Hot Formed I Sections

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Hot-formed I-sections are structural steel shapes produced by hot rolling, giving them an "I" shaped cross-section with parallel flanges and a central web, optimised for carrying bending and shear in buildings and civil works.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Partial Factors

The partial factor for the resistance of cross-sections

γ_{M0}

1.00

The partial factor for the resistance of cross-sections

γ_{M1}

1.00

Design resistance under uniform compression

N_{c,Rd}

24171.1

kN

BS EN 1993-1-1, 6.2.4

N_{c,Rd}

=

\frac{A_{eff} \cdot f_{y,section}}{γ_{M0}} \cdot (\frac{1}{10^{3}})

=

\frac{74372.6 \cdot 325.00}{1.00} \cdot (\frac{1}{10^{3}})

Buckling resistance under uniform compression (Y axis)

Buckling length

L_{cr,y}

14000.0

mm

N_{cr,y}

(1.318e+8)

N

N_{cr,y}

=

\frac{π^{2} \cdot E_{t} \cdot I_{yy}}{{L_{cr,y}}^{2}}

=

\frac{π^{2} \cdot 210000 \cdot (1.246e+10)}{{14000.0}^{2}}

Non-dimensional slenderness

λ_{yy}

0.42830

BS EN 1993-1-1, 6.3.1.3

λ_{yy}

=

{\begin{cases} \sqrt{\frac{A_{eff} \cdot f_{y,section}}{N_{cr,y}} \cdot Δ_{A,reduction}} & if isClassFour \\ \sqrt{\frac{A_{eff} \cdot f_{y,section}}{N_{cr,y}}} & otherwise. \end{cases}

=

{\begin{cases} \sqrt{\frac{74372.6 \cdot 325.00}{(1.318e+8)} \cdot 1.00} & if false \\ \sqrt{\frac{74372.6 \cdot 325.00}{(1.318e+8)}} & otherwise. \end{cases}

Imperfection factor

α_{buckling,y,1}

0.34000

BS EN 1993-1-1, Table 6.2

α_{buckling,y,1}

=

{\begin{cases} {\begin{cases} 0.21 & if t_{f} \leq 40 \\ 0.34 & otherwise. \end{cases} & if \frac{h_{t}}{b_{t}} > 1.2 \\ {\begin{cases} 0.34 & if t_{f} \leq 100 \\ 0.76 & otherwise. \end{cases} & otherwise. \end{cases}

=

{\begin{cases} {\begin{cases} 0.21 & if 64.00 \leq 40 \\ 0.34 & otherwise. \end{cases} & if \frac{1056.00}{314.00} > 1.2 \\ {\begin{cases} 0.34 & if 64.00 \leq 100 \\ 0.76 & otherwise. \end{cases} & otherwise. \end{cases}

Imperfection factor (2)

α_{buckling,y,2}

0.21000

BS EN 1993-1-1, Table 6.2

α_{buckling,y,2}

=

{\begin{cases} {\begin{cases} 0.13 & if t_{f} \leq 40 \\ 0.21 & otherwise. \end{cases} & if \frac{h_{t}}{b_{t}} > 1.2 \\ {\begin{cases} 0.21 & if t_{f} \leq 100 \\ 0.49 & otherwise. \end{cases} & otherwise. \end{cases}

=

{\begin{cases} {\begin{cases} 0.13 & if 64.00 \leq 40 \\ 0.21 & otherwise. \end{cases} & if \frac{1056.00}{314.00} > 1.2 \\ {\begin{cases} 0.21 & if 64.00 \leq 100 \\ 0.49 & otherwise. \end{cases} & otherwise. \end{cases}

Imperfection factor

α_{buckling,y}

0.34000

BS EN 1993-1-1, Table 6.2

α_{buckling,y}

=

{\begin{cases} α_{buckling,y,2} & if SteelGrade = 460 \\ α_{buckling,y,1} & otherwise. \end{cases}

