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Rectangle Hollow

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The rectangular hollow structural shape (HSS) has a rectangular profile with a hollow interior. It provides excellent torsional resistance and is highly efficient for resisting bending and compression, particularly when the primary load direction is known and the section can be oriented optimally. Its closed form offers good stability against buckling, making it suitable for columns, beams, and frames in various structural applications, balancing strength with material efficiency.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Hollow Rectangle

figure wim5a78577ab2

Outer breadth

b_{out}

10.00

mm

Inner breadth

b_{i n}

9.00

mm

Outer depth

a_{out}

5.00

mm

Inner depth

a_{i n}

4.00

mm

Horizontal plate thickness

t_{horizontal}

0.50000

mm

t_{horizontal}

=

(a_{out} - a_{i n}) \cdot 0.5

=

(5.00 - 4.00) \cdot 0.5

Vertical plate thickness

t_{vertical}

0.50000

mm

t_{vertical}

=

(b_{out} - b_{i n}) \cdot 0.5

=

(10.00 - 9.00) \cdot 0.5

Area

A_{t}

14.00

{mm}^{2}

A_{t}

=

b_{out} \cdot a_{out} - b_{i n} \cdot a_{i n}

=

10.00 \cdot 5.00 - 9.00 \cdot 4.00

Outer perimeter

P_{out}

30.00

mm

P_{out}

=

2 \cdot (a_{out} + b_{out})

=

2 \cdot (5.00 + 10.00)

Inner perimeter

P_{i n}

26.00

mm

P_{i n}

=

2 \cdot (a_{i n} + b_{i n})

=

2 \cdot (4.00 + 9.00)

Distance to centroid (x-axis)

C_{x}

5.00

mm

C_{x}

=

\frac{b_{out}}{2}

=

\frac{10.00}{2}

Distance to centroid (y-axis)

C_{y}

2.50

mm

C_{y}

=

\frac{a_{out}}{2}

=

\frac{5.00}{2}

Second moment of area about x-axis

I_{x}

56.17

{mm}^{4}

I_{x}

=

\frac{b_{out} \cdot {a_{out}}^{3}}{12} - \frac{b_{i n} \cdot {a_{i n}}^{3}}{12}

=

\frac{10.00 \cdot {5.00}^{3}}{12} - \frac{9.00 \cdot {4.00}^{3}}{12}

Second moment of area about y-axis

I_{y}

173.67

{mm}^{4}

I_{y}

=

\frac{{b_{out}}^{3} \cdot a_{out}}{12} - \frac{{b_{i n}}^{3} \cdot a_{i n}}{12}

=

\frac{{10.00}^{3} \cdot 5.00}{12} - \frac{{9.00}^{3} \cdot 4.00}{12}

Second moment of area about x1-axis

I_{x_{1}}

143.67

{mm}^{4}

I_{x_{1}}

=

\frac{b_{out} \cdot {a_{out}}^{3}}{3} - \frac{b_{i n} \cdot a_{i n} \cdot ({a_{i n}}^{2} + 3 \cdot {a_{out}}^{2})}{12}

=

\frac{10.00 \cdot {5.00}^{3}}{3} - \frac{9.00 \cdot 4.00 \cdot ({4.00}^{2} + 3 \cdot {5.00}^{2})}{12}

Second moment of area about y1-axis

I_{y_{1}}

523.67

{mm}^{4}

I_{y_{1}}

=

\frac{{b_{out}}^{3} \cdot a_{out}}{3} - \frac{b_{i n} \cdot a_{i n} \cdot ({b_{i n}}^{2} + 3 \cdot {b_{out}}^{2})}{12}

=

\frac{{10.00}^{3} \cdot 5.00}{3} - \frac{9.00 \cdot 4.00 \cdot ({9.00}^{2} + 3 \cdot {10.00}^{2})}{12}

Polar moment of inertia about centre

J_{z}

229.83

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

56.17 + 173.67

Polar moment of inertia about vertex

J_{z_{1}}

667.33

{mm}^{4}

J_{z_{1}}

=

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

=

143.67 + 523.67

Radius of gyration about x-axis

K_{x}

2.00

mm

K_{x}

=

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

=

\sqrt{\frac{56.17}{14.00}}

Radius of gyration about y-axis

K_{y}

3.52

mm

K_{y}

=

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

=

\sqrt{\frac{173.67}{14.00}}

Radius of gyration about z-axis

K_{z}

4.05

mm

K_{z}

=

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

=

\sqrt{{2.00}^{2} + {3.52}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

3.20

mm

K_{x_{1}}

=

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

=

\sqrt{\frac{143.67}{14.00}}

Radius of gyration about y1-axis

K_{y_{1}}

6.12

mm

K_{y_{1}}

=

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

=

\sqrt{\frac{523.67}{14.00}}

Radius of gyration about z1-axis

K_{z_{1}}

6.90

mm

K_{z_{1}}

=

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

=

\sqrt{{3.20}^{2} + {6.12}^{2}}

Elastic section modulus about x-axis

S_{x}

22.47

{mm}^{3}

S_{x}

=

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

=

\frac{56.17}{2.50}

Elastic section modulus about y-axis

S_{y}

34.73

{mm}^{3}

S_{y}

=

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

=

\frac{173.67}{5.00}

Plastic section modulus about x-axis

Z_{x}

26.50

{mm}^{3}

Z_{x}

=

\frac{(b_{out} \cdot {a_{out}}^{2} - b_{i n} \cdot {a_{i n}}^{2})}{4}

=

\frac{(10.00 \cdot {5.00}^{2} - 9.00 \cdot {4.00}^{2})}{4}

Plastic section modulus about y-axis

Z_{y}

44.00

{mm}^{3}

Z_{y}

=

\frac{(a_{out} \cdot {b_{out}}^{2} - a_{i n} \cdot {b_{i n}}^{2})}{4}

=

\frac{(5.00 \cdot {10.00}^{2} - 4.00 \cdot {9.00}^{2})}{4}