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Hot Formed Circular Hollow Sections

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Hot-formed Circular Hollow Sections (CHS) are tubular profiles formed at high temperatures, offering uniform strength in all directions and superior torsional resistance.

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Calculations

Description

Symbol Name

Value

Unit

Comment

0

Steel grade factor

ε_{t}

0.92442

ε_{t}

=

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

=

\sqrt{\frac{235}{275.00}}

1

isClassFour

false

isClassFour

=

\frac{d_{out}}{t_{t}} > 90 \cdot {ε_{t}}^{2}

=

13.25 > 90 \cdot {0.92442}^{2}

2

isClassThree

false

isClassThree

=

{\begin{cases} 1 = 0 & if isClassFour \\ \frac{d_{out}}{t_{t}} > 70 \cdot {ε_{t}}^{2} & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if false \\ 13.25 > 70 \cdot {0.92442}^{2} & otherwise. \end{cases}

3

isClassTwo

false

isClassTwo

=

{\begin{cases} 1 = 0 & if or (isClassThree, isClassFour) \\ \frac{d_{out}}{t_{t}} > 50 \cdot {ε_{t}}^{2} & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if or (false, false) \\ 13.25 > 50 \cdot {0.92442}^{2} & otherwise. \end{cases}

4

isClassOne

true

isClassOne

=

{\begin{cases} 1 = 1 & if \frac{d_{out}}{t_{t}} \leq 50 \cdot {ε_{t}}^{2} \\ 1 = 0 & otherwise. \end{cases}

=

{\begin{cases} 1 = 1 & if 13.25 \leq 50 \cdot {0.92442}^{2} \\ 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}

0.25235

λ_{p}

=

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

=

\frac{13.25}{(28.4 \cdot 0.92442 \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} (0.25235 - 0.055 \cdot (3 + 1.00)) \cdot (\frac{1}{{0.25235}^{2}}) & if 0.25235 > 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}

394.08

{mm}^{2}

A_{eff}

=

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

=

{\begin{cases} 394.08 - 4 \cdot {3.20}^{2} \cdot 13.25 \cdot (1 - 1.00) & if false \\ 394.08 & otherwise. \end{cases}

11

Δ_{a,reduction}

1.00

Δ_{a,reduction}

=

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

=

\frac{394.08}{394.08}