=

{\begin{cases} 0.21000 & if 355.00 = 460 \\ 0.34000 & otherwise. \end{cases}

An intermediate auxiliary factor

Φ_{yy}

0.63053

BS EN 1993-1-1, (6.49)

Φ_{yy}

=

0.5 \cdot (1 + α_{buckling,y} \cdot (λ_{yy} - 0.2) + {λ_{yy}}^{2})

=

0.5 \cdot (1 + 0.34000 \cdot (0.42830 - 0.2) + {0.42830}^{2})

Buckling reduction factor

χ_{yy,1}

0.91469

BS EN 1993-1-1, (6.49)

χ_{yy,1}

=

\frac{1}{(Φ_{yy} + \sqrt{{Φ_{yy}}^{2} - {λ_{yy}}^{2}})}

=

\frac{1}{(0.63053 + \sqrt{{0.63053}^{2} - {0.42830}^{2}})}

χ_{yy}

0.91469

χ_{yy}

=

{\begin{cases} 1 & if χ_{yy,1} > 1 \\ χ_{yy,1} & otherwise. \end{cases}

=

{\begin{cases} 1 & if 0.91469 > 1 \\ 0.91469 & otherwise. \end{cases}

N_{b,y,Rd}

22109.0

kN

N_{b,y,Rd}

=

\frac{χ_{yy} \cdot A_{eff} \cdot f_{y,section}}{γ_{M1}} \cdot (\frac{1}{10^{3}})

=

\frac{0.91469 \cdot 74372.6 \cdot 325.00}{1.00} \cdot (\frac{1}{10^{3}})

Buckling resistance under uniform compression (Z axis)

L_{cr,z}

14000.0

mm

N_{cr,z}

(3.535e+6)

N

N_{cr,z}

=

\frac{π^{2} \cdot E_{t} \cdot I_{zz}}{{L_{cr,z}}^{2}}

=

\frac{π^{2} \cdot 210000 \cdot (3.343e+8)}{{14000.0}^{2}}

λ_{zz}

2.61

λ_{zz}

=

{\begin{cases} \sqrt{\frac{A_{eff} \cdot f_{y,section}}{N_{cr,z}} \cdot Δ_{A,reduction}} & if isClassFour \\ \sqrt{\frac{A_{eff} \cdot f_{y,section}}{N_{cr,z}}} & otherwise. \end{cases}

=

{\begin{cases} \sqrt{\frac{74372.6 \cdot 325.00}{(3.535e+6)} \cdot 1.00} & if false \\ \sqrt{\frac{74372.6 \cdot 325.00}{(3.535e+6)}} & otherwise. \end{cases}

α_{buckling,z,1}

0.49000

α_{buckling,z,1}

=

{\begin{cases} {\begin{cases} 0.34 & if t_{f} \leq 40 \\ 0.49 & otherwise. \end{cases} & if \frac{h_{t}}{b_{t}} > 1.2 \\ {\begin{cases} 0.49 & if t_{f} \leq 40 \\ 0.76 & otherwise. \end{cases} & otherwise. \end{cases}

=

{\begin{cases} {\begin{cases} 0.34 & if 64.00 \leq 40 \\ 0.49 & otherwise. \end{cases} & if \frac{1056.00}{314.00} > 1.2 \\ {\begin{cases} 0.49 & if 64.00 \leq 40 \\ 0.76 & otherwise. \end{cases} & otherwise. \end{cases}

α_{buckling,z,2}

0.21000

α_{buckling,z,2}

=

{\begin{cases} {\begin{cases} 0.13 & if t_{f} \leq 40 \\ 0.21 & otherwise. \end{cases} & if \frac{h_{t}}{b_{t}} > 1.2 \\ {\begin{cases} 0.21 & if t_{f} \leq 100 \\ 0.49 & otherwise. \end{cases} & otherwise. \end{cases}

=

{\begin{cases} {\begin{cases} 0.13 & if 64.00 \leq 40 \\ 0.21 & otherwise. \end{cases} & if \frac{1056.00}{314.00} > 1.2 \\ {\begin{cases} 0.21 & if 64.00 \leq 100 \\ 0.49 & otherwise. \end{cases} & otherwise. \end{cases}

