Hollow Rectangle
A two-dimensional figure that is a quadrilateral with two pair of parallel edges.- A hollow rectangle is a structural shape used in construction.
- Interior angles are 90°
- Exterior angles are 90°
- Angle \(\;A = B = C = D\)
- 2 diagonals
- 4 edges
- 4 vertexs
Structural Shapes
Area of a Hollow Rectangle formula
| \( \large{ A = b\;a - b_1\;a_1 }\) |
Where:
\(\large{ A }\) = area
\(\large{ a, b, a_1, b_1 }\) = side
Distance from Centroid of a Hollow Rectangle formulas
| \( \large{ C_x = \frac{ b }{ 2 } }\) | |
| \( \large{ C_y = \frac{ a }{ 2} }\) |
Where:
\(\large{ C }\) = distance from centroid
\(\large{ a, b, a_1, b_1 }\) = side
Elastic Section Modulus of a Hollow Rectangle formulas
| \( \large{ S_x = \frac{ I_x }{ C_y } }\) | |
| \( \large{ S_y = \frac{ I_y }{ C_x } }\) |
Where:
\(\large{ S }\) = elastic section modulus
\(\large{ C }\) = distance from centroid
\(\large{ I }\) = moment of inertia
Perimeter of a Hollow Rectangle formulas
| \( \large{ P_o = 2\; \left( a + b \right) }\) | (outside) |
| \( \large{ P_i = 2\; \left( a_1 + b_2 \right) }\) | (inside) |
Where:
\(\large{ P }\) = perimeter
\(\large{ a, b, a_1, b_1 }\) = side
Polar Moment of Inertia of a Hollow Rectangle formulas
| \(\large{ J_{z} = I_x + I_y }\) | |
| \(\large{ J_{z1} = I_{x1} + I_{y1} }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ I }\) = moment of inertia
Radius of Gyration of a Hollow Rectangle formulas
| \(\large{ k_{x} = \sqrt{ \frac{ b\;a^3 \;-\; b_1\; a_{1}{^3} }{ 12 \; \left( b\;a \;-\; b_1\; a_1 \right) } } }\) | |
| \(\large{ k_{y} = \sqrt{ \frac{ b^3 \;a \;-\; b_{1}{^3} \; a_1 }{ 12\; \left( b\;a \;-\; b_1\; a_1 \right) } } }\) | |
| \(\large{ k_{z} = \sqrt{ k_{x}{^2} + k_{y}{^2} } }\) | |
| \(\large{ k_{x1} = \sqrt{ \frac{ I_{x1} }{ A } } }\) | |
| \(\large{ k_{y1} = \sqrt{ \frac{ I_{y1} }{ A } } }\) | |
| \(\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }\) |
Where:
\(\large{ k }\) = radius of gyration
\(\large{ A }\) = area
\(\large{ a, b, a_1, b_1 }\) = side
\(\large{ I }\) = moment of inertia
\(\large{ k }\) = radius of gyration
Second Moment of Area of a Hollow Rectangle formulas
| \(\large{ I_{x} = \frac{ b\;a^3 \;-\; b_1\; a_{1}{^3} }{12} }\) | |
| \(\large{ I_{y} = \frac{ b^3 \;a \;-\; b_{1}{^3}\; a_1 }{12} }\) | |
| \(\large{ I_{x1} = \frac{ b\;a^3 }{3} - \frac { b_1 \; a_1 \; \left( a_{1}{^2} \;+\; 3\;a^2 \right) }{12} }\) | |
| \(\large{ I_{y1} = \frac{ b^3 \;a }{3} - \frac { b_1 \; a_1 \; \left( b_{1}{^2} \;+\; 3\;b^2 \right) }{12} }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ a, b, a_1, b_1 }\) = side
Side of a Hollow Rectangle formulas
| \( \large{ a = \frac{P}{2} - b }\) | |
| \( \large{ b = \frac{P}{2} - a }\) |
Where:
\(\large{ a, b, a_1, b_1 }\) = side
\(\large{ P }\) = perimeter
Tags: Equations for Inertia Equations for Structural Steel Equations for Modulus