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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.

Calculations

Description

Symbol Name

Value

Unit

Comment

Yield strength

f_{y}

355.00

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

Reduced yield strength

f_{y,red}

355.00

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

For thickness between 40 and 80, and nominal yield strength above 420, the reduction is different. See BS EN 1993-1-1 Table 3.1

f_{y,red} = {\begin{cases} f_{y} & if t_{t} \leq 40 \\ f_{y} - 20 & otherwise. \end{cases} = {\begin{cases} 355.00 & if 12.50 \leq 40 \\ 355.00 - 20 & otherwise. \end{cases}

Steel grade factor

ε

0.81362

ε = \sqrt{\frac{235}{f_{y,red}}} = \sqrt{\frac{235}{355.00}}

isClassFour

false

isClassFour = c_{t} \div t_{t} > 42 \cdot ε = 11.40 > 42 \cdot 0.81362

Initial stress distribution for pure compression - Internal compression elements

ψ_{t}

1.00

BS EN 1993-1-5 Table 4.1

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

k_{σ}

4.00

BS EN 1993-1-4 Table 4.1

Plate slenderness

λ_{p}

0.24668

λ_{p} = \frac{c_{t} \div t_{t}}{(28.4 \cdot ε \cdot \sqrt{k_{σ}})} = \frac{11.40}{(28.4 \cdot 0.81362 \cdot \sqrt{4.00})}

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} (0.24668 - 0.055 \cdot (3 + 1.00)) \cdot (\frac{1}{{0.24668}^{2}}) & if 0.24668 > 0.5 + \sqrt{0.085 - 0.055 \cdot 1.00} \\ 1 & otherwise. \end{cases}

checkPsi

true

checkPsi = ρ_{internal} \leq 1 = 1.00 \leq 1

A_{eff}

7704.37

{mm}^{2}

A_{eff} = {\begin{cases} A_{t} - 4 \cdot {t_{t}}^{2} \cdot c_{t} \div t_{t} \cdot (1 - ρ_{internal}) & if isClassFour \\ A_{t} & otherwise. \end{cases} = {\begin{cases} 7704.37 - 4 \cdot {12.50}^{2} \cdot 11.40 \cdot (1 - 1.00) & if false \\ 7704.37 & otherwise. \end{cases}

Δ_{a, reduction}

1.00

Δ_{a, reduction} = \frac{A_{eff}}{A_{t}} = \frac{7704.37}{7704.37}

Calculations

Description

Symbol Name

Value

Unit

Comment

Yield strength

f_{y}

355.00

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

Reduced yield strength

f_{y,red}

355.00

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

For thickness between 40 and 80, and nominal yield strength above 420, the reduction is different. See BS EN 1993-1-1 Table 3.1

f_{y,red} = {\begin{cases} f_{y} & if t_{t} \leq 40 \\ f_{y} - 20 & otherwise. \end{cases} = {\begin{cases} 355.00 & if 12.50 \leq 40 \\ 355.00 - 20 & otherwise. \end{cases}

Steel grade factor

ε

0.81362

ε = \sqrt{\frac{235}{f_{y,red}}} = \sqrt{\frac{235}{355.00}}

isClassFour

false

isClassFour = c_{t} \div t_{t} > 42 \cdot ε = 11.40 > 42 \cdot 0.81362

Initial stress distribution for pure compression - Internal compression elements

ψ_{t}

1.00

BS EN 1993-1-5 Table 4.1

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

k_{σ}

4.00

BS EN 1993-1-4 Table 4.1

Plate slenderness

λ_{p}

0.24668

λ_{p} = \frac{c_{t} \div t_{t}}{(28.4 \cdot ε \cdot \sqrt{k_{σ}})} = \frac{11.40}{(28.4 \cdot 0.81362 \cdot \sqrt{4.00})}

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} (0.24668 - 0.055 \cdot (3 + 1.00)) \cdot (\frac{1}{{0.24668}^{2}}) & if 0.24668 > 0.5 + \sqrt{0.085 - 0.055 \cdot 1.00} \\ 1 & otherwise. \end{cases}

checkPsi

true

checkPsi = ρ_{internal} \leq 1 = 1.00 \leq 1

A_{eff}

7704.37

{mm}^{2}

A_{eff} = {\begin{cases} A_{t} - 4 \cdot {t_{t}}^{2} \cdot c_{t} \div t_{t} \cdot (1 - ρ_{internal}) & if isClassFour \\ A_{t} & otherwise. \end{cases} = {\begin{cases} 7704.37 - 4 \cdot {12.50}^{2} \cdot 11.40 \cdot (1 - 1.00) & if false \\ 7704.37 & otherwise. \end{cases}

Δ_{a, reduction}

1.00

Δ_{a, reduction} = \frac{A_{eff}}{A_{t}} = \frac{7704.37}{7704.37}