Square Channel

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The square channel section, or C-section (where web height and flange width may be similar), features a central web with two flanges extending from one side. It is an open section, making it less efficient in torsion than closed sections. Channels are primarily designed to resist bending about the axis parallel to the web. Due to its asymmetry, it tends to twist if not loaded through its shear centre, often requiring use in pairs or with bracing. Common applications include purlins, girts, studs in light steel framing, and chassis components.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Squared Channel

Section depth

d_{t}

100.00

mm

Section breadth

b_{t}

50.00

mm

Thickness of the top flange

t_{f}

10.00

mm

Thickness of web

t_{web}

10.00

mm

Web depth

a_{t}

80.00

mm

a_{t}

=

d_{t} - 2 \cdot t_{f}

=

100.00 - 2 \cdot 10.00

Area

A_{t}

1800.00

{mm}^{2}

A_{t}

=

b_{t} \cdot d_{t} - a_{t} \cdot (b_{t} - t_{web})

=

50.00 \cdot 100.00 - 80.00 \cdot (50.00 - 10.00)

Perimeter

P_{t}

380.00

mm

P_{t}

=

2 \cdot (2 \cdot b_{t} + d_{t}) - 2 \cdot t_{web}

=

2 \cdot (2 \cdot 50.00 + 100.00) - 2 \cdot 10.00

Distance to centroid (x-axis)

C_{x}

16.11

mm

C_{x}

=

\frac{(2 \cdot {b_{t}}^{2} \cdot t_{f} + a_{t} \cdot {t_{web}}^{2})}{(2 \cdot b_{t} \cdot d_{t} - 2 \cdot a_{t} \cdot (b_{t} - t_{web}))}

=

\frac{(2 \cdot {50.00}^{2} \cdot 10.00 + 80.00 \cdot {10.00}^{2})}{(2 \cdot 50.00 \cdot 100.00 - 2 \cdot 80.00 \cdot (50.00 - 10.00))}

Distance to centroid (y-axis)

C_{y}

50.00

mm

C_{y}

=

\frac{d_{t}}{2}

=

\frac{100.00}{2}

Second moment of area about x-axis

I_{x}

(2.460e+6)

{mm}^{4}

I_{x}

=

\frac{(b_{t} \cdot {d_{t}}^{3} - {a_{t}}^{3} \cdot (b_{t} - t_{web}))}{12}

=

\frac{(50.00 \cdot {100.00}^{3} - {80.00}^{3} \cdot (50.00 - 10.00))}{12}

Second moment of area about y-axis

I_{y}

392778

{mm}^{4}

I_{y}

=

\frac{2 \cdot t_{f} \cdot {b_{t}}^{3}}{3} + \frac{a_{t} \cdot {t_{web}}^{3}}{3} - A_{t} \cdot {C_{x}}^{2}

=

\frac{2 \cdot 10.00 \cdot {50.00}^{3}}{3} + \frac{80.00 \cdot {10.00}^{3}}{3} - 1800.00 \cdot {16.11}^{2}

Second moment of area about x1-axis

I_{x_{1}}

(6.960e+6)

{mm}^{4}

I_{x_{1}}

=

I_{x} + A_{t} \cdot {C_{y}}^{2}

=

(2.460e+6) + 1800.00 \cdot {50.00}^{2}

Second moment of area about y1-axis

I_{y_{1}}

860000

{mm}^{4}

I_{y_{1}}

=

I_{y} + A_{t} \cdot {C_{x}}^{2}

=

392778 + 1800.00 \cdot {16.11}^{2}

Polar moment of inertia about centre

J_{z}

(2.853e+6)

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

(2.460e+6) + 392778

Polar moment of inertia about vertex

J_{z_{1}}

(7.820e+6)

