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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

Steel grade factor

ε_{t}

0.81362

ε_{t}

=

\sqrt{\frac{235}{f_{y}}}

=

\sqrt{\frac{235}{355.00}}

1

isClassFour

false

isClassFour

=

\frac{h_{t}}{t_{t}} > 11.5 \cdot ε_{t}

=

9.29 > 11.5 \cdot 0.81362

2

Stress ratio

ψ_{t}

0

3

Buckling factor

k_{σ}

0.57000

4

Plate slenderness

λ_{p}

0.53228

λ_{p}

=

\frac{\frac{h_{t}}{t_{t}}}{(28.4 \cdot ε_{t} \cdot \sqrt{k_{σ}})}

=

\frac{9.29}{(28.4 \cdot 0.81362 \cdot \sqrt{0.57000})}

5

Reduction factor

ρ_{t}

1.00

ρ_{t}

=

{\begin{cases} \frac{(λ_{p} - 0.188)}{{λ_{p}}^{2}} & if λ_{p} > 0.748 \\ 1 & otherwise. \end{cases}

=

{\begin{cases} \frac{(0.53228 - 0.188)}{{0.53228}^{2}} & if 0.53228 > 0.748 \\ 1 & otherwise. \end{cases}

6

checkPsi

true

checkPsi

=

ρ_{t} \leq 1

=

1.00 \leq 1

7

b_{eff}

65.00

mm

b_{eff}

=

ρ_{t} \cdot h_{t}

=

1.00 \cdot 65.00

8

b_{lost}

0

mm

b_{lost}

=

h_{t} - b_{eff}

=

65.00 - 65.00

9

A_{lost}

0

{mm}^{2}

A_{lost}

=

2 \cdot t_{t} \cdot b_{lost}

=

2 \cdot 7.00 \cdot 0

10

Effective area

A_{eff}

1739.38

{mm}^{2}

A_{eff}

=

{\begin{cases} A_{t} - A_{lost} & if isClassFour \\ A_{t} & otherwise. \end{cases}

=

{\begin{cases} 1739.38 - 0 & if false \\ 1739.38 & otherwise. \end{cases}

11

Δ_{a,reduction}

1.00

Δ_{a,reduction}

=

\frac{A_{eff}}{A_{t}}

=

\frac{1739.38}{1739.38}

12

d_{w}

3.50

mm

d_{w}

=

\frac{t_{t}}{2}

=

\frac{7.00}{2}

13

d_{f}

32.50

mm

d_{f}

=

\frac{h_{t}}{2} - \frac{b_{lost}}{2}

=

\frac{65.00}{2} - \frac{0}{2}

14

Neutral axis shift

e_{N}

0

mm

e_{N}

=

\frac{(t_{t} \cdot b_{lost} \cdot (d_{w} + d_{f}))}{A_{eff}}

=

\frac{(7.00 \cdot 0 \cdot (3.50 + 32.50))}{1739.38}

15

I_{lost,w}

0

{mm}^{4}

I_{lost,w}

=

\frac{b_{lost} \cdot {t_{t}}^{3}}{12} + \frac{A_{lost}}{2} \cdot {d_{w}}^{2}

=

\frac{0 \cdot {7.00}^{3}}{12} + \frac{0}{2} \cdot {3.50}^{2}

16

I_{lost,f}

0

{mm}^{4}

I_{lost,f}

=

\frac{t_{t} \cdot {b_{lost}}^{3}}{12} + \frac{A_{lost}}{2} \cdot {d_{f}}^{2}

=

\frac{7.00 \cdot 0^{3}}{12} + \frac{0}{2} \cdot {32.50}^{2}

17

Effective second moment of area

I_{eff}

(1.262e+6)

{mm}^{4}

I_{eff}

=

I_{yy} - I_{lost,w} - I_{lost,f} - A_{eff} \cdot {e_{N}}^{2}

=

(1.262e+6) - 0 - 0 - 1739.38 \cdot 0^{2}

18

Section modulus (Compression)

W_{eff,c}

19421.4

{mm}^{3}

W_{eff,c}

=

\frac{I_{eff}}{(h_{t} + e_{N})}

=

\frac{(1.262e+6)}{(65.00 + 0)}

19

Section modulus (Tension)

W_{eff,t}

19421.4

{mm}^{3}

W_{eff,t}

=

\frac{I_{eff}}{(h_{t} - e_{N})}

=

\frac{(1.262e+6)}{(65.00 - 0)}

20

Effective section modulus

W_{eff}

19421.4

{mm}^{3}

W_{eff}

=

\min (W_{eff,c}, W_{eff,t})

=

\min (19421.4, 19421.4)