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Hollow Circle

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The hollow circular structural shape, often referred to as a pipe or circular HSS, features an annular cross-section. It is exceptionally efficient in resisting torsional loads and offers excellent resistance to buckling when used as a compression member (column). Its uniform strength in all directions makes it versatile for beams and members in truss systems. This shape provides a high strength-to-weight ratio and is widely used in pipelines, columns, and various structural frameworks.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Hollow Circle

figure wim8e57bec9b6

Outer radius

R_{out}

15.00

mm

Inner radius

r_{i n}

5.00

mm

Area

A_{t}

628.32

{mm}^{2}

A_{t}

=

π \cdot ({R_{out}}^{2} - {r_{i n}}^{2})

=

π \cdot ({15.00}^{2} - {5.00}^{2})

Outer perimeter

P_{out}

94.25

mm

P_{out}

=

2 \cdot π \cdot R_{out}

=

2 \cdot π \cdot 15.00

Inner perimeter

P_{i n}

31.42

mm

P_{i n}

=

2 \cdot π \cdot r_{i n}

=

2 \cdot π \cdot 5.00

Distance to centroid (x-axis)

C_{x}

5.00

mm

C_{x}

=

r_{i n}

=

5.00

Distance to centroid (y-axis)

C_{y}

5.00

mm

C_{y}

=

r_{i n}

=

5.00

Second moment of area about x-axis

I_{x}

39269.9

{mm}^{4}

I_{x}

=

\frac{π}{4} \cdot ({R_{out}}^{4} - {r_{i n}}^{4})

=

\frac{π}{4} \cdot ({15.00}^{4} - {5.00}^{4})

Second moment of area about y-axis

I_{y}

39269.9

{mm}^{4}

I_{y}

=

I_{x}

=

39269.9

Polar moment of inertia about centre

J_{z}

78539.8

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

39269.9 + 39269.9

Second moment of area about x1-axis

I_{x_{1}}

180642

{mm}^{4}

I_{x_{1}}

=

\frac{π}{4} \cdot ({R_{out}}^{4} - {r_{i n}}^{4}) + π \cdot {R_{out}}^{2} \cdot ({R_{out}}^{2} - {r_{i n}}^{2})

=

\frac{π}{4} \cdot ({15.00}^{4} - {5.00}^{4}) + π \cdot {15.00}^{2} \cdot ({15.00}^{2} - {5.00}^{2})

Second moment of area about y1-axis

I_{y_{1}}

180642

{mm}^{4}

I_{y_{1}}

=

I_{x_{1}}

=

180642

Polar moment of inertia about vertex

J_{z_{1}}

361283

{mm}^{4}

J_{z_{1}}

=

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

=

180642 + 180642

Radius of gyration about x-axis

K_{x}

7.91

mm

K_{x}

=

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

=

\sqrt{\frac{39269.9}{628.32}}

Radius of gyration about y-axis

K_{y}

7.91

mm

K_{y}

=

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

=

\sqrt{\frac{39269.9}{628.32}}

Radius of gyration about z-axis

K_{z}

11.18

mm

K_{z}

=

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

=

\sqrt{{7.91}^{2} + {7.91}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

16.96

mm

K_{x_{1}}

=

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

=

\sqrt{\frac{180642}{628.32}}

Radius of gyration about y1-axis

K_{y_{1}}

16.96

mm

K_{y_{1}}

=

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

=

\sqrt{\frac{180642}{628.32}}

Radius of gyration about z1-axis

K_{z_{1}}

23.98

mm

K_{z_{1}}

=

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

=

\sqrt{{16.96}^{2} + {16.96}^{2}}

Elastic section modulus

S_{t}

2617.99

{mm}^{3}

S_{t}

=

\frac{π \cdot ({R_{out}}^{4} - {r_{i n}}^{4})}{(4 \cdot R_{out})}

=

\frac{π \cdot ({15.00}^{4} - {5.00}^{4})}{(4 \cdot 15.00)}

Plastic section modulus

Z_{t}

4333.33

{mm}^{3}

Z_{t}

=

\frac{4 \cdot ({R_{out}}^{3} - {r_{i n}}^{3})}{3}

=

\frac{4 \cdot ({15.00}^{3} - {5.00}^{3})}{3}