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.
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Arc Length of a Half Circle formula |
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| \(\large{ l = \frac{2 \; \pi \; r}{2} }\) | ||
| Symbol | English | Metric |
| \(\large{ l }\) = length | \(\large{ in }\) | \(\large{mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{mm }\) |
Area of a Half Circle formula |
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| \(\large{ A_{area} = \frac{ \pi \; r^2 }{2} }\) | ||
| Symbol | English | Metric |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{mm }\) |
Perimeter of a Half Circle formula |
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| \(\large{ P = \frac{2 \; \pi \; r}{2} + 2 \; r }\) | ||
| Symbol | English | Metric |
| \(\large{ P }\) = perimeter | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{mm }\) |
Radius of a Half Circle formula |
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| \(\large{ r = \sqrt {\frac {2 \; A_{area}} {\pi} } }\) | ||
| Symbol | English | Metric |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{mm }\) |
Distance from Centroid of a Half Circle formulas |
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\(\large{ C_x = 0 }\) \(\large{ C_y = \frac {4 \; r} {3 \; \pi} }\) |
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| Symbol | English | Metric |
| \(\large{ C_x, C_y }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{mm }\) |
Elastic Section Modulus of a Half Circle formula |
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| \(\large{ S = \frac { I_x } { C_y } }\) | ||
| Symbol | English | Metric |
| \(\large{ S }\) = elastic section modulus | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ C_x, C_y }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
Polar Moment of Inertia of a Circle formulas |
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\(\large{ J_{z} = \left( \frac { \pi}{ 4 } - \frac { 8 }{ 9 \; \pi } \right) r^4 }\) \(\large{ J_{z1} = \frac { \pi \; r^4 } { 4 } }\) |
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| Symbol | English | Metric |
| \(\large{ J }\) = torsional constant | \(\large{ in^4 }\) | \(\large{mm^4 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{mm }\) |
Radius of Gyration of a Half Circle formulas |
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\(\large{ k_{x} = r \; \sqrt { \frac { 1 } { 4 } - \frac { 16 } { 9 \; \pi^2 } } }\) \(\large{ k_{y} = \frac { r } { 2 } }\) \(\large{ k_{z} = r \; \sqrt { \frac { 1 } { 2 } - \frac { 16 } { 9 \; \pi^2 } } }\) \(\large{ k_{x1} = \frac { r } { 2 } }\) \(\large{ k_{y1} = \frac { r } { 2 } }\) \(\large{ k_{z1} = \frac { \sqrt {2} } { 2 } \; r }\) |
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| Symbol | English | Metric |
| \(\large{ k }\) = radius of gyration | \(\large{ in}\) | \(\large{mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{mm }\) |
Second Moment of Area of a Half circle formulas |
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\(\large{ I_{x} = \left( \frac { \pi}{ 8 } - \frac { 8 }{ 9 \; \pi } \right) r^4 }\) \(\large{ I_{y} = \frac { \pi \; r^4}{ 8 } }\) \(\large{ I_{x1} = \frac { \pi \; r^4}{ 8 } }\) \(\large{ I_{y1} = \frac { \pi \; r^4}{ 8 } }\) |
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| Symbol | English | Metric |
| \(\large{ I }\) = moment of inertia | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{mm }\) |
Tags: Inertia Equations Structural Steel Equations Modulus Equations