Cold And Hot Formed Square Hollow Sections

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Square Hollow Sections include both cold-formed and hot-finished box-section profiles. Cold-formed sections are produced at ambient temperatures, while hot-finished sections are manufactured at elevated temperatures, offering excellent torsional resistance and column strength. Both types offer efficient structural performance for columns and bracing.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Square Hollow Sections

Geometry Input

Section depth

h_{t}

180.00

mm

Section thickness

t_{t}

12.50

mm

Material Properties

Young's modulus

E_{t}

210000

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

Poisson's ratio

v_{t}

0.30000

-

Density

ρ_{t}

7850.00

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

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))}

Calculated geometry parameters

Inner corner radii

r_{in}

25.00

mm

BS EN 10219-2

r_{in}

=

{\begin{cases} t_{t} & if t_{t} \leq 6 \\ {\begin{cases} 1.5 \cdot t_{t} & if and (t_{t} > 6, t_{t} \leq 10) \\ 2 \cdot t_{t} & otherwise. \end{cases} & otherwise. \end{cases}

=

{\begin{cases} 12.50 & if 12.50 \leq 6 \\ {\begin{cases} 1.5 \cdot 12.50 & if and (12.50 > 6, 12.50 \leq 10) \\ 2 \cdot 12.50 & otherwise. \end{cases} & otherwise. \end{cases}

Outer corner radii

r_{out}

37.50

mm

BS EN 10219-2

r_{out}

=

{\begin{cases} 2 \cdot t_{t} & if t_{t} \leq 6 \\ {\begin{cases} 2.5 \cdot t_{t} & if and (t_{t} > 6, t_{t} \leq 10) \\ 3 \cdot t_{t} & otherwise. \end{cases} & otherwise. \end{cases}

=

{\begin{cases} 2 \cdot 12.50 & if 12.50 \leq 6 \\ {\begin{cases} 2.5 \cdot 12.50 & if and (12.50 > 6, 12.50 \leq 10) \\ 3 \cdot 12.50 & otherwise. \end{cases} & otherwise. \end{cases}

Average of inner and outer corner radii

R_{c}

31.25

mm

R_{c}

=

\frac{(r_{in} + r_{out})}{2}

=

\frac{(25.00 + 37.50)}{2}

Area of section

A_{t}

7704.37

{mm}^{2}

A_{t}

=

{h_{t}}^{2} - {(h_{t} - 2 \cdot t_{t})}^{2} - ({r_{out}}^{2} - {r_{in}}^{2}) \cdot (4 - π)

=

{180.00}^{2} - {(180.00 - 2 \cdot 12.50)}^{2} - ({37.50}^{2} - {25.00}^{2}) \cdot (4 - π)

Mass per meter length

m_{m}

60.48

\frac{kg}{m}

m_{m}

=

\frac{A_{t} \cdot ρ_{t}}{10^{6}}

=

\frac{7704.37 \cdot 7850.00}{10^{6}}

Ratio for local buckling

\frac{c}{t}

11.40

-

\frac{c}{t}

=

\frac{(h_{t} - 3 \cdot t_{t})}{t_{t}}

=

\frac{(180.00 - 3 \cdot 12.50)}{12.50}

Second moment of area

I_{corners}

(1.321e+7)

{mm}^{4}

Includes the necessary correction for the centroidal offset ($2DQ_x$ term) to ensure precision

I_{corners}

=

4 \cdot (\frac{π \cdot ({r_{out}}^{4} - {r_{in}}^{4})}{16} + \frac{π \cdot ({r_{out}}^{2} - {r_{in}}^{2})}{4} \cdot {(\frac{h_{t}}{2} - r_{out})}^{2} + \frac{2}{3} \cdot (\frac{h_{t}}{2} - r_{out}) \cdot ({r_{out}}^{3} - {r_{in}}^{3}))

=

4 \cdot (\frac{π \cdot ({37.50}^{4} - {25.00}^{4})}{16} + \frac{π \cdot ({37.50}^{2} - {25.00}^{2})}{4} \cdot {(\frac{180.00}{2} - 37.50)}^{2} + \frac{2}{3} \cdot (\frac{180.00}{2} - 37.50) \cdot ({37.50}^{3} - {25.00}^{3}))

