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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

Steel grade factor

ε_{t}

0.92442

ε_{t}

=

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

=

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

isClassFour

false

isClassFour

=

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

=

13.25 > 90 \cdot {0.92442}^{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}

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}

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}

Mid-surface radius

r_{m}

19.60

mm

r_{m}

=

\frac{(d_{out} - t_{t})}{2}

=

\frac{(42.40 - 3.20)}{2}

Effective shell length

L_{t}

90.00

m

Dimensionless shell length

ω_{t}

6.35

ω_{t}

=

\frac{L_{t}}{(\sqrt{r_{m}} \cdot t_{t})}

=

\frac{90.00}{(\sqrt{19.60} \cdot 3.20)}

Tolerance class (Class A = 40, Class B = 25, Class C = 16)

Q_{wk}

40.00

Geometric imperfections amplitude

{deltaw}_{k}

0.49000

{deltaw}_{k}

=

\frac{r_{m}}{Q_{wk}}

=

\frac{19.60}{40.00}

Meridional imperfection sensitivity factor

α_{x}

0.90186

α_{x}

=

\frac{1.44}{(1 + 1.91 \cdot {(\frac{{deltaw}_{k}}{t_{t}})}^{0.62})}

=

\frac{1.44}{(1 + 1.91 \cdot {(\frac{0.49000}{3.20})}^{0.62})}

BC Coefficient (BC1-BC1 = 6, BC1-BC2 = 3, BC2-BC2 = 1)

C_{xb}

6.00

Max coeffcient for long cylinders

C_{x,l}

1.10

C_{x,l}

=

\max (0.6, 1 + 0.2 \cdot {(1 - \frac{(2 \cdot C_{xb} \cdot t_{t})}{(r_{m} \cdot ω_{t})})}^{2})

=

\max (0.6, 1 + 0.2 \cdot {(1 - \frac{(2 \cdot 6.00 \cdot 3.20)}{(19.60 \cdot 6.35)})}^{2})

Buckling coefficient

C_{x}

1.10

C_{x}

=

{\begin{cases} 1.36 - \frac{1.83}{ω_{t}} - \frac{2.07}{{ω_{t}}^{2}} & if ω_{t} \leq 1.7 \\ {\begin{cases} 1 & if ω_{t} \leq 0.5 \cdot (\frac{r_{m}}{t_{t}}) \\ C_{x,l} & otherwise. \end{cases} & otherwise. \end{cases}

=

{\begin{cases} 1.36 - \frac{1.83}{6.35} - \frac{2.07}{{6.35}^{2}} & if 6.35 \leq 1.7 \\ {\begin{cases} 1 & if 6.35 \leq 0.5 \cdot (\frac{19.60}{3.20}) \\ 1.10 & otherwise. \end{cases} & otherwise. \end{cases}

Meridional elastic critical stress

σ_{x.Rcr}

22727.2

\frac{N}{{mm}^{2}}

σ_{x.Rcr}

=

0.605 \cdot E_{t} \cdot C_{x} \cdot (\frac{t_{t}}{r_{m}})

=

0.605 \cdot 210000 \cdot 1.10 \cdot (\frac{3.20}{19.60})

Shell relative slenderness

λ_{x}

0.11000

λ_{x}

=

\sqrt{\frac{f_{y}}{σ_{x.Rcr}}}

=

\sqrt{\frac{275.00}{22727.2}}

β

0.60000

Plastic limit slenderness

λ_{xp}

1.50

λ_{xp}

=

\sqrt{\frac{α_{x}}{(1 - β)}}

=

\sqrt{\frac{0.90186}{(1 - 0.60000)}}

Reduction factor

χ_{t}

1.00

χ_{t}

=

{\begin{cases} 1 & if λ_{x} \leq 0.2 \\ {\begin{cases} 1 - β \cdot (\frac{(λ_{x} - 0.2)}{(λ_{xp} - 0.2)}) & if λ_{x} \leq λ_{xp} \\ \frac{α_{x}}{{λ_{x}}^{2}} & otherwise. \end{cases} & otherwise. \end{cases}

=

{\begin{cases} 1 & if 0.11000 \leq 0.2 \\ {\begin{cases} 1 - 0.60000 \cdot (\frac{(0.11000 - 0.2)}{(1.50 - 0.2)}) & if 0.11000 \leq 1.50 \\ \frac{0.90186}{{0.11000}^{2}} & otherwise. \end{cases} & otherwise. \end{cases}

Effective area

A_{eff}

394.08

{mm}^{2}

A_{eff}

=

{\begin{cases} χ_{t} \cdot A_{t} & if isClassFour \\ A_{t} & otherwise. \end{cases}

=

{\begin{cases} 1.00 \cdot 394.08 & if false \\ 394.08 & otherwise. \end{cases}

Δ_{a,reduction}

1.00

Δ_{a,reduction}

=

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

=

\frac{394.08}{394.08}

Effective section modulus

W_{eff}

3594.32

{mm}^{3}

W_{eff}

=

{\begin{cases} χ_{t} \cdot (\frac{I}{(\frac{d_{out}}{2})}) & if isClassFour \\ \frac{I}{(\frac{d_{out}}{2})} & otherwise. \end{cases}

=

{\begin{cases} 1.00 \cdot (\frac{76199.6}{(\frac{42.40}{2})}) & if false \\ \frac{76199.6}{(\frac{42.40}{2})} & otherwise. \end{cases}