Quarter Circle
A part of the interior of a circle having two radius boundries at a 90° angle and an arc.- Center of a circle having all points on the line circumference are at equal distance from the center point.
- A quarter circle is a structural shape used in construction.
- See Article Link - Geometric Properties of Structural Shapes
- Tags: Structural Steel Circle
Quarter Circle Index
- Arc Length of a Quarter Circle
- Area of a Quarter Circle
- Distance from Centroid of a Quarter Circle
- Elastic Section Modulus of a Quarter Circle
- Perimeter of a Quarter Circle
- Polar Moment of Inertia of a Circle
- Radius of a Quarter Circle
- Radius of Gyration of a Half Circle
- Second Moment of Area of a Half Circle
arc Length of a Quarter Circle formula |
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| \( L \;=\; 2 \; \pi \; r\;/\;4 \) | ||
| Symbol | English | Metric |
| \( L \) = arc length | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( r \) = radius | \( in \) | \( mm \) |
area of a Quarter Circle formula |
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| \( A \;=\; \pi \; r^2 \;/\;4 \) | ||
| Symbol | English | Metric |
| \( A \) = area | \( in^2 \) | \( mm^2 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( r \) = radius | \( in \) | \( mm \) |
Distance from Centroid of a Quarter Circle formulas |
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\( C_x \;=\; 4 \; r\;/\;3 \; \pi \) \( C_y \;=\; 4 \; r\;/\;3 \; \pi \) |
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| Symbol | English | Metric |
| \( C_x, C_y \) = distance from centroid | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( r \) = radius | \( in \) | \( mm \) |
Elastic Section Modulus of a Quarter Circle formula |
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| \( S \;=\; I_x \;/\; C_y \) | ||
| Symbol | English | Metric |
| \( S \) = elastic section modulus | \(in^3\) | \(mm^3\) |
| \( I \) = moment of inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
Perimeter of a Quarter Circle formulas |
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\( P \;=\; (2 \; \pi \; r\;/\;4)+ 2 \; r \) \( P \;=\; L + 2 \; r \) |
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| Symbol | English | Metric |
| \( P \) = perimeter | \( in \) | \( mm \) |
| \( L \) = arc length | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( r \) = radius | \( in \) | \( mm \) |
Polar Moment of Inertia of a Circle formulas |
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\( J_{z} \;=\; [\; ( \pi\;/\; 8 ) - ( 8 \;/\; 9 \; \pi ) \;] \; r^4 \) \( J_{z1} \;=\; \pi \; r^4 \;/\; 8 \) |
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| Symbol | English | Metric |
| \( L \) = arc length | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( r \) = radius | \( in \) | \( mm \) |
Radius of a Quarter Circle formula |
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| \( r \;=\; \sqrt{ 2 \; A \;/\; \pi } \) | ||
| Symbol | English | Metric |
| \( r \) = radius | \( in \) | \( mm \) |
| \( A \) = area | \( in^2 \) | \( mm^2 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
Radius of Gyration of a Half Circle formulas |
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\( k_{x} \;=\; r \; \sqrt{ ( 1 \;/\; 4 ) - ( 16 \;/\; 9 \; \pi^2) } \) \( k_{y} \;=\; r \; \sqrt{ ( 1 \;/\; 4 ) - ( 16 \;/\; 9 \; \pi^2) } \) \( k_{z} \;=\; r \; \sqrt{ ( 1 \;/\; 2 ) - ( 16 \;/\; 9 \; \pi^2) } \) \( k_{x1} \;=\; r \;/\; 2 \) \( k_{y1} \;=\; r \;/\; 2 \) \( k_{z1} \;=\; ( \sqrt {2} \;/\; 2 ) \; r \) |
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| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( r \) = radius | \( in \) | \( mm \) |
Second Moment of Area of a Half circle formulas |
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\( I_{x} \;=\; [\; ( \pi\;/\; 16 ) - ( 4 \;/\; 9 \; \pi ) \;] \; r^4 \) \( I_{y} \;=\; [\; ( \pi\;/\; 16 ) - ( 4 \;/\; 9 \; \pi ) \;] \; r^4 \) \( I_{x1} \;=\; \pi \; r^4\;/\; 16 \) \( I_{y1} \;=\; \pi \; r^4\;/\; 8 \) |
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| Symbol | English | Metric |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | |
| \( r \) = radius | \( in \) | \( mm \) |
Tags: Structural Steel Circle