Hot Formed I Sections

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Hot-formed I-sections are structural steel shapes produced by hot rolling, giving them an "I" shaped cross-section with parallel flanges and a central web, optimised for carrying bending and shear in buildings and civil works.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Flange width

c_{f}

109.30

mm

c_{f}

=

\frac{(b_{t} - t_{w} - 2 \cdot r_{t})}{2}

=

\frac{(303.00 - 24.40 - 2 \cdot 30.00)}{2}

Web clear height

c_{w}

868.10

mm

c_{w}

=

h_{t} - 2 \cdot t_{f} - 2 \cdot r_{t}

=

1015.90 - 2 \cdot 43.90 - 2 \cdot 30.00

Steel grade factor for the web

ε_{web}

0.82532

ε_{web}

=

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

=

\sqrt{\frac{235}{345.00}}

Steel grade factor for the flange

ε_{flange}

0.83755

ε_{flange}

=

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

=

\sqrt{\frac{235}{335.00}}

isClassFour

false

isClassFour

=

or (\frac{c_{w}}{t_{w}} > 124 \cdot ε_{web}, \frac{c_{f}}{t_{f}} > 14 \cdot ε_{flange})

=

or (35.58 > 124 \cdot 0.82532, 2.49 > 14 \cdot 0.83755)

isClassThree

false

isClassThree

=

{\begin{cases} 1 = 0 & if isClassFour \\ or (\frac{c_{w}}{t_{w}} > 83 \cdot ε_{web}, \frac{c_{f}}{t_{f}} > 10 \cdot ε_{flange}) & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if false \\ or (35.58 > 83 \cdot 0.82532, 2.49 > 10 \cdot 0.83755) & otherwise. \end{cases}

isClassTwo

false

isClassTwo

=

{\begin{cases} 1 = 0 & if isClassFour \\ or (\frac{c_{w}}{t_{w}} > 72 \cdot ε_{web}, \frac{c_{f}}{t_{f}} > 9 \cdot ε_{flange}) & otherwise. \end{cases}

=

{\begin{cases} 1 = 0 & if false \\ or (35.58 > 72 \cdot 0.82532, 2.49 > 9 \cdot 0.83755) & otherwise. \end{cases}

isClassOne

true

isClassOne

=

{\begin{cases} 1 = 1 & if and (\frac{c_{w}}{t_{w}} \leq 72 \cdot ε_{web}, \frac{c_{f}}{t_{f}} \leq 9 \cdot ε_{flange}) \\ 1 = 0 & otherwise. \end{cases}

=

{\begin{cases} 1 = 1 & if and (35.58 \leq 72 \cdot 0.82532, 2.49 \leq 9 \cdot 0.83755) \\ 1 = 0 & otherwise. \end{cases}

Initial stress distribution for pure bending (Web)

ψ_{t,web}

-1.00

ψ_{t,web}

=

- 1

Buckling factor (Web)

k_{sigma,web}

23.90

Plate slenderness of the web

λ_{p,web}

0.31048

λ_{p,web}

=

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

=

\frac{35.58}{(28.4 \cdot 0.82532 \cdot \sqrt{23.90})}

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} (0.31048 - 0.055 \cdot (3 + -1.00)) \cdot (\frac{1}{{0.31048}^{2}}) & if 0.31048 > 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

Initial stress distribution for pure bending (Flange)

ψ_{t,flange}

1.00

Buckling factor (Flange)

k_{sigma,"flange"}

0.43000

Plate slenderness of the flange

λ_{p,flange}

0.15962

λ_{p,flange}

=

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

=

\frac{2.49}{(28.4 \cdot 0.83755 \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{(0.15962 - 0.188)}{{0.15962}^{2}} & if 0.15962 > 0.748 \\ 1 & otherwise. \end{cases}

checkFlange

true

checkFlange

=

ρ_{flange} \leq 1

=

1.00 \leq 1

Effective flange width

b_{eff,f}

109.30

mm

b_{eff,f}

=

ρ_{flange} \cdot c_{f}

=

1.00 \cdot 109.30

Flange area loss

A_{lost,f}

{mm}^{2}

A_{lost,f}

=

2 \cdot (c_{f} - b_{eff,f}) \cdot t_{f}

=

2 \cdot (109.30 - 109.30) \cdot 43.90

Web area loss

A_{loss,w}

{mm}^{2}

A_{loss,w}

=

\frac{c_{w}}{2} \cdot (1 - ρ_{web}) \cdot t_{w}

=

\frac{868.10}{2} \cdot (1 - 1.00) \cdot 24.40

Effective area of the section

A_{eff}

50021.6

{mm}^{2}

A_{eff}

=

{\begin{cases} A_{t} - A_{lost,f} - A_{loss,w} & if isClassFour \\ A_{t} & otherwise. \end{cases}

=

{\begin{cases} 50021.6 - 0 - 0 & if false \\ 50021.6 & otherwise. \end{cases}

Total reduction factor

Δ_{A,reduction}

1.00

Δ_{A,reduction}

=

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

=

\frac{50021.6}{50021.6}

Distance to flange loss centre

d_{f}

486.00

mm

d_{f}

=

\frac{h_{t}}{2} - \frac{t_{f}}{2}

=

\frac{1015.90}{2} - \frac{43.90}{2}

Distance to web loss centre

d_{w}

253.97

mm

d_{w}

=

\frac{h_{t}}{4}

=

\frac{1015.90}{4}

Shift of neutral axis

e_{N}

mm

e_{N}

=

\frac{((A_{lost,f} \cdot d_{f}) + (A_{loss,w} \cdot d_{w}))}{A_{eff}}

=

\frac{((0 \cdot 486.00) + (0 \cdot 253.97))}{50021.6}

Effective second moment of area

I_{eff}

(8.075e+9)

{mm}^{4}

I_{eff}

=

I_{yy} + A_{t} \cdot {e_{N}}^{2} - (A_{lost,f} \cdot {(d_{f} + e_{N})}^{2} + A_{loss,w} \cdot {(d_{w} + e_{N})}^{2})

=

(8.075e+9) + 50021.6 \cdot 0^{2} - (0 \cdot {(486.00 + 0)}^{2} + 0 \cdot {(253.97 + 0)}^{2})

Compression section modulus

W_{eff,c}

(1.590e+7)

{mm}^{3}

W_{eff,c}

=

\frac{I_{eff}}{(\frac{h_{t}}{2} + e_{N})}

=

\frac{(8.075e+9)}{(\frac{1015.90}{2} + 0)}

Tension section modulus

W_{eff,t}

(1.590e+7)

{mm}^{3}

W_{eff,t}

=

\frac{I_{eff}}{(\frac{h_{t}}{2} - e_{N})}

=

\frac{(8.075e+9)}{(\frac{1015.90}{2} - 0)}

Effective section modulus

W_{eff}

(1.590e+7)

{mm}^{3}

W_{eff}

=

\min (W_{eff,c}, W_{eff,t})

=

\min ((1.590e+7), (1.590e+7))