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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

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{c_{w}}{t_{t}} > 42 \cdot ε_{t}

=

13.67 > 42 \cdot 0.81362

2

isClassThree

false

isClassThree

=

{\begin{cases} 1 = 0 & if isClassFour \\ \frac{c_{w}}{t_{t}} > 38 \cdot ε_{t} & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if false \\ 13.67 > 38 \cdot 0.81362 & otherwise. \end{cases}

3

isClassTwo

false

isClassTwo

=

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

=

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

4

isClassOne

true

isClassOne

=

{\begin{cases} 1 = 1 & if \frac{c_{w}}{t_{t}} \leq 33 \cdot ε_{t} \\ 1 = 0 & otherwise. \end{cases}

=

{\begin{cases} 1 = 1 & if 13.67 \leq 33 \cdot 0.81362 \\ 1 = 0 & otherwise. \end{cases}

5

Initial stress distribution for pure compression - Internal compression elements

ψ_{t}

1.00

BS EN 1993-1-5 Table 4.1

6

Buckling factor for constant compressive stress throughout the section - Internal compression elements

k_{σ}

4.00

BS EN 1993-1-4 Table 4.1

7

Plate slenderness

λ_{p}

0.29573

λ_{p}

=

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

=

\frac{13.67}{(28.4 \cdot 0.81362 \cdot \sqrt{4.00})}

8

Reduction factor

ρ_{internal}

1.00

ρ_{internal}

=

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

=

{\begin{cases} (0.29573 - 0.055 \cdot (3 + 1.00)) \cdot (\frac{1}{{0.29573}^{2}}) & if 0.29573 > 0.5 + \sqrt{0.085 - 0.055 \cdot 1.00} \\ 1 & otherwise. \end{cases}

9

checkPsi

true

checkPsi

=

ρ_{internal} \leq 1

=

1.00 \leq 1

10

A_{eff}

1563.29

{mm}^{2}

A_{eff}

=

{\begin{cases} A_{t} - 4 \cdot {t_{t}}^{2} \cdot \frac{c_{w}}{t_{t}} \cdot (1 - ρ_{internal}) & if isClassFour \\ A_{t} & otherwise. \end{cases}

=

{\begin{cases} 1563.29 - 4 \cdot {6.00}^{2} \cdot 13.67 \cdot (1 - 1.00) & if false \\ 1563.29 & otherwise. \end{cases}

11

Δ_{a,reduction}

1.00

Δ_{a,reduction}

=

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

=

\frac{1563.29}{1563.29}