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

Flat element width

c_{f}

162.50

mm

c_{f}

=

h_{t} - 3 \cdot t_{t}

=

200.00 - 3 \cdot 12.50

Flat element height

c_{w}

162.50

mm

c_{w}

=

c_{f}

=

162.50

Steel grade factor

ε_{t}

0.81362

ε_{t}

=

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

=

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

isClassFour

false

isClassFour

=

\frac{c_{t}}{t_{t}} > 124 \cdot ε_{t}

=

13.00 > 124 \cdot 0.81362

isClassThree

false

isClassThree

=

{\begin{cases} 1 = 0 & if isClassFour \\ \frac{c_{t}}{t_{t}} > 83 \cdot ε_{t} & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if false \\ 13.00 > 83 \cdot 0.81362 & otherwise. \end{cases}

isClassTwo

false

isClassTwo

=

{\begin{cases} 1 = 0 & if or (isClassThree, isClassFour) \\ \frac{c_{t}}{t_{t}} > 72 \cdot ε_{t} & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if or (false, false) \\ 13.00 > 72 \cdot 0.81362 & otherwise. \end{cases}

isClassOne

true

isClassOne

=

{\begin{cases} 1 = 1 & if \frac{c_{t}}{t_{t}} \leq 72 \cdot ε_{t} \\ 1 = 0 & otherwise. \end{cases}

=

{\begin{cases} 1 = 1 & if 13.00 \leq 72 \cdot 0.81362 \\ 1 = 0 & otherwise. \end{cases}

Initial stress distribution for pure bending (Flange)

ψ_{t,f}

1.00

Buckling factor (Flange)

k_{sigma,f}

4.00

Plate slenderness

λ_{p,f}

0.28130

λ_{p,f}

=

\frac{\frac{c_{t}}{t_{t}}}{(28.4 \cdot ε_{t} \cdot \sqrt{k_{sigma,f}})}

=

\frac{13.00}{(28.4 \cdot 0.81362 \cdot \sqrt{4.00})}

Reduction factor

ρ_{internal,f}

1.00

ρ_{internal,f}

=

{\begin{cases} (λ_{p,f} - 0.055 \cdot (3 + ψ_{t,f})) \cdot (\frac{1}{{λ_{p,f}}^{2}}) & if λ_{p,f} > 0.5 + \sqrt{0.085 - 0.055 \cdot ψ_{t,f}} \\ 1 & otherwise. \end{cases}

=

{\begin{cases} (0.28130 - 0.055 \cdot (3 + 1.00)) \cdot (\frac{1}{{0.28130}^{2}}) & if 0.28130 > 0.5 + \sqrt{0.085 - 0.055 \cdot 1.00} \\ 1 & otherwise. \end{cases}

checkPsi

true

checkPsi

=

ρ_{internal,f} \leq 1

=

1.00 \leq 1

Initial stress distribution for pure bending (Web)

ψ_{t,w}

-1.00

mm

ψ_{t,w}

=

- 1

Buckling factor for constant compressive stress throughout the section (Web)

k_{sigma,w}

23.90

Plate slenderness

λ_{p,w}

0.11508

λ_{p,w}

=

\frac{(\frac{c_{t}}{t_{t}})}{(28.4 \cdot ε_{t} \cdot \sqrt{k_{sigma,w}})}

=

\frac{(13.00)}{(28.4 \cdot 0.81362 \cdot \sqrt{23.90})}

Reduction factor

ρ_{internal,w}

1.00

ρ_{internal,w}

=

{\begin{cases} λ_{p,w} - 0.055 \cdot (3 + ψ_{t,w}) \cdot (\frac{1}{{λ_{p,w}}^{2}}) & if λ_{p,w} > 0.5 + \sqrt{0.085 - 0.055 \cdot ψ_{t,w}} \\ 1 & otherwise. \end{cases}

