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Hot Formed Parallel Flange Channels

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Hot-formed Parallel Flange Channels (PFC) are C-shaped sections with parallel inner and outer flange surfaces, simplifying connections. Used for columns, lintels, and beams.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Steel grade factor for the web

ε_{web}

0.92442

BS EN 1993-1-1 Table 5.2

ε_{web}

=

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

=

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

Steel grade factor for the flange

ε_{flange}

0.94170

BS EN 1993-1-1 Table 5.2

ε_{flange}

=

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

=

\sqrt{\frac{235}{265.00}}

isClassFour

false

BS EN 1993-1-1 Table 5.2

isClassFour

=

or (\frac{c_{w}}{t_{w}} > 42 \cdot ε_{web}, \frac{c_{f}}{t_{f}} > 14 \cdot ε_{flange})

=

or (32.91 > 42 \cdot 0.92442, 3.89 > 14 \cdot 0.94170)

isClassThree

false

isClassThree

=

{\begin{cases} 1 = 0 & if isClassFour \\ or (\frac{c_{w}}{t_{w}} > 38 \cdot ε_{web}, \frac{c_{f}}{t_{f}} > 10 \cdot ε_{flange}) & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if false \\ or (32.91 > 38 \cdot 0.92442, 3.89 > 10 \cdot 0.94170) & otherwise. \end{cases}

isClassTwo

true

isClassTwo

=

{\begin{cases} 1 = 0 & if or (isClassThree, isClassFour) \\ or (\frac{c_{w}}{t_{w}} > 33 \cdot ε_{web}, \frac{c_{f}}{t_{f}} > 9 \cdot ε_{flange}) & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if or (false, false) \\ or (32.91 > 33 \cdot 0.92442, 3.89 > 9 \cdot 0.94170) & otherwise. \end{cases}

isClassOne

false

isClassOne

=

{\begin{cases} 1 = 1 & if and (\frac{c_{w}}{t_{w}} \leq 33 \cdot ε_{web}, \frac{c_{f}}{t_{f}} \leq 9 \cdot ε_{flange}) \\ 1 = 0 & otherwise. \end{cases}

=

{\begin{cases} 1 = 1 & if and (32.91 \leq 33 \cdot 0.92442, 3.89 \leq 9 \cdot 0.94170) \\ 1 = 0 & otherwise. \end{cases}

Initial stress distribution for pure compression - Internal compression elements

ψ_{t,web}

1.00

BS EN 1993-1-5 Table 4.1

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

k_{sigma,web}

4.00

BS EN 1993-1-4 Table 4.1

Plate slenderness of the web

λ_{p,web}

0.62676

λ_{p,web}

=

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

=

\frac{32.91}{(28.4 \cdot 0.92442 \cdot \sqrt{4.00})}

Reduction factor for the web

ρ_{web}

1.00

ρ_{web}

=

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

=

{\begin{cases} (0.62676 - 0.055 \cdot (3 + 1.00)) \cdot (\frac{1}{{0.62676}^{2}}) & if 0.62676 > 0.5 + \sqrt{0.085 - 0.055 \cdot 1.00} \\ 1 & otherwise. \end{cases}

checkWeb

true

checkWeb

=

ρ_{web} \leq 1

=

1.00 \leq 1

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

k_{sigma,"flange"}

0.43000

BS EN 1993-1-4 Table 4.2

Plate slenderness of the flange

λ_{p,flange}

0.22208

λ_{p,flange}

=

\frac{\frac{c_{f}}{t_{f}}}{(28.4 \cdot ε_{flange} \cdot \sqrt{k_{sigma,"flange"}})}

=

\frac{3.89}{(28.4 \cdot 0.94170 \cdot \sqrt{0.43000})}

Reduction factor for the flange

ρ_{flange}

1.00

ρ_{flange}

=

{\begin{cases} \frac{(λ_{p,flange} - 0.188)}{{λ_{p,flange}}^{2}} & if λ_{p,flange} > 0.748 \\ 1 & otherwise. \end{cases}

=

{\begin{cases} \frac{(0.22208 - 0.188)}{{0.22208}^{2}} & if 0.22208 > 0.748 \\ 1 & otherwise. \end{cases}

checkFlange

true

checkFlange

=

ρ_{flange} \leq 1

=

1.00 \leq 1

Effective area of the section

A_{eff}

8208.57

{mm}^{2}

A_{eff}

=

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

=

{\begin{cases} 8208.57 - 4 \cdot {19.00}^{2} \cdot 3.89 \cdot (1 - 1.00) - {11.00}^{2} \cdot 32.91 \cdot (1 - 1.00) & if false \\ 8208.57 & otherwise. \end{cases}

Total reduction factor

Δ_{A,reduction}

1.00

Δ_{A,reduction}

=

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

=

\frac{8208.57}{8208.57}