Hot Formed Rectangular Hollow Sections

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Hot-formed Rectangular Hollow Sections are rectangular profiles formed at elevated temperatures, providing lower residual stresses. Suitable for columns, beams, and trusses.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Steel grade factor

ε_{t}

0.81362

ε_{t}

=

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

=

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

isClassFour

false

isClassFour

=

or (\frac{c_{w}}{t_{t}} > 124 \cdot ε_{t}, \frac{c_{f}}{t_{t}} > 42 \cdot ε_{t})

=

or (13.67 > 124 \cdot 0.81362, 5.33 > 42 \cdot 0.81362)

isClassThree

false

isClassThree

=

{\begin{cases} 1 = 0 & if isClassFour \\ or (\frac{c_{w}}{t_{t}} > 83 \cdot ε_{t}, \frac{c_{f}}{t_{t}} > 38 \cdot ε_{t}) & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if false \\ or (13.67 > 83 \cdot 0.81362, 5.33 > 38 \cdot 0.81362) & otherwise. \end{cases}

isClassTwo

false

isClassTwo

=

{\begin{cases} 1 = 0 & if or (isClassThree, isClassFour) \\ or (\frac{c_{w}}{t_{t}} > 72 \cdot ε_{t}, \frac{c_{f}}{t_{t}} > 33 \cdot ε_{t}) & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if or (false, false) \\ or (13.67 > 72 \cdot 0.81362, 5.33 > 33 \cdot 0.81362) & otherwise. \end{cases}

isClassOne

true

isClassOne

=

{\begin{cases} 1 = 1 & if and (\frac{c_{w}}{t_{t}} \leq 72 \cdot ε_{t}, \frac{c_{f}}{t_{t}} \leq 33 \cdot ε_{t}) \\ 1 = 0 & otherwise. \end{cases}

=

{\begin{cases} 1 = 1 & if and (13.67 \leq 72 \cdot 0.81362, 5.33 \leq 33 \cdot 0.81362) \\ 1 = 0 & otherwise. \end{cases}

Initial stress distribution for pure bending (Web)

ψ_{t,w}

-1.00

ψ_{t,w}

=

- 1

Buckling factor (Web)

k_{sigma,w}

23.90

Initial stress distribution for pure bending (Flange)

ψ_{t,f}

1.00

Buckling factor (Flange)

k_{sigma,f}

4.00

Plate slenderness (Web)

λ_{p,w}

0.12098

λ_{p,w}

=

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

=

\frac{13.67}{(28.4 \cdot 0.81362 \cdot \sqrt{23.90})}

Plate slenderness (Flange)

λ_{p,f}

0.11706

λ_{p,f}

=

\frac{\frac{c_{f}}{t_{t}}}{(28 \cdot ε_{t} \cdot \sqrt{k_{sigma,f}})}

=

\frac{5.33}{(28 \cdot 0.81362 \cdot \sqrt{4.00})}

Reduction factor (Web)

ρ_{web}

1.00

ρ_{web}

=

{\begin{cases} \frac{(λ_{p,w} - 0.11)}{{λ_{p,w}}^{2}} & if λ_{p,w} > 0.874 \\ 1 & otherwise. \end{cases}

=

{\begin{cases} \frac{(0.12098 - 0.11)}{{0.12098}^{2}} & if 0.12098 > 0.874 \\ 1 & otherwise. \end{cases}

Reduction factor (Flange)

ρ_{flange}

1.00

ρ_{flange}

=

{\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} (0.12098 - 0.055 \cdot (3 + -1.00)) \cdot (\frac{1}{{0.12098}^{2}}) & if 0.12098 > 0.5 + \sqrt{0.085 - 0.055 \cdot -1.00} \\ 1 & otherwise. \end{cases}

{checkPsi}_{web}

true

{checkPsi}_{web}

=

ρ_{web} \leq 1

=

1.00 \leq 1

{checkPsi}_{flange}

true

{checkPsi}_{flange}

=

ρ_{flange} \leq 1

=

1.00 \leq 1

b_{eff,w}

41.00

mm

b_{eff,w}

=

\frac{ρ_{web} \cdot (\frac{c_{w}}{t_{t}} \cdot t_{t})}{2}

=

\frac{1.00 \cdot (13.67 \cdot 6.00)}{2}

b_{lost,w}

mm

b_{lost,w}

=

\frac{(\frac{c_{w}}{t_{t}} \cdot t_{t})}{2} - b_{eff,w}

=

\frac{(13.67 \cdot 6.00)}{2} - 41.00

b_{eff,f}

32.00

mm

b_{eff,f}

=

ρ_{flange} \cdot \frac{c_{f}}{t_{t}} \cdot t_{t}

=

1.00 \cdot 5.33 \cdot 6.00

b_{lost,f}

mm

b_{lost,f}

=

\frac{c_{f}}{t_{t}} \cdot t_{t} - b_{eff,f}

=

5.33 \cdot 6.00 - 32.00

A_{lost,w}

{mm}^{2}

A_{lost,w}

=

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

=

6.00 \cdot 0

A_{lost,f}

{mm}^{2}

A_{lost,f}

=

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

=

6.00 \cdot 0

A_{eff}

1563.29

{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} 1563.29 - 0 - 2 \cdot 0 & if false \\ 1563.29 & otherwise. \end{cases}

Δ_{a,reduction}

1.00

Δ_{a,reduction}

=

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

=

\frac{1563.29}{1563.29}

d_{w}

25.00

mm

d_{w}

=

\frac{h_{t}}{4}

=

\frac{100.00}{4}

d_{f}

47.00

mm

d_{f}

=

\frac{h_{t}}{2} - \frac{t_{t}}{2}

=

\frac{100.00}{2} - \frac{6.00}{2}

Neutral axis shift

e_{N}

mm

e_{N}

=

\frac{(2 \cdot A_{lost,w} \cdot d_{w} + A_{lost,f} \cdot d_{f})}{A_{eff}}

=

\frac{(2 \cdot 0 \cdot 25.00 + 0 \cdot 47.00)}{1563.29}

I_{lost,w}

{mm}^{4}

I_{lost,w}

=

A_{lost,w} \cdot {d_{w}}^{2}

=

0 \cdot {25.00}^{2}

I_{lost,f}

{mm}^{4}

I_{lost,f}

=

A_{lost,f} \cdot {d_{f}}^{2}

=

0 \cdot {47.00}^{2}

Effective second moment of area

I_{eff}

(1.788e+6)

{mm}^{4}

I_{eff}

=

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

=

{\begin{cases} (1.788e+6) - 0 - 2 \cdot 0 - 1563.29 \cdot 0^{2} & if false \\ (1.788e+6) & otherwise. \end{cases}

Effective section modulus (Compression)

W_{eff,c}

35750.8

{mm}^{2}

W_{eff,c}

=

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

=

\frac{(1.788e+6)}{(\frac{100.00}{2} + 0)}

Effective section modulus (Tension)

W_{eff,t}

35750.8

{mm}^{3}

W_{eff,t}

=

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

=

\frac{(1.788e+6)}{(\frac{100.00}{2} - 0)}

Effective section modulus

W_{eff}

35750.8

{mm}^{3}

W_{eff}

=

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

=

\min (35750.8, 35750.8)