Hot Formed Equal Leg Angles

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Hot-formed Equal Leg Angles (L) are L-shaped sections with equal length legs, versatile for bracing, trusses, and connections.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Steel grade factor

ε_{t}

0.92442

ε_{t}

=

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

=

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

isClassFour

false

isClassFour

=

\frac{h_{t}}{t_{t}} > 14 \cdot ε_{t}

=

10.00 > 14 \cdot 0.92442

Stress distribution ratio

ψ_{t}

-1.00

ψ_{t}

=

- 1

Buckling factor for pure bending

k_{σ}

0.85000

Plate slenderness

λ_{p}

0.41315

λ_{p}

=

\frac{\frac{h_{t}}{t_{t}}}{(28.4 \cdot ε_{t} \cdot \sqrt{k_{σ}})}

=

\frac{10.00}{(28.4 \cdot 0.92442 \cdot \sqrt{0.85000})}

Reduction factor

ρ_{internal}

1.00

ρ_{internal}

=

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

=

{\begin{cases} \frac{(0.41315 - 0.188)}{{0.41315}^{2}} & if 0.41315 > 0.748 \\ 1 & otherwise. \end{cases}

checkPsi

true

checkPsi

=

ρ_{internal} \leq 1

=

1.00 \leq 1

Compression depth

b_{c}

50.00

mm

b_{c}

=

\frac{h_{t}}{(1 - ψ_{t})}

=

\frac{100.00}{(1 - -1.00)}

Effective width

b_{eff}

50.00

mm

b_{eff}

=

ρ_{internal} \cdot b_{c}

=

1.00 \cdot 50.00

Lost width

b_{lost}

mm

b_{lost}

=

b_{c} - b_{eff}

=

50.00 - 50.00

Lost area

A_{lost}

{mm}^{2}

A_{lost}

=

b_{lost} \cdot t_{t}

=

0 \cdot 10.00

Effective area

A_{eff}

1927.47

{mm}^{2}

A_{eff}

=

{\begin{cases} A_{t} - 2 \cdot A_{lost} & if isClassFour \\ A_{t} & otherwise. \end{cases}

=

{\begin{cases} 1927.47 - 2 \cdot 0 & if false \\ 1927.47 & otherwise. \end{cases}

Δ_{a,reduction}

1.00

Δ_{a,reduction}

=

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

=

\frac{1927.47}{1927.47}

x_{lost,X}

50.00

mm

x_{lost,X}

=

b_{c} - \frac{b_{lost}}{2}

=

50.00 - \frac{0}{2}

y_{lost,x}

5.00

mm

y_{lost,x}

=

\frac{t_{t}}{2}

=

\frac{10.00}{2}

x_{lost,Y}

5.00

mm

x_{lost,Y}

=

\frac{t_{t}}{2}

=

\frac{10.00}{2}

y_{lost,y}

50.00

mm

y_{lost,y}

=

b_{c} - \frac{b_{lost}}{2}

=

50.00 - \frac{0}{2}

Effective centroid about x-axis

x_{eff}

27.90

mm

x_{eff}

=

\frac{(A_{t} \cdot c_{t} - (A_{lost} \cdot (x_{lost,X} + x_{lost,Y})))}{A_{eff}}

=

\frac{(1927.47 \cdot 27.90 - (0 \cdot (50.00 + 5.00)))}{1927.47}

Effective centroid about y-axis

y_{eff}

27.90

mm

y_{eff}

=

\frac{(A_{t} \cdot c_{t} - A_{lost} \cdot (y_{lost,x} + y_{lost,y}))}{A_{eff}}

=

\frac{(1927.47 \cdot 27.90 - 0 \cdot (5.00 + 50.00))}{1927.47}

d_{xx,h}

-22.90

mm

d_{xx,h}

=

\frac{t_{t}}{2} - c_{t}

=

\frac{10.00}{2} - 27.90

d_{xx,v}

22.10

mm

d_{xx,v}

=

(b_{c} - \frac{b_{lost}}{2}) - c_{t}

=

(50.00 - \frac{0}{2}) - 27.90

d_{yy,h}

22.10

mm

d_{yy,h}

=

(b_{c} - \frac{b_{lost}}{2}) - c_{t}

=

(50.00 - \frac{0}{2}) - 27.90

d_{yy,v}

-22.90

mm

d_{yy,v}

=

\frac{t_{t}}{2} - c_{t}

=

\frac{10.00}{2} - 27.90

Lost second moment of area about x-axis

I_{x,lost}

{mm}^{4}

I_{x,lost}

=

\frac{b_{lost} \cdot {t_{t}}^{3}}{12} + \frac{t_{t} \cdot {b_{lost}}^{3}}{12} + A_{lost} \cdot ({d_{xx,h}}^{2} + {d_{xx,v}}^{2})

=

\frac{0 \cdot {10.00}^{3}}{12} + \frac{10.00 \cdot 0^{3}}{12} + 0 \cdot ({-22.90}^{2} + {22.10}^{2})

Lost second moment of area about y-axis

I_{y,lost}

{mm}^{4}

I_{y,lost}

=

\frac{t_{t} \cdot {b_{lost}}^{3}}{12} + \frac{b_{lost} \cdot {t_{t}}^{3}}{12} + A_{lost} \cdot ({d_{yy,h}}^{2} + {d_{yy,v}}^{2})

=

\frac{10.00 \cdot 0^{3}}{12} + \frac{0 \cdot {10.00}^{3}}{12} + 0 \cdot ({22.10}^{2} + {-22.90}^{2})

Neutral axis shift

e_{N}

mm

e_{N}

=

x_{eff} - c_{t}

=

27.90 - 27.90

Effective second moment of area about x-axis

I_{x,eff}

(1.742e+6)

{mm}^{4}

I_{x,eff}

=

{\begin{cases} I_{xx} - I_{x,lost} - A_{eff} \cdot {e_{N}}^{2} & if isClassFour \\ I_{xx} & otherwise. \end{cases}

=

{\begin{cases} (1.742e+6) - 0 - 1927.47 \cdot 0^{2} & if false \\ (1.742e+6) & otherwise. \end{cases}

Effective second moment of area about y-axis

I_{y,eff}

(1.742e+6)

{mm}^{4}

I_{y,eff}

=

{\begin{cases} I_{yy} - I_{y,lost} - A_{eff} \cdot {e_{N}}^{2} & if isClassFour \\ I_{yy} & otherwise. \end{cases}

=

{\begin{cases} (1.742e+6) - 0 - 1927.47 \cdot 0^{2} & if false \\ (1.742e+6) & otherwise. \end{cases}

Section modulus about x-axis

W_{eff,x}

78856.2

{mm}^{3}

W_{eff,x}

=

{\begin{cases} \frac{I_{x,eff}}{(b_{c} - x_{eff})} & if isClassFour \\ \frac{I_{x,eff}}{(b_{c} - c_{t})} & otherwise. \end{cases}

=

{\begin{cases} \frac{(1.742e+6)}{(50.00 - 27.90)} & if false \\ \frac{(1.742e+6)}{(50.00 - 27.90)} & otherwise. \end{cases}

Section modulus about y-axis

W_{eff,y}

78856.2

{mm}^{3}

W_{eff,y}

=

{\begin{cases} \frac{I_{y,eff}}{(b_{c} - y_{eff})} & if isClassFour \\ \frac{I_{y,eff}}{(b_{c} - c_{t})} & otherwise. \end{cases}

=

{\begin{cases} \frac{(1.742e+6)}{(50.00 - 27.90)} & if false \\ \frac{(1.742e+6)}{(50.00 - 27.90)} & otherwise. \end{cases}