- C1 = 1.000 and C2 = 0.000
- The value of the elastic critical moment for lateral-torsional buckling is obtained as: Mcr =
**kNm** - The ratio of the applied bending moment to the elastic critical buckling moment is My,Ed/Mcr =

- The appropriate buckling curve is determined from EN1993-1-1 Table 6.5 . For rolled I-sections, h/b = , the corresponding buckling curve is curve "".
- The imperfection factor αLT corresponding to the buckling curve is determined from EN1993-1-1 Table 6.4 as αLT =
- The non-dimensional slenderness λLT for flexural buckling is given in EN1993-1-1 §6.3.2.2(1):
- λLT = (Wy⋅fy / Mcr)0.5 =
- According to EN1993-1-1 §6.3.2.2(4) lateral-torsional buckling effects may be ignored when λLT ≤ λLT,0 or My,Ed/Mcr ≤ λ
_{LT,0}^{2}, where λLT,0 = 0.400. - Result:

- The factors ΦLT and χLT are calculated in accordance with EN1993-1-1 §6.3.2.3:
- ΦLT = 0.5⋅[1 + αLT⋅(λLT - λLT,0) + β⋅λLT2] =
- χLT = min[1.0, 1 / λLT2, 1 / (ΦLT + [ΦLT2 - β⋅λLT2]0.5)] =
- The effect of moment distribution is taken into account in accordance with EN1993-1-1 §6.3.2.3(2):
- For uniform bending moment diagram, corresponding to no internal loading, and ratio of the end moments ψ = 1.0 the corresponding value of the correction factor is kc = 1.000 according to EN1993-1-1 Table 6.6.
- The modification factor f is calculated in accordance with EN1993-1-1 §6.3.2.3(2):
- f = min(1.0, 1 - 0.5⋅(1 - kc)⋅[1 - 2.0⋅(λLT - 0.8)2] ) =
- The modified reduction factor χLT,mod is calculated according to EN1993-1-1 equation (6.58):
- χLT,mod = min(1, 1 / λLT2, χLT / f) =
- The design buckling resistance moment Mb,Rd given in EN1993-1-1 §6.3.2.1(3) is calculated as:
- Mb,Rd = χLT,mod⋅Wy⋅fy / γM1 = kNm

The stability of the steel member subjected to compression force, end moments and transverse loads is verified in accordance with EN1993-1-1 §6.3.3. The individual member is considered as cut out of the system. The interaction effects are described by EN1993-1-1 equations (6.61) and (6.62). For the case of class 1, 2, or 3 cross-sections the equations simplify to:

- NEd / (χy⋅NRk / γM1) + kyy⋅My,Ed / (χLT⋅My,Rk / γM1) + kyz⋅Mz,Ed / (Mz,Rk / γM1) ≤ 1.0
- NEd / (χz⋅NRk / γM1) + kzy⋅My,Ed / (χLT⋅My,Rk / γM1) + kzz⋅Mz,Ed / (Mz,Rk / γM1) ≤ 1.0
- Where χLT, χy and χz are the corresponding reduction factors for lateral-torsional buckling and flexural buckling as calculated in previous sections.
- NRk = A⋅fy = kN
- My,Rk = Wy⋅fy = kN
- Mz,Rk = Wz⋅fy = kN
- The interaction factors kyy, kyz, kzy, kzy depend on the calculation method chosen.
- Method 1 (EN1993-1-1 Annex A) is selected for buckling interaction analysis.

- The equivalent uniform moment factors Cmi,0 are obtained from EN1993-1-1 Table A.2.
- For flexural buckling about major axis y-y the moment diagram My,Ed is considered between points braced along z-z direction.
- For uniform or linearly varying bending moment diagram:
- Cmy,0 = 0.79 + 0.21⋅ψy + 0.36⋅(ψy - 0.33)⋅NEd / Ncr,y =
- For flexural buckling about minor axis z-z the moment diagram Mz,Ed is considered between points braced along y-y direction.
- For uniform or linearly varying bending moment diagram:
- Cmz,0 = 0.79 + 0.21⋅ψz + 0.36⋅(ψz - 0.33)⋅NEd / Ncr,z =

- The following intermediate factors and coefficients are calculated:
- Normalized axial force npl = NEd / (NRk / γM0) =
- The non-dimensional slenderness λLT for lateral-torsional buckling was calculated in the section above as λLT =
- The non-dimensional slenderness λ0 for lateral-torsional buckling due to uniform moment is calculated by repeating previous calculations using C1 = 1.0 and C2 = 0.0. The obtained values are Mcr,0 = kNm and λ0 =
- The maximum non-dimensional slenderness for flexural buckling is λmax = max(λy, λz) =
- Coefficient εy = (My,Ed / Wel,y) / (NEd / A) =
- The ratios of plastic to elastic section modulii are: wy = min(1.5, Wpl,y/Wel,y) = wz = min(1.5, Wpl,z/Wel,z) =
- The coefficient μy is obtained as: μy = (1 - NEd / Ncr,y) / (1 - χy⋅NEd / Ncr,y) =
- The coefficient μz is obtained as: μz = (1 - NEd / Ncr,z) / (1 - χz⋅NEd / Ncr,z) =
- The coefficient aLT is calculated as: aLT = max(0, 1 - IT / Iy) =
- The elastic critical force for torsional buckling is calculated using EN1993-1-3 equation (6.33a) as kN
- The effect of lateral torsional buckling is taken into account in the moment factors Cmy, Cmz, CmLT which depend on the value of λ0, i.e. the non-dimensional slenderness for lateral-torsional buckling due to uniform bending moment.
- Slenderness limit for lateral torsional buckling:
- Where C1 is a factor depending on the loading and end conditions and may be taken as C1 = kc-2 = 1.000-2 = 1.000, where the coefficient kc depends on the shape of the bending moment diagram was calculated above.
- Cmy =
- Cmz =
- CCmLT =
- The following intermediate factors and coefficients are calculated:
- The coefficients bLT to eLT are calculated in accordance with EN1993-1-1 Table A.1 as bLT = , cLT = , dLT = , eLT =
- The coefficients Cyy to Czz are calculated in accordance with EN1993-1-1 Table A.1 as Cyy = , Cyz = , Czy = , Czz =

- The interaction factors kyy, kyz, kzy, kzz are calculated in accordance with EN1993-1-1 Table A.1 For class 1 or 2 cross-sections:
- kyy = Cmy⋅CmLT⋅μy / (1 - NEd / Ncr,y) ⋅ (1 / Cyy) =
- kyz = Cmy⋅CmLT⋅μz / (1 - NEd / Ncr,y) ⋅ (1 / Czy) ⋅ 0.6⋅(wy / wz)0.5 =
- kzy = Cmy⋅CmLT⋅μz / (1 - NEd / Ncr,y) ⋅ (1 / Czy) ⋅ 0.6⋅(wy / wz)0.5 =
- kzz = Cmz⋅μz / (1 - NEd / Ncr,z) ⋅ (1 / Czz) =

- The interaction formulae for the resistance verification according to Method 1 are expressed as:
- NEd / (χy⋅NRk / γM1) + kyy⋅My,Ed / (χLT⋅My,Rk / γM1) + kyz⋅Mz,Ed / (Mz,Rk / γM1) =
- NEd / (χz⋅NRk / γM1) + kzy⋅My,Ed / (χLT⋅My,Rk / γM1) + kzz⋅Mz,Ed / (Mz,Rk / γM1) =