Hot Formed Tees Split From I Section

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Hot-formed Tees split from Universal Columns (UC) are T-shaped sections created by cutting a UC section longitudinally. Used for truss chords or stiffeners.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Steel grade factor for the web

ε_{web}

0.81362

BS EN 1993-1-1 Table 5.2

ε_{web}

=

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

=

\sqrt{\frac{235}{355.00}}

Steel grade factor for the flange

ε_{flange}

0.82532

BS EN 1993-1-1 Table 5.2

ε_{flange}

=

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

=

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

isClassFour

true

BS EN 1993-1-1 Table 5.2

isClassFour

=

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

=

or (12.82 > 14 \cdot 0.81362, 1.79 > 14 \cdot 0.82532)

isClassThree

false

isClassThree

=

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

=

{\begin{cases} 1 = 0 & if true \\ or (12.82 > 10 \cdot 0.81362, 1.79 > 10 \cdot 0.82532) & otherwise. \end{cases}

isClassTwo

false

isClassTwo

=

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

=

{\begin{cases} 1 = 0 & if or (false, true) \\ or (12.82 > 9 \cdot 0.81362, 1.79 > 9 \cdot 0.82532) & otherwise. \end{cases}

isClassOne

false

isClassOne

=

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

=

{\begin{cases} 1 = 1 & if and (12.82 \leq 9 \cdot 0.81362, 1.79 \leq 9 \cdot 0.82532) \\ 1 = 0 & otherwise. \end{cases}

Initial stress distribution for pure bending

ψ_{t,web}

Buckling factor (Web)

k_{sigma,web}

1.70

Plate slenderness of the web

λ_{p,web}

0.42554

λ_{p,web}

=

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

=

\frac{12.82}{(28.4 \cdot 0.81362 \cdot \sqrt{1.70})}

Reduction factor for the web

ρ_{web}

1.00

ρ_{web}

=

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

=

{\begin{cases} \frac{(0.42554 - 0.188)}{{0.42554}^{2}} & if 0.42554 > 0.748 \\ 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}

0.11627

λ_{p,flange}

=

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

=

\frac{1.79}{(28.4 \cdot 0.82532 \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{(0.11627 - 0.188)}{{0.11627}^{2}} & if 0.11627 > 0.748 \\ 1 & otherwise. \end{cases}

checkFlange

true

checkFlange

=

ρ_{flange} \leq 1

=

1.00 \leq 1

b_{eff,w}

150.00

mm

b_{eff,w}

=

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

=

1.00 \cdot (12.82 \cdot 11.70)

b_{lost,w}

b_{lost,w}

=

(\frac{c_{w}}{t_{w}} \cdot t_{w}) - b_{eff,w}

=

(12.82 \cdot 11.70) - 150.00

b_{eff,f}

28.95

mm

b_{eff,f}

=

ρ_{flange} \cdot \frac{c_{f}}{t_{f}} \cdot t_{f}

=

1.00 \cdot 1.79 \cdot 16.20

b_{lost,f}

mm

b_{lost,f}

=

\frac{c_{f}}{t_{f}} \cdot t_{f} - b_{eff,f}

=

1.79 \cdot 16.20 - 28.95

A_{lost,w}

{mm}^{2}

A_{lost,w}

=

t_{w} \cdot b_{lost,w}

=

11.70 \cdot 0

A_{lost,f}

{mm}^{2}

A_{lost,f}

=

2 \cdot t_{f} \cdot b_{lost,f}

=

2 \cdot 16.20 \cdot 0

Effective area of the section

A_{eff}

3284.62

{mm}^{2}

A_{eff}

=

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

=

{\begin{cases} 3284.62 - 0 - 0 & if true \\ 3284.62 & otherwise. \end{cases}

Total reduction factor

Δ_{A,reduction}

1.00

Δ_{A,reduction}

=

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

=

\frac{3284.62}{3284.62}

d_{w}

mm

d_{w}

=

\frac{b_{lost,w}}{2}

=

\frac{0}{2}

d_{f}

36.09

mm

d_{f}

=

C_{y} - \frac{t_{f}}{2}

=

44.19 - \frac{16.20}{2}

Neutral axis shift

e_{N}

mm

e_{N}

=

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

=

\frac{(0 \cdot 0 + 0 \cdot 36.09)}{3284.62}

I_{lost,w}

{mm}^{4}

I_{lost,w}

=

\frac{t_{w} \cdot {b_{lost,w}}^{3}}{12} + A_{lost,w} \cdot {d_{w}}^{2}

=

\frac{11.70 \cdot 0^{3}}{12} + 0 \cdot 0^{2}

I_{lost,f}

{mm}^{4}

I_{lost,f}

=

2 \cdot (\frac{b_{lost,f} \cdot {t_{f}}^{3}}{12} + b_{lost,f} \cdot t_{f} \cdot {d_{f}}^{2})

=

2 \cdot (\frac{0 \cdot {16.20}^{3}}{12} + 0 \cdot 16.20 \cdot {36.09}^{2})

Effective second moment of area

I_{eff}

(6.884e+6)

{mm}^{4}

I_{eff}

=

I_{yy} - I_{lost,f} - I_{lost,w} - A_{eff} \cdot {e_{N}}^{2}

=

(6.884e+6) - 0 - 0 - 3284.62 \cdot 0^{2}

W_{eff,top}

155772

{mm}^{3}

W_{eff,top}

=

\frac{I_{eff}}{(C_{y} + e_{N})}

=

\frac{(6.884e+6)}{(44.19 + 0)}

W_{eff,bot}

155772

{mm}^{3}

W_{eff,bot}

=

\frac{I_{eff}}{(C_{y} - e_{N})}

=

\frac{(6.884e+6)}{(44.19 - 0)}

Effective section modulus

W_{eff}

155772

{mm}^{3}

W_{eff}

=

\min (W_{eff,bot}, W_{eff,top})

=

\min (155772, 155772)