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.

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}