Hollow Circle
Two circles each having all points on each circle at a fixed equal distance from a center point.- Center of a circle having all points on the line circumference are at equal distance from the center point.
- A hollow circle is a structural shape used in construction.
Structural Shapes
area of a Hollow Circle formula
| \(\large{ A_{area} = \pi \; \left( R^2 - r^2 \right) }\) |
Where:
\(\large{ A_{area} }\) = area
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
\(\large{ \pi }\) = Pi
Circumference of a Hollow Circle formulas
| \(\large{ C = 2 \; \pi \; R }\) | (outside) |
| \(\large{ C = 2 \; \pi \; r }\) | (inside) |
Where:
\(\large{ C }\) = circumference
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
\(\large{ \pi }\) = Pi
Distance from Centroid of a Hollow Circle formulas
| \(\large{ C_x = r}\) | |
| \(\large{ C_y = r}\) |
Where:
\(\large{ C_x, C_y }\) = distance from centroid
\(\large{ r }\) = inside radius
Elastic Section Modulus of a Hollow Circle formula
| \(\large{ S = \frac{ \pi \; \left( R^4 \;-\; r^4 \right) }{ 4\;R } }\) |
Where:
\(\large{ S }\) = elastic section modulus
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
\(\large{ \pi }\) = Pi
Plastic Section Modulus of a Hollow Circle formula
| \(\large{ Z = \frac { 4 \; \left( R^3 \;-\; r^3 \right) } { 3 } }\) |
Where:
\(\large{ Z }\) = plastic section modulus
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
Polar Moment of Inertia of a Hollow Circle formulas
| \(\large{ J_{z} = \frac { \pi }{2} \; \left( R^4 - r^4 \right) }\) | |
| \(\large{ J_{z1} = \frac { \pi }{2} \; \left( R^4 - r^4 \right) + 2\; \pi \; R^2 \left( R^2 - r^2 \right) }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
\(\large{ \pi }\) = Pi
Radius of a Hollow Circle formula
| \(\large{ r = \sqrt {\frac {2 \; A_{area}} {\pi} } }\) |
Where:
\(\large{ r }\) = inside radius
\(\large{ A_{area} }\) = area
\(\large{ r }\) = inside radius
Radius of Gyration of a Hollow Circle formulas
| \(\large{ k_{x} = \frac {1}{2} \; \sqrt { R^2 + r^2 } }\) | |
| \(\large{ k_{y} = \frac {1}{2} \; \sqrt { R^2 + r^2 } }\) | |
| \(\large{ k_{z} = \frac { \sqrt { 2 } }{2} \; \sqrt { R^2 + r^2 } }\) | |
| \(\large{ k_{x1} = \frac {1}{2} \; \sqrt { 5 \; R^2 + r^2 } }\) | |
| \(\large{ k_{y1} = \frac {1}{2} \; \sqrt { 5 \; R^2 + r^2 } }\) | |
| \(\large{ k_{z1} = \frac { \sqrt { 2 } }{2} \; \sqrt { 5 \; R^2 + r^2 } }\) |
Where:
\(\large{ k }\) = radius of gyration
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
Second Moment of Area of a Hollow circle formulas
| \(\large{ I_{x} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) }\) | |
| \(\large{ I_{y} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) }\) | |
| \(\large{ I_{x1} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) + \pi \; R^2 \left( R^2 - r^2 \right) }\) | |
| \(\large{ I_{y1} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) + \pi \; R^2 \left( R^2 - r^2 \right) }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
\(\large{ \pi }\) = Pi
Sector of a Hollow Circle formula
| \(\large{ A = \frac{\pi \; \theta \; \left( r^2 \;-\; R^2 \right) }{360} }\) |
Where:
\(\large{ A }\) = sector area
\(\large{ \theta }\) = angle
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
\(\large{ \pi }\) = Pi
Torsional Constant of a Hollow Circle formulas
| \(\large{ J = \frac { \pi \; \left( R^4 \;-\; r^4 \right) } { 2 } }\) | |
| \(\large{ J = \frac { \pi \; \left( D^4 \;-\; d^4 \right) } { 32 } }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ d }\) = inside diameter
\(\large{ D }\) = outside diameter
\(\large{ r }\) = inside radius
\(\large{ R }\) = outside radius
\(\large{ \pi }\) = Pi
Tags: Equations for Inertia Equations for Structural Steel Equations for Modulus