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.
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arc Length of a Quarter Circle formula |
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| \(\large{ L = \frac {2 \; \pi \; r} {4} }\) | ||
| Symbol | English | Metric |
| \(\large{ L }\) = arc length | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
area of a Quarter Circle formula |
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| \(\large{ A = \frac{ \pi \; r^2 }{4} }\) | ||
| 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 Quarter Circle formulas |
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\(\large{ C_x = \frac {4 \; r} {3 \; \pi} }\) \(\large{ C_y = \frac {4 \; r} {3 \; \pi} }\) |
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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 Quarter Circle formula |
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| \(\large{ S = \frac { I_x } { C_y } }\) | ||
| Symbol | English | Metric |
| \(\large{ S }\) = elastic section modulus | \(\large{in^3}\) | \(\large{mm^3}\) |
| \(\large{ I }\) = moment of inertia | \(\large{\frac{lbm}{ft^2-sec} }\) | \(\large{\frac{kg}{m^2} }\) |
Perimeter of a Quarter Circle formulas |
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\(\large{ P = \frac {2 \; \pi \; r} {4} + 2 \; r }\) \(\large{ P = L + 2 \; r }\) |
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| Symbol | English | Metric |
| \(\large{ P }\) = perimeter | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ L }\) = arc length | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Polar Moment of Inertia of a Circle formulas |
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\(\large{ J_{z} = \left( \frac { \pi}{ 8 } - \frac { 8 }{ 9 \; \pi } \right) r^4 }\) \(\large{ J_{z1} = \frac { \pi \; r^4 } { 8 } }\) |
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| Symbol | English | Metric |
| \(\large{ L }\) = arc length | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Radius of a Quarter Circle formula |
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| \(\large{ r = \sqrt {\frac {2 \; A } {\pi} } }\) | ||
| Symbol | English | Metric |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
Radius of Gyration of a Half Circle formulas |
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\(\large{ k_{x} = r \; \sqrt { \frac { 1 } { 4 } - \frac { 16 } { 9 \; \pi^2 } } }\) \(\large{ k_{y} = r \; \sqrt { \frac { 1 } { 4 } - \frac { 16 } { 9 \; \pi^2 } } }\) \(\large{ k_{z} = r \; \sqrt { \frac { 1 } { 2 } - \frac { 16 } { 9 \; \pi^2 } } }\) \(\large{ k_{x1} = \frac { r } { 2 } }\) \(\large{ k_{y1} = \frac { r } { 2 } }\) \(\large{ k_{z1} = \frac { \sqrt {2} } { 2 } \; r }\) |
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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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\(\large{ I_{x} = \left( \frac { \pi}{ 16 } - \frac { 4 }{ 9 \; \pi } \right) \; r^4 }\) \(\large{ I_{y} = \left( \frac { \pi}{ 16 } - \frac { 4 }{ 9 \; \pi } \right) \; r^4 }\) \(\large{ I_{x1} = \frac { \pi \; r^4}{ 16 } }\) \(\large{ I_{y1} = \frac { \pi \; r^4}{ 8 } }\) |
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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 Structural Steel Modulus