=

{\begin{cases} 0.11508 - 0.055 \cdot (3 + -1.00) \cdot (\frac{1}{{0.11508}^{2}}) & if 0.11508 > 0.5 + \sqrt{0.085 - 0.055 \cdot -1.00} \\ 1 & otherwise. \end{cases}

b_{eff,f}

162.50

mm

b_{eff,f}

=

ρ_{internal,f} \cdot c_{f}

=

1.00 \cdot 162.50

b_{lost,f}

mm

b_{lost,f}

=

c_{f} - b_{eff,f}

=

162.50 - 162.50

A_{lost,f}

{mm}^{2}

A_{lost,f}

=

t_{t} \cdot b_{lost,f}

=

12.50 \cdot 0

b_{eff,w}

81.25

mm

b_{eff,w}

=

ρ_{internal,w} \cdot (\frac{c_{w}}{2})

=

1.00 \cdot (\frac{162.50}{2})

b_{lost,w}

mm

b_{lost,w}

=

\frac{c_{w}}{2} - b_{eff,w}

=

\frac{162.50}{2} - 81.25

A_{lost,w}

{mm}^{2}

A_{lost,w}

=

b_{lost,w} \cdot t_{t}

=

0 \cdot 12.50

Effective area

A_{eff}

8704.37

{mm}^{2}

A_{eff}

=

{\begin{cases} A_{t} - A_{lost,f} - 2 \cdot A_{lost,w} & if isClassFour \\ A_{t} & otherwise. \end{cases}

=

{\begin{cases} 8704.37 - 0 - 2 \cdot 0 & if false \\ 8704.37 & otherwise. \end{cases}

Δ_{a,reduction}

1.00

Δ_{a,reduction}

=

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

=

\frac{8704.37}{8704.37}

Shift of neutral axis

e_{N}

mm

e_{N}

=

\frac{((A_{lost,f} \cdot (\frac{h_{t}}{2} - \frac{t_{t}}{2})) + 2 \cdot A_{lost,w} \cdot (\frac{h_{t}}{4}))}{A_{eff}}

=

\frac{((0 \cdot (\frac{200.00}{2} - \frac{12.50}{2})) + 2 \cdot 0 \cdot (\frac{200.00}{4}))}{8704.37}

I_{lost,f}

{mm}^{4}

I_{lost,f}

=

\frac{b_{lost,f} \cdot {t_{t}}^{3}}{12} + A_{lost,f} \cdot {(\frac{h_{t}}{2} - \frac{t_{t}}{2})}^{2}

=

\frac{0 \cdot {12.50}^{3}}{12} + 0 \cdot {(\frac{200.00}{2} - \frac{12.50}{2})}^{2}

I_{lost,w}

{mm}^{4}

I_{lost,w}

=

\frac{t_{t} \cdot {b_{lost,w}}^{3}}{12} + A_{lost,w} \cdot {(\frac{h_{t}}{4})}^{2}

=

\frac{12.50 \cdot 0^{3}}{12} + 0 \cdot {(\frac{200.00}{4})}^{2}

I_{eff}

(4.859e+7)

{mm}^{4}

I_{eff}

=

{\begin{cases} I_{xx} - I_{lost,f} - 2 \cdot I_{lost,w} - A_{eff} \cdot {e_{N}}^{2} & if isClassFour \\ I_{xx} & otherwise. \end{cases}

=

{\begin{cases} (4.859e+7) - 0 - 2 \cdot 0 - 8704.37 \cdot 0^{2} & if false \\ (4.859e+7) & otherwise. \end{cases}

Effective section modulus (compression)

W_{eff,c}

485942

{mm}^{3}

W_{eff,c}

=

\frac{I_{eff}}{(\frac{h_{t}}{2} + e_{N})}

=

\frac{(4.859e+7)}{(\frac{200.00}{2} + 0)}

Effective section modulus (tension)

W_{eff,t}

485942

{mm}^{3}

W_{eff,t}

=

\frac{I_{eff}}{(\frac{h_{t}}{2} - e_{N})}

=

\frac{(4.859e+7)}{(\frac{200.00}{2} - 0)}

Effective section modulus

W_{eff}

485942

{mm}^{3}

W_{eff}

=

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

=

\min (485942, 485942)