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Hot Formed Square Hollow Sections

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Hot-formed Square Hollow Sections are box-section profiles formed at elevated temperatures. They offer efficient structural performance for columns and bracing.

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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}

8783.89

kN

BS EN 1993-1-1, 6.2.4

N_{c,Rd}

=

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

=

\frac{25460.6 \cdot 345.00}{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}

(6.369e+6)

N

N_{cr,y}

=

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

=

\frac{π^{2} \cdot 210000 \cdot (6.023e+8)}{{14000.0}^{2}}

Non-dimensional slenderness

λ_{yy}

1.17

BS EN 1993-1-1, 6.3.1.3

λ_{yy}

=

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

=

{\begin{cases} \sqrt{\frac{25460.6 \cdot 345.00}{(6.369e+6)} \cdot 1.00} & if false \\ \sqrt{\frac{25460.6 \cdot 345.00}{(6.369e+6)}} & otherwise. \end{cases}

Imperfection factor

α_{buckling}

0.21000

BS EN 1993-1-1, Table 6.2

α_{buckling}

=

{\begin{cases} 0.13 & if SteelGrade = 460 \\ 0.21 & otherwise. \end{cases}

=

{\begin{cases} 0.13 & if 355.00 = 460 \\ 0.21 & otherwise. \end{cases}

An intermediate auxiliary factor

Φ_{yy}

1.29

BS EN 1993-1-1, (6.49)

Φ_{yy}

=

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

=

0.5 \cdot (1 + 0.21000 \cdot (1.17 - 0.2) + {1.17}^{2})

Buckling reduction factor

χ_{yy,1}

0.54638

BS EN 1993-1-1, (6.49)

χ_{yy,1}

=

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

=

\frac{1}{(1.29 + \sqrt{{1.29}^{2} - {1.17}^{2}})}

χ_{yy}

0.54638

χ_{yy}

=

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

=

{\begin{cases} 1 & if 0.54638 > 1 \\ 0.54638 & otherwise. \end{cases}

N_{b,Rd}

4799.31

kN

N_{b,Rd}

=

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

=

\frac{0.54638 \cdot 25460.6 \cdot 345.00}{1.00} \cdot (\frac{1}{10^{3}})

Buckling resistance under uniform compression (Torsion)

L_{cr,t}

14000.0

mm

N_{cr,t}

(1.723e+9)

N

For closed sections, resistance provided by warping is negligible

N_{cr,t}

=

\frac{1}{(2 \cdot {K_{t}}^{2})} \cdot (\frac{π^{2} \cdot E_{t} \cdot 0}{{L_{cr,t}}^{2}} + G_{t} \cdot I_{T})

=

\frac{1}{(2 \cdot {153.80}^{2})} \cdot (\frac{π^{2} \cdot 210000 \cdot 0}{{14000.0}^{2}} + 80769.2 \cdot (1.009e+9))

λ_{torsion}

0.07139

λ_{torsion}

=

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

=

\sqrt{\frac{25460.6 \cdot 345.00}{(1.723e+9)}}

Φ_{torsion}

0.48904

Φ_{torsion}

=

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

=

0.5 \cdot (1 + 0.21000 \cdot (0.07139 - 0.2) + {0.07139}^{2})

χ_{torsion,1}

1.03

χ_{torsion,1}

=

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

=

\frac{1}{(0.48904 + \sqrt{{0.48904}^{2} - {0.07139}^{2}})}

χ_{torsion}

1.00

χ_{torsion}

=

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

=

{\begin{cases} 1 & if 1.03 > 1 \\ 1.03 & otherwise. \end{cases}

N_{b,t,Rd}

8783.89

kN

N_{b,t,Rd}

=

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

=

\frac{1.00 \cdot 25460.6 \cdot 345.00}{1.00} \cdot (\frac{1}{10^{3}})