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Hot Formed Back To Back Equal Angles

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Hot-formed Back-to-Back Equal Angles consist of two equal leg angles connected together to form a T-shape or star-shape profile, improving stability for compression members.

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Calculations

Description

Symbol Name

Value

Unit

Comment

0

Partial safety factor (yielding)

γ_{M0}

1.00

1

Partial safety factor (buckling)

γ_{M1}

1.00

2

Design resistance under uniform compression

N_{c,Rd}

617.48

kN

N_{c,Rd}

=

\frac{A_{eff} \cdot f_{y}}{(γ_{M0} \cdot 1000)}

=

\frac{1739.38 \cdot 355.00}{(1.00 \cdot 1000)}

3

Buckling length (x-axis)

L_{cr,x}

1000.00

mm

4

Euler critical load (x-axis)

N_{cr,x}

(1.387e+6)

N

N_{cr,x}

=

\frac{(π^{2} \cdot E_{t} \cdot I_{xx})}{{L_{cr,x}}^{2}}

=

\frac{(π^{2} \cdot 210000 \cdot 669182)}{{1000.00}^{2}}

5

Non-dimensional slenderness (x-axis)

λ_{x}

0.66724

λ_{x}

=

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

=

\sqrt{\frac{1739.38 \cdot 355.00}{(1.387e+6)}}

6

Imperfection factor (x-axis)

α_{x}

0.49000

7

ϕ_{x}

0.83708

ϕ_{x}

=

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

=

0.5 \cdot (1 + 0.49000 \cdot (0.66724 - 0.2) + {0.66724}^{2})

8

Buckling reduction factor (x-axis)

χ_{x,1}

0.74486

χ_{x,1}

=

\frac{1}{(ϕ_{x} + \sqrt{{ϕ_{x}}^{2} - {λ_{x}}^{2}})}

=

\frac{1}{(0.83708 + \sqrt{{0.83708}^{2} - {0.66724}^{2}})}

9

χ_{x}

0.74486

χ_{x}

=

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

=

{\begin{cases} 1 & if 0.74486 > 1 \\ 0.74486 & otherwise. \end{cases}

10

Buckling resistance (x-axis)

N_{b,x,Rd}

459.94

kN

N_{b,x,Rd}

=

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

=

\frac{0.74486 \cdot 1739.38 \cdot 355.00}{(1.00 \cdot 10^{3})}

11

Buckling length (y-axis)

L_{cr,y}

1000.00

mm

12

Euler critical load (y-axis)

N_{cr,y}

(2.616e+6)

N

N_{cr,y}

=

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

=

\frac{π^{2} \cdot 210000 \cdot (1.262e+6)}{{1000.00}^{2}}

13

Non-dimensional slenderness (y-axis)

λ_{y}

0.48580

λ_{y}

=

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

=

\sqrt{\frac{1739.38 \cdot 355.00}{(2.616e+6)}}

14

Imperfection factor (y-axis)

α_{y}

0.49000

15

ϕ_{y}

0.68802

ϕ_{y}

=

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

=

0.5 \cdot (1 + 0.49000 \cdot (0.48580 - 0.2) + {0.48580}^{2})

16

Buckling resistance factor (y-axis)

χ_{y,1}

0.85090

χ_{y,1}

=

\frac{1}{(ϕ_{y} + \sqrt{{ϕ_{y}}^{2} - {λ_{y}}^{2}})}

=

\frac{1}{(0.68802 + \sqrt{{0.68802}^{2} - {0.48580}^{2}})}

17

χ_{y}

0.85090

χ_{y}

=

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

=

{\begin{cases} 1 & if 0.85090 > 1 \\ 0.85090 & otherwise. \end{cases}

18

Buckling resistance (y-axis)

N_{b,y,Rd}

525.41

kN

N_{b,y,Rd}

=

(\frac{χ_{y} \cdot A_{eff} \cdot f_{y}}{(γ_{M1} \cdot 1000)})

=

(\frac{0.85090 \cdot 1739.38 \cdot 355.00}{(1.00 \cdot 1000)})