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Circle

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The solid circular structural shape has a completely filled, round cross-section. Its key characteristic is isotropic behaviour in bending, meaning its resistance to bending is uniform in all directions perpendicular to its axis. It possesses good compressive strength and is also effective in resisting torsional loads, although hollow circular sections are generally more efficient for torsion per unit of material. Common applications include shafts, pins, columns, and foundation piles.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Circle

figure wim2095d5968d

Radius

r_{t}

5.00

mm

Diameter

D_{t}

10.00

mm

D_{t}

=

2 \cdot r_{t}

=

2 \cdot 5.00

Area

A_{t}

78.54

{mm}^{2}

A_{t}

=

π \cdot {r_{t}}^{2}

=

π \cdot {5.00}^{2}

Circumference

P_{t}

31.42

mm

P_{t}

=

2 \cdot π \cdot r_{t}

=

2 \cdot π \cdot 5.00

Distance to centroid (x-axis)

C_{x}

5.00

mm

C_{x}

=

r_{t}

=

5.00

Distance to centroid (x-axis)

C_{y}

5.00

mm

C_{y}

=

r_{t}

=

5.00

Second moment of area about x-axis

I_{x}

490.87

{mm}^{4}

I_{x}

=

\frac{π \cdot {r_{t}}^{4}}{4}

=

\frac{π \cdot {5.00}^{4}}{4}

Second moment of area about y-axis

I_{y}

490.87

{mm}^{4}

I_{y}

=

\frac{π \cdot {r_{t}}^{4}}{4}

=

\frac{π \cdot {5.00}^{4}}{4}

Second moment of area about x1-axis

I_{x_{1}}

2454.37

{mm}^{4}

I_{x_{1}}

=

\frac{5 \cdot π \cdot {r_{t}}^{4}}{4}

=

\frac{5 \cdot π \cdot {5.00}^{4}}{4}

Second moment of area about y1-axis

I_{y_{1}}

2454.37

{mm}^{4}

I_{y_{1}}

=

\frac{5 \cdot π \cdot {r_{t}}^{4}}{4}

=

\frac{5 \cdot π \cdot {5.00}^{4}}{4}

Polar moment of inertia about centre

J_{z}

981.75

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

490.87 + 490.87

Polar moment of inertia about vertex

J_{z_{1}}

4908.74

{mm}^{4}

J_{z_{1}}

=

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

=

2454.37 + 2454.37

Radius of gyration about x-axis

K_{x}

2.50

mm

K_{x}

=

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

=

\sqrt{\frac{490.87}{78.54}}

Radius of gyration about y-axis

K_{y}

2.50

mm

K_{y}

=

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

=

\sqrt{\frac{490.87}{78.54}}

Radius of gyration about z-axis

K_{z}

3.54

mm

K_{z}

=

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

=

\sqrt{{2.50}^{2} + {2.50}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

5.59

mm

K_{x_{1}}

=

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

=

\sqrt{\frac{2454.37}{78.54}}

Radius of gyration about y1-axis

K_{y_{1}}

5.59

mm

K_{y_{1}}

=

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

=

\sqrt{\frac{2454.37}{78.54}}

Radius of gyration about z1-axis

K_{z_{1}}

7.91

mm

K_{z_{1}}

=

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

=

\sqrt{{5.59}^{2} + {5.59}^{2}}

Elastic section modulus

S

98.17

{mm}^{3}

S

=

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

=

\frac{490.87}{5.00}

Plastic section modulus

Z

166.67

{mm}^{3}

Z

=

\frac{4 \cdot {r_{t}}^{3}}{3}

=

\frac{4 \cdot {5.00}^{3}}{3}