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Hot Formed Tees Split From I Section

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Hot-formed Tees split from Universal Columns (UC) are T-shaped sections created by cutting a UC section longitudinally. Used for truss chords or stiffeners.

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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}

2028.05

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{5878.41 \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}

946705

N

N_{cr,y}

=

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

=

\frac{π^{2} \cdot 210000 \cdot (8.953e+7)}{{14000.0}^{2}}

Non-dimensional slenderness

λ_{yy}

1.46

BS EN 1993-1-1, 6.3.1.3

λ_{yy}

=

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

=

\sqrt{\frac{5878.41 \cdot 345.00}{946705}}

Imperfection factor

α_{buckling,y}

0.49000

BS EN 1993-1-1, Table 6.2

An intermediate auxiliary factor

Φ_{yy}

1.88

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 + 0.49000 \cdot (1.46 - 0.2) + {1.46}^{2})

Buckling reduction factor

χ_{yy,1}

0.32661

BS EN 1993-1-1, (6.49)

χ_{yy,1}

=

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

=

\frac{1}{(1.88 + \sqrt{{1.88}^{2} - {1.46}^{2}})}

χ_{yy}

0.32661

χ_{yy}

=

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

=

{\begin{cases} 1 & if 0.32661 > 1 \\ 0.32661 & otherwise. \end{cases}

N_{b,y,Rd}

662.39

kN

N_{b,y,Rd}

=

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

=

\frac{0.32661 \cdot 5878.41 \cdot 345.00}{1.00} \cdot (\frac{1}{10^{3}})

Buckling resistance under uniform compression (Z axis)

L_{cr,z}

14000.0

mm

N_{cr,z}

231702

N

N_{cr,z}

=

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

=

\frac{π^{2} \cdot 210000 \cdot (2.191e+7)}{{14000.0}^{2}}

λ_{zz}

2.96

λ_{zz}

=

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

=

\sqrt{\frac{5878.41 \cdot 345.00}{231702}}

α_{buckling,z}

0.49000

Φ_{zz}

5.55

Φ_{zz}

=

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

=

0.5 \cdot (1 + 0.49000 \cdot (2.96 - 0.2) + {2.96}^{2})

χ_{zz,1}

0.09755

χ_{zz,1}

=

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

=

\frac{1}{(5.55 + \sqrt{{5.55}^{2} - {2.96}^{2}})}

χ_{zz}

0.09755

χ_{zz}

=

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

=

{\begin{cases} 1 & if 0.09755 > 1 \\ 0.09755 & otherwise. \end{cases}

N_{b,z,Rd}

197.85

kN

N_{b,z,Rd}

=

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

=

\frac{0.09755 \cdot 5878.41 \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}

(3.348e+6)

N

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}{({105.96}^{2} + {52.42}^{2})} \cdot (\frac{π^{2} \cdot 210000 \cdot (2.089e+9)}{{14000.0}^{2}} + 80769.2 \cdot 578994)

λ_{torsion}

0.77835

λ_{torsion}

=

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

=

\sqrt{\frac{5878.41 \cdot 345.00}{(3.348e+6)}}

Φ_{torsion}

0.94461

Φ_{torsion}

=

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

=

0.5 \cdot (1 + 0.49000 \cdot (0.77835 - 0.2) + {0.77835}^{2})

χ_{torsion,1}

0.67576

χ_{torsion,1}

=

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

=

\frac{1}{(0.94461 + \sqrt{{0.94461}^{2} - {0.77835}^{2}})}

χ_{torsion}

0.67576

χ_{torsion}

=

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

=

{\begin{cases} 1 & if 0.67576 > 1 \\ 0.67576 & otherwise. \end{cases}

N_{b,t,Rd}

1370.47

kN

N_{b,t,Rd}

=

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

=

\frac{0.67576 \cdot 5878.41 \cdot 345.00}{1.00} \cdot (\frac{1}{10^{3}})