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Cold And Hot Formed Elliptical Hollow Sections

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Elliptical Hollow Sections include both cold-formed and hot-finished profiles featuring an oval/elliptical cross-section. These sections offer unique aesthetics and provide a structural compromise between circular and rectangular sections, with directional strength characteristics.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Hot-Finished Elliptical Hollow Sections

figure wim9c06558de7

Geometry Input

Outer diameter in the major axis

h_{t}

300.00

mm

Outer diameter in the minor axis

b_{t}

150.00

mm

Section thickness

t_{t}

8.00

mm

Material Properties

Young's modulus

E_{t}

210000

\frac{N}{{mm}^{2}}

Poisson's ratio

v_{t}

0.30000

-

Shear modulus

G_{t}

80769.2

\frac{N}{{mm}^{2}}

G_{t}

=

\frac{E_{t}}{(2 \cdot (1 + v_{t}))}

=

\frac{210000}{(2 \cdot (1 + 0.30000))}

Density

ρ_{t}

7850.00

\frac{kg}{m^{3}}

Section Properties

Perimeter

P_{t}

726.63

mm

P_{t}

=

π \cdot (3 \cdot (\frac{b_{t}}{2} + \frac{h_{t}}{2}) - \sqrt{(\frac{3 \cdot b_{t}}{2} + \frac{h_{t}}{2}) \cdot (\frac{b_{t}}{2} + \frac{3 \cdot h_{t}}{2})})

=

π \cdot (3 \cdot (\frac{150.00}{2} + \frac{300.00}{2}) - \sqrt{(\frac{3 \cdot 150.00}{2} + \frac{300.00}{2}) \cdot (\frac{150.00}{2} + \frac{3 \cdot 300.00}{2})})

Total section area

A_{t}

5453.80

{mm}^{2}

A_{t}

=

\frac{π}{4} \cdot (b_{t} \cdot h_{t} - (b_{t} - 2 \cdot t_{t}) \cdot (h_{t} - 2 \cdot t_{t}))

=

\frac{π}{4} \cdot (150.00 \cdot 300.00 - (150.00 - 2 \cdot 8.00) \cdot (300.00 - 2 \cdot 8.00))

Mass per metre length

m_{m}

42.81

\frac{kg}{m}

m_{m}

=

\frac{A_{t} \cdot ρ_{t}}{10^{6}}

=

\frac{5453.80 \cdot 7850.00}{10^{6}}

Distance to centroid (y-axis)

C_{y}

75.00

mm

C_{y}

=

\frac{b_{t}}{2}

=

\frac{150.00}{2}

Distance to centroid (z-axis)

C_{z}

150.00

mm

C_{z}

=

\frac{h_{t}}{2}

=

\frac{300.00}{2}

Second moment of area about y-axis

I_{yy}

(4.813e+7)

{mm}^{4}

I_{yy}

=

\frac{π}{64} \cdot ({h_{t}}^{3} \cdot b_{t} - {(h_{t} - 2 \cdot t_{t})}^{3} \cdot (b_{t} - 2 \cdot t_{t}))

=

\frac{π}{64} \cdot ({300.00}^{3} \cdot 150.00 - {(300.00 - 2 \cdot 8.00)}^{3} \cdot (150.00 - 2 \cdot 8.00))

Second moment of area about z-axis

I_{zz}

(1.616e+7)

{mm}^{4}

I_{zz}

=

\frac{π}{64} \cdot (h_{t} \cdot {b_{t}}^{3} - (h_{t} - 2 \cdot t_{t}) \cdot {(b_{t} - 2 \cdot t_{t})}^{3})

=

\frac{π}{64} \cdot (300.00 \cdot {150.00}^{3} - (300.00 - 2 \cdot 8.00) \cdot {(150.00 - 2 \cdot 8.00)}^{3})

Radius of gyration about y-axis

K_{yy}

93.94

mm

K_{yy}

=

\sqrt{\frac{I_{yy}}{A_{t}}}

=

\sqrt{\frac{(4.813e+7)}{5453.80}}

Radius of gyration about z-axis

K_{zz}

54.43

mm

K_{zz}

=

\sqrt{\frac{I_{zz}}{A_{t}}}

=

\sqrt{\frac{(1.616e+7)}{5453.80}}

Elastic section modulus about y-axis

S_{yy}

320886

{mm}^{3}

S_{yy}

=

\frac{I_{yy}}{C_{z}}

=

\frac{(4.813e+7)}{150.00}

Elastic section modulus about z-axis

S_{zz}

215439

{mm}^{3}

S_{zz}

=

\frac{I_{zz}}{C_{y}}

=

\frac{(1.616e+7)}{75.00}

Plastic section modulus about y-axis

Z_{yy}

448683

{mm}^{3}

Z_{yy}

=

\frac{4}{3} \cdot ({(\frac{h_{t}}{2})}^{2} \cdot (\frac{b_{t}}{2}) - {((\frac{h_{t}}{2}) - t_{t})}^{2} \cdot ((\frac{b_{t}}{2}) - t_{t}))

=

\frac{4}{3} \cdot ({(\frac{300.00}{2})}^{2} \cdot (\frac{150.00}{2}) - {((\frac{300.00}{2}) - 8.00)}^{2} \cdot ((\frac{150.00}{2}) - 8.00))

Plastic section modulus about z-axis

Z_{zz}

275083

{mm}^{3}

Z_{zz}

=

\frac{4}{3} \cdot ((\frac{h_{t}}{2}) \cdot {(\frac{b_{t}}{2})}^{2} - (\frac{h_{t}}{2} - t_{t}) \cdot {(\frac{b_{t}}{2} - t_{t})}^{2})

=

\frac{4}{3} \cdot ((\frac{300.00}{2}) \cdot {(\frac{150.00}{2})}^{2} - (\frac{300.00}{2} - 8.00) \cdot {(\frac{150.00}{2} - 8.00)}^{2})

Area enclosed by mean perimeter

A_{p}

32565.7

{mm}^{2}

A_{p}

=

\frac{π}{4} \cdot (h_{t} - t_{t}) \cdot (b_{t} - t_{t})

=

\frac{π}{4} \cdot (300.00 - 8.00) \cdot (150.00 - 8.00)

Mean perimeter length

p

702.08

mm

p

=

\frac{π}{2} \cdot (h_{t} + b_{t} - 2 \cdot t_{t}) \cdot (1 + 0.25 \cdot {(\frac{(h_{t} - b_{t})}{(h_{t} + b_{t} - 2 \cdot t_{t})})}^{2})

=

\frac{π}{2} \cdot (300.00 + 150.00 - 2 \cdot 8.00) \cdot (1 + 0.25 \cdot {(\frac{(300.00 - 150.00)}{(300.00 + 150.00 - 2 \cdot 8.00)})}^{2})

Torsional constant

I_{T}

(4.846e+7)

{mm}^{4}

I_{T}

=

\frac{4 \cdot {A_{p}}^{2} \cdot t_{t}}{p} + \frac{{t_{t}}^{3} \cdot p}{3}

=

\frac{4 \cdot {32565.7}^{2} \cdot 8.00}{702.08} + \frac{{8.00}^{3} \cdot 702.08}{3}

Torsional section modulus

W_{t}

480875

{mm}^{3}

W_{t}

=

\frac{I_{T}}{(t_{t} + \frac{2 \cdot A_{p}}{p})}

=

\frac{(4.846e+7)}{(8.00 + \frac{2 \cdot 32565.7}{702.08})}