α_{buckling,z}

0.49000

α_{buckling,z}

=

{\begin{cases} α_{buckling,z,2} & if SteelGrade = 460 \\ α_{buckling,z,1} & otherwise. \end{cases}

=

{\begin{cases} 0.21000 & if 355.00 = 460 \\ 0.49000 & otherwise. \end{cases}

Φ_{zz}

4.51

Φ_{zz}

=

0.5 \cdot (1 + α_{buckling,z} \cdot (λ_{zz} - 0.2) + {λ_{zz}}^{2})

=

0.5 \cdot (1 + 0.49000 \cdot (2.61 - 0.2) + {2.61}^{2})

χ_{zz,1}

0.12217

χ_{zz,1}

=

\frac{1}{(Φ_{zz} + \sqrt{{Φ_{zz}}^{2} - {λ_{zz}}^{2}})}

=

\frac{1}{(4.51 + \sqrt{{4.51}^{2} - {2.61}^{2}})}

χ_{zz}

0.12217

χ_{zz}

=

{\begin{cases} 1 & if χ_{zz,1} > 1 \\ χ_{zz,1} & otherwise. \end{cases}

=

{\begin{cases} 1 & if 0.12217 > 1 \\ 0.12217 & otherwise. \end{cases}

N_{b,z,Rd}

2953.02

kN

N_{b,z,Rd}

=

\frac{χ_{zz} \cdot A_{eff} \cdot f_{y,section}}{γ_{M1}} \cdot (\frac{1}{10^{3}})

=

\frac{0.12217 \cdot 74372.6 \cdot 325.00}{1.00} \cdot (\frac{1}{10^{3}})

Buckling resistance under uniform compression (Torsion)

L_{cr,t}

14000.0

mm

N_{cr,t}

(3.864e+7)

N_{cr,t}

=

\frac{1}{({K_{yy}}^{2} + {K_{zz}}^{2})} \cdot (\frac{π^{2} \cdot E_{t} \cdot I_{w}}{{L_{cr,t}}^{2}} + G_{t} \cdot I_{T})

=

\frac{1}{({409.32}^{2} + {67.05}^{2})} \cdot (\frac{π^{2} \cdot 210000 \cdot (8.225e+13)}{{14000.0}^{2}} + 80769.2 \cdot (7.154e+7))

λ_{torsion}

0.79090

λ_{torsion}

=

\sqrt{\frac{A_{eff} \cdot f_{y,section}}{N_{cr,t}}}

=

\sqrt{\frac{74372.6 \cdot 325.00}{(3.864e+7)}}

Φ_{torsion}

0.95753

Φ_{torsion}

=

0.5 \cdot (1 + α_{buckling,z} \cdot (λ_{torsion} - 0.2) + {λ_{torsion}}^{2})

=

0.5 \cdot (1 + 0.49000 \cdot (0.79090 - 0.2) + {0.79090}^{2})

χ_{torsion,1}

0.66787

χ_{torsion,1}

=

\frac{1}{(Φ_{torsion} + \sqrt{{Φ_{torsion}}^{2} - {λ_{torsion}}^{2}})}

=

\frac{1}{(0.95753 + \sqrt{{0.95753}^{2} - {0.79090}^{2}})}

χ_{torsion}

0.66787

χ_{torsion}

=

{\begin{cases} 1 & if χ_{torsion,1} > 1 \\ χ_{torsion,1} & otherwise. \end{cases}

=

{\begin{cases} 1 & if 0.66787 > 1 \\ 0.66787 & otherwise. \end{cases}

N_{b,t,Rd}

16143.2

N_{b,t,Rd}

=

\frac{χ_{torsion} \cdot A_{eff} \cdot f_{y,section}}{γ_{M1}} \cdot (\frac{1}{10^{3}})

=

\frac{0.66787 \cdot 74372.6 \cdot 325.00}{1.00} \cdot (\frac{1}{10^{3}})