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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

f_{y,section}

345.00

f_{y,section}

=

\min (f_{y,w}, f_{y,fl})

=

\min (355.00, 345.00)

Steel grade factor for the web

ε_{web}

0.81362

ε_{web}

=

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

=

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

Steel grade factor for the flange

ε_{flange}

0.82532

ε_{flange}

=

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

=

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

isClassFour

true

isClassFour

=

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

=

or (28.97 > 14 \cdot 0.81362, 6.51 > 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 (28.97 > 10 \cdot 0.81362, 6.51 > 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 (28.97 > 9 \cdot 0.81362, 6.51 > 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 (28.97 \leq 9 \cdot 0.81362, 6.51 \leq 9 \cdot 0.82532) \\ 1 = 0 & otherwise. \end{cases}

Initial stress distribution for pure compression

ψ_{t,web}

1.00

Buckling factor for constant compressive stress throughout the section

k_{sigma,web}

0.43000

Plate slenderness of the web

λ_{p,web}

1.91

λ_{p,web}

=

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

=

\frac{28.97}{(28.4 \cdot 0.81362 \cdot \sqrt{0.43000})}

Reduction factor for the web

ρ_{web}

0.47166

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{(1.91 - 0.188)}{{1.91}^{2}} & if 1.91 > 0.748 \\ 1 & otherwise. \end{cases}

checkWeb

true

checkWeb

=

ρ_{web} \leq 1

=

0.47166 \leq 1

Buckling factor for constant compressive stress throughout the section

k_{sigma,"flange"}

0.43000

Plate slenderness of the flange

λ_{p,flange}

0.42350

λ_{p,flange}

=

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

=

\frac{6.51}{(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{(0.42350 - 0.188)}{{0.42350}^{2}} & if 0.42350 > 0.748 \\ 1 & otherwise. \end{cases}

checkFlange

true

checkFlange

=

ρ_{flange} \leq 1

=

1.00 \leq 1

Effective area of the section

A_{eff}

5878.41

{mm}^{2}

A_{eff}

=

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

=

{\begin{cases} 7973.35 - 11.70 \cdot 28.97 \cdot 11.70 \cdot (1 - 0.47166) - 2 \cdot 6.51 \cdot 16.20 \cdot 16.20 \cdot (1 - 1.00) & if true \\ 7973.35 & otherwise. \end{cases}

Total reduction factor

Δ_{A,reduction}

0.73726

Δ_{A,reduction}

=

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

=

\frac{5878.41}{7973.35}