Half Circle
Half of the interior of a circle having a straight chord and an arc.- Center of a circle having all points on the line circumference are at equal distance from the center point.
- A half circle is a structural shape used in construction.
- See Article Links - Geometric Properties of Structural Shapes
- Tags: Structural Steel Circle
Half Circle Index
- Arc Length of a Half Circle
- Area of a Half Circle
- Perimeter of a Half Circle
- Radius of a Half Circle
- Distance from Centroid of a Half Circle
- Elastic Section Modulus of a Half Circle
- Polar Moment of Inertia of a Circle
- Radius of Gyration of a Half Circle
- Second Moment of Area of a Half Circle
Arc Length of a Half Circle formula |
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| \( l \;=\; 2 \; \pi \; r\;/\;2 \) | ||
| Symbol | English | Metric |
| \(\large{ l }\) = length | \( in \) | \( mm \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Area of a Half Circle formula |
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| \( A_{area} \;=\; \pi \; r^2 \;/\;2 \) | ||
| Symbol | English | Metric |
| \(\large{ A }\) = area | \( in^2 \) | \( mm^2 \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Perimeter of a Half Circle formula |
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| \( P \;=\; (2 \; \pi \; r\;/\;2) + (2 \; r) \) | ||
| Symbol | English | Metric |
| \(\large{ P }\) = perimeter | \( in \) | \( mm \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Radius of a Half Circle formula |
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| \( r \;=\; \sqrt{2 \; A_{area} \;/\; \pi } \) | ||
| Symbol | English | Metric |
| \(\large{ A }\) = area | \( in^2 \) | \( mm^2 \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Distance from Centroid of a Half Circle formulas |
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\( C_x \;=\; 0 \) \( C_y \;=\; 4 \; r \;/\; 3 \; \pi \) |
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| Symbol | English | Metric |
| \(\large{ C_x, C_y }\) = distance from centroid | \( in \) | \( mm \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Elastic Section Modulus of a Half Circle formula |
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| \( S \;=\; I_x \;/\; C_y \) | ||
| Symbol | English | Metric |
| \(\large{ S }\) = elastic section modulus | \( in^3 \) | \( mm^3 \) |
| \(\large{ C_x, C_y }\) = distance from centroid | \( in \) | \( mm \) |
Polar Moment of Inertia of a Circle formulas |
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\( J_{z} \;=\; [\; ( \pi\;/\; 4 ) - ( 8 \;/\; 9 \; \pi )\;] \; r^4 \) \( J_{z1} \;=\; \pi \; r^4 \;/\; 4 \) |
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| Symbol | English | Metric |
| \(\large{ J }\) = torsional constant | \( in^4 \) | \( mm^4 \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Radius of Gyration of a Half Circle formulas |
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\( k_{x} \;=\; r \; \sqrt{ (1 \;/\; 4 ) - (16 \;/\; 9 \; \pi^2 ) } \) \( k_{y} \;=\; r \;/\; 2 \) \( k_{z} \;=\; r \; \sqrt{ (1 \;/\; 2 ) - (16 \;/\; 9 \; \pi^2 ) } \) \( k_{x1} \;=\; r \;/\; 2 \) \( k_{y1} \;=\; r \;/\; 2 \) \( k_{z1} \;=\; ( \sqrt {2} \;/\; 2 ) \; r \) |
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| Symbol | English | Metric |
| \(\large{ k }\) = radius of gyration | \( in \) | \( mm \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Second Moment of Area of a Half circle formulas |
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\( I_{x} \;=\; [\; ( \pi \;/\; 8 ) - ( 8 \;/\; 9 \; \pi ) \;] \; r^4 \) \( I_{y} \;=\; \pi \; r^4\;/\; 8 \) \( I_{x1} \;=\; \pi \; r^4\;/\; 8 \) \( I_{y1} \;=\; \pi \; r^4\;/\; 8 \) |
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| Symbol | English | Metric |
| \(\large{ I }\) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Tags: Structural Steel Circle