{mm}^{4}

J_{z_{1}}

=

I_{x_{1}} + I_{y_{1}}

=

(6.960e+6) + 860000

Radius of gyration about x-axis

K_{x}

36.97

mm

K_{x}

=

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

=

\sqrt{\frac{(2.460e+6)}{1800.00}}

Radius of gyration about y-axis

K_{y}

14.77

mm

K_{y}

=

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

=

\sqrt{\frac{392778}{1800.00}}

Radius of gyration about z-axis

K_{z}

39.81

mm

K_{z}

=

\sqrt{{K_{x}}^{2} + {K_{y}}^{2}}

=

\sqrt{{36.97}^{2} + {14.77}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

62.18

mm

K_{x_{1}}

=

\sqrt{\frac{I_{x_{1}}}{A_{t}}}

=

\sqrt{\frac{(6.960e+6)}{1800.00}}

Radius of gyration about y1-axis

K_{y_{1}}

21.86

mm

K_{y_{1}}

=

\sqrt{\frac{I_{y_{1}}}{A_{t}}}

=

\sqrt{\frac{860000}{1800.00}}

K_{z_{1}}

65.91

mm

K_{z_{1}}

=

\sqrt{{K_{x_{1}}}^{2} + {K_{y_{1}}}^{2}}

=

\sqrt{{62.18}^{2} + {21.86}^{2}}

Elastic section modulus about x-axis

S_{x}

49200.0

{mm}^{3}

S_{x}

=

\frac{I_{x}}{C_{y}}

=

\frac{(2.460e+6)}{50.00}

Elastic section modulus about y-axis

S_{y}

11590.2

{mm}^{3}

Modulus is taken at the tips of the flanges

S_{y}

=

\frac{I_{y}}{(b_{t} - C_{x})}

=

\frac{392778}{(50.00 - 16.11)}

Plastic section modulus around the X axis

Z_{x}

61000.0

{mm}^{3}

Z_{x}

=

\frac{b_{t} \cdot {d_{t}}^{2}}{4} - \frac{(b_{t} - t_{web}) \cdot {a_{t}}^{2}}{4}

=

\frac{50.00 \cdot {100.00}^{2}}{4} - \frac{(50.00 - 10.00) \cdot {80.00}^{2}}{4}

Plastic section modulus around the Y axis (1)

Z_{y,1}

20500.0

{mm}^{3}

Z_{y,1}

=

\frac{t_{f} \cdot {(b_{t} - t_{web})}^{2}}{2} + \frac{b_{t} \cdot d_{t} \cdot t_{web}}{2} - \frac{{d_{t}}^{2} \cdot {t_{web}}^{2}}{(8 \cdot t_{f})}

=

\frac{10.00 \cdot {(50.00 - 10.00)}^{2}}{2} + \frac{50.00 \cdot 100.00 \cdot 10.00}{2} - \frac{{100.00}^{2} \cdot {10.00}^{2}}{(8 \cdot 10.00)}

Z_{y,2,temp}

(1.600e+6)

{mm}^{3}

Z_{y,2,temp}

=

4 \cdot b_{t} \cdot t_{f} \cdot t_{web} \cdot (d_{t} - 2 \cdot t_{f})

=

4 \cdot 50.00 \cdot 10.00 \cdot 10.00 \cdot (100.00 - 2 \cdot 10.00)

Plastic section modulus around the Y axis (2)

Z_{y,2}

20900.0

{mm}^{3}

Z_{y,2}

=

\frac{1}{(4 \cdot d_{t})} \cdot (4 \cdot t_{f} \cdot {b_{t}}^{2} \cdot (d_{t} - t_{f}) + {t_{web}}^{2} \cdot ({d_{t}}^{2} - 4 \cdot {t_{f}}^{2}) - Z_{y,2,temp})

=

\frac{1}{(4 \cdot 100.00)} \cdot (4 \cdot 10.00 \cdot {50.00}^{2} \cdot (100.00 - 10.00) + {10.00}^{2} \cdot ({100.00}^{2} - 4 \cdot {10.00}^{2}) - (1.600e+6))

Plastic section modulus around the Y axis - Final

Z_{y}

20900.0

{mm}^{3}

Z_{y}

=

{\begin{cases} Z_{y,2} & if t_{web} > \frac{A_{t}}{(2 \cdot d_{t})} \\ Z_{y,1} & otherwise. \end{cases}

=

{\begin{cases} 20900.0 & if 10.00 > \frac{1800.00}{(2 \cdot 100.00)} \\ 20500.0 & otherwise. \end{cases}