Thin Wall 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 thin wall circle is a structural shape used in construction.
Structural Shapes
area of a Thin Walled Circle formulas
| \(\large{ A_{area} = 2\; \pi \;r\; t }\) | |
| \(\large{ A_{area} = \pi \;D\; t }\) |
Where:
\(\large{ A_{area} }\) = area
\(\large{ D }\) = outside diameter
\(\large{ r }\) = inside radius
\(\large{ t }\) = thickness
\(\large{ \pi }\) = Pi
Perimeter of a Thin Walled Circle formulas
| \(\large{ P = 2\; \pi \;r }\) | (outside) |
| \(\large{ P = 2\; \pi \; \left( r - t \right) }\) | (inside) |
Where:
\(\large{ P }\) = perimeter
\(\large{ r }\) = inside radius
\(\large{ t }\) = thickness
\(\large{ \pi }\) = Pi
Radius of a Thin Walled Circle formula
| \(\large{ r = \sqrt {\frac {2\;A_{area}} {\pi} } }\) |
Where:
\(\large{ r }\) = inside radius
\(\large{ A_{area} }\) = area
\(\large{ \pi }\) = Pi
Distance from Centroid of a Thin Walled 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 Thin Walled Circle formula
| \(\large{ S = \frac { 2\; \pi \;r \;t } { 3 } }\) |
Where:
\(\large{ S }\) = elastic section modulus
\(\large{ r }\) = inside radius
\(\large{ t }\) = thickness
\(\large{ \pi }\) = Pi
Plastic Section Modulus of a Thin Walled Circle formula
| \(\large{ Z = \pi \;r^2 \;t }\) |
Where:
\(\large{ Z }\) = plastic section modulus
\(\large{ r }\) = inside radius
\(\large{ t }\) = thickness
\(\large{ \pi }\) = Pi
Polar Moment of Inertia of a Thin Walled Circle formulas
| \(\large{ J_{z} = 2\; \pi \;r^3 \;t }\) | |
| \(\large{ J_{z1} = 6\; \pi \;r^3 \;t }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ r }\) = inside radius
\(\large{ t }\) = thickness
\(\large{ \pi }\) = Pi
Radius of Gyration of a Thin Walled Circle formulas
| \(\large{ k_{x} = \frac { \sqrt {2} } { 2 } \; r }\) | |
| \(\large{ k_{y} = \frac { \sqrt {2} } { 2 } \; r }\) | |
| \(\large{ k_{z} = r }\) | |
| \(\large{ k_{x1} = \frac { \sqrt {6} } { 2 } \; r }\) | |
| \(\large{ k_{y1} = \frac { \sqrt {6} } { 2 } \; r }\) | |
| \(\large{ k_{z1} = \sqrt {3} \; r }\) |
Where:
\(\large{ k }\) = radius of gyration
\(\large{ r }\) = inside radius
Second Moment of Area of a Thin Walled Circle formulas
| \(\large{ I_{x} = \pi \;r^3 \;t }\) | |
| \(\large{ I_{x1} = 3\; \pi \;r^3 \;t }\) | |
| \(\large{ I_{y1} = 3\; \pi \;r^3 \;t }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ r }\) = inside radius
\(\large{ t }\) = thickness
\(\large{ \pi }\) = Pi
Torsional Constant of a Thin Walled Circle formula
| \(\large{ J = 2\; \pi \;r^3 \; t }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ r }\) = radius
\(\large{ t }\) = thickness
\(\large{ \pi }\) = Pi
Tags: Equations for Perimeter Equations for Inertia Equations for Structural Steel Equations for Modulus