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Square Hollow

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The square hollow structural shape (HSS) features four equal-length sides forming a square profile with a hollow interior. This design offers excellent resistance to torsional (twisting) forces and provides high strength and stability against buckling, especially when used as columns. Compared to solid square sections of similar outer dimensions, square hollow sections are more material-efficient for resisting bending and compressive loads, making them ideal for applications such as columns, beams, and elements in truss structures where a good strength-to-weight ratio is beneficial.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Square Hollow

figure wim8ada2dec20

Outer depth

a_{outer}

10.00

mm

Inner depth

a_{inner}

9.00

mm

Thickness of the section

t_{t}

0.50000

mm

t_{t}

=

(a_{outer} - a_{inner}) \cdot 0.5

=

(10.00 - 9.00) \cdot 0.5

Area

A_{t}

19.00

{mm}^{2}

A_{t}

=

{a_{outer}}^{2} - {a_{inner}}^{2}

=

{10.00}^{2} - {9.00}^{2}

Outer perimeter

P_{out}

40.00

mm

P_{out}

=

4 \cdot a_{outer}

=

4 \cdot 10.00

Inner perimeter

P_{i n}

36.00

mm

P_{i n}

=

4 \cdot a_{inner}

=

4 \cdot 9.00

Distance to centroid (x-axis)

C_{x}

5.00

mm

C_{x}

=

\frac{a_{outer}}{2}

=

\frac{10.00}{2}

Distance to centroid (y-axis)

C_{y}

5.00

mm

C_{y}

=

C_{x}

=

5.00

Second moment of area about x-axis

I_{x}

286.58

{mm}^{4}

I_{x}

=

\frac{{a_{outer}}^{4}}{12} - \frac{{a_{inner}}^{4}}{12}

=

\frac{{10.00}^{4}}{12} - \frac{{9.00}^{4}}{12}

Second moment of area about y-axis

I_{y}

286.58

{mm}^{4}

I_{y}

=

I_{x}

=

286.58

Second moment of area about x1-axis

I_{x_{1}}

761.58

{mm}^{4}

I_{x_{1}}

=

\frac{{a_{outer}}^{4}}{3} - \frac{{a_{inner}}^{2} \cdot ({a_{inner}}^{2} + 3 \cdot {a_{outer}}^{2})}{12}

=

\frac{{10.00}^{4}}{3} - \frac{{9.00}^{2} \cdot ({9.00}^{2} + 3 \cdot {10.00}^{2})}{12}

Second moment of area about y1-axis

I_{y_{1}}

761.58

{mm}^{4}

I_{y_{1}}

=

I_{x_{1}}

=

761.58

Polar moment of inertia about centre

J_{z}

573.17

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

286.58 + 286.58

Polar moment of inertia about vertex

J_{z_{1}}

1523.17

{mm}^{4}

J_{z_{1}}

=

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

=

761.58 + 761.58

Radius of gyration about x-axis

K_{x}

3.88

mm

K_{x}

=

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

=

\sqrt{\frac{286.58}{19.00}}

Radius of gyration about y-axis

K_{y}

3.88

mm

K_{y}

=

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

=

\sqrt{\frac{286.58}{19.00}}

Radius of gyration about y-axis

K_{z}

5.49

mm

K_{z}

=

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

=

\sqrt{{3.88}^{2} + {3.88}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

6.33

mm

K_{x_{1}}

=

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

=

\sqrt{\frac{761.58}{19.00}}

Radius of gyration about y1-axis

K_{y_{1}}

6.33

mm

K_{y_{1}}

=

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

=

\sqrt{\frac{761.58}{19.00}}

Radius of gyration about z1-axis

K_{z_{1}}

8.95

mm

K_{z_{1}}

=

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

=

\sqrt{{6.33}^{2} + {6.33}^{2}}

Elastic section modulus

S_{t}

57.32

{mm}^{3}

S_{t}

=

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

=

\frac{286.58}{5.00}

Plastic section modulus

Z_{t}

67.75

{mm}^{3}

Z_{t}

=

\frac{({a_{outer}}^{3} - {a_{inner}}^{3})}{4}

=

\frac{({10.00}^{3} - {9.00}^{3})}{4}