I_{xx}

(3.406e+7)

I_{xx}

=

\frac{t_{t} \cdot {(h_{t} - 2 \cdot r_{out})}^{3}}{6} + 2 \cdot (h_{t} - 2 \cdot r_{out}) \cdot t_{t} \cdot (\frac{{t_{t}}^{2}}{12} + {(\frac{(h_{t} - t_{t})}{2})}^{2}) + I_{corners}

=

\frac{12.50 \cdot {(180.00 - 2 \cdot 37.50)}^{3}}{6} + 2 \cdot (180.00 - 2 \cdot 37.50) \cdot 12.50 \cdot (\frac{{12.50}^{2}}{12} + {(\frac{(180.00 - 12.50)}{2})}^{2}) + (1.321e+7)

Other parameters

Radius of gyration

K_{t}

66.49

mm

For Square Hollow Section, Radius of Gyration is equal for both axis.

K_{t}

=

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

=

\sqrt{\frac{(3.406e+7)}{7704.37}}

Elastic section modulus about major/minor axis

S_{t}

378493

{mm}^{3}

For Square Hollow Section, Elastic Section Modulus is equal for both axis

S_{t}

=

\frac{I_{xx}}{(\frac{h_{t}}{2})}

=

\frac{(3.406e+7)}{(\frac{180.00}{2})}

Corner component

Z_{corner}

89166.8

{mm}^{3}

Z_{corner}

=

2 \cdot (\frac{π \cdot ({r_{out}}^{2} - {r_{in}}^{2})}{4} \cdot (\frac{h_{t}}{2} - r_{out}) + \frac{({r_{out}}^{3} - {r_{in}}^{3})}{3})

=

2 \cdot (\frac{π \cdot ({37.50}^{2} - {25.00}^{2})}{4} \cdot (\frac{180.00}{2} - 37.50) + \frac{({37.50}^{3} - {25.00}^{3})}{3})

Plastic section modulus about major/minor axis

Z_{t}

467084

{mm}^{3}

For Square Hollow Section, Plastic Section Modulus is equal for both axis.

Z_{t}

=

2 \cdot (\frac{(h_{t} - 2 \cdot r_{out}) \cdot t_{t} \cdot (h_{t} - t_{t})}{2} + t_{t} \cdot {(\frac{(h_{t} - 2 \cdot r_{out})}{2})}^{2} + Z_{corner})

=

2 \cdot (\frac{(180.00 - 2 \cdot 37.50) \cdot 12.50 \cdot (180.00 - 12.50)}{2} + 12.50 \cdot {(\frac{(180.00 - 2 \cdot 37.50)}{2})}^{2} + 89166.8)

Mean perimeter length

P_{t}

616.35

mm

P_{t}

=

(4 \cdot (h_{t} - t_{t})) - R_{c} \cdot 2 \cdot (4 - π)

=

(4 \cdot (180.00 - 12.50)) - 31.25 \cdot 2 \cdot (4 - π)

Area enclosed by mean parameter

A_{p}

27218.0

{mm}^{2}

A_{p}

=

{(h_{t} - t_{t})}^{2} - {R_{c}}^{2} \cdot (4 - π)

=

{(180.00 - 12.50)}^{2} - {31.25}^{2} \cdot (4 - π)

Torsional constant

I_{T}

(6.050e+7)

{mm}^{4}

I_{T}

=

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

=

\frac{4 \cdot {27218.0}^{2} \cdot 12.50}{616.35} + \frac{{12.50}^{3} \cdot 616.35}{3}

Torsional section modulus

W_{t}

600065

{mm}^{3}

W_{t}

=

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

=

\frac{(6.050e+7)}{(12.50 + \frac{2 \cdot 27218.0}{616.35})}

Surface area per metre

A_{s}

0.65562

\frac{m^{2}}{m}

A_{s}

=

\frac{(4 \cdot (h_{t} - 2 \cdot r_{out}) + 2 \cdot π \cdot r_{out})}{1000}

=

\frac{(4 \cdot (180.00 - 2 \cdot 37.50) + 2 \cdot π \cdot 37.50)}{1000}