Rotated Rectangle
Rectangle is a quadrilateral with two pair of parallel lines.- A rotated 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
formulas that use
Structural Shapes
Area of a Rotated Rectangle formula
| \( \large{ A_{area} = a\;b }\) |
Where:
\(\large{ A }\) = area
\(\large{ a, b }\) = side
Distance from Centroid of a Rotated Rectangle formulas
| \( \large{ C_x = \frac { b \; cos \; \theta \;+\; a \; sin \; \theta } { 2 } }\) | |
| \( \large{ C_y = \frac { a \; cos \; \theta \;+\; b \; sin \; \theta } { 2 } }\) |
Where:
\(\large{ a, b }\) = side
\(\large{ C }\) = distance from centroid
Elastic Section Modulus of a Rotated Rectangle formula
| \( \large{ S_x = \frac{ b\;a\; \left(a^2 \; cos^2 \; \theta \;+\; b^2 sin^2\; \theta \right) }{ 6 \; \left( a \; cos\;\theta \;+\; b\;sin\;\theta\right) } }\) |
Where:
\(\large{ S }\) = elastic section modulus
\(\large{ a, b }\) = side
Perimeter of a Rotated Rectangle formula
| \( \large{ P= 2\; \left( a \;+\; b \right) }\) |
Where:
\(\large{ P }\) = perimeter
\(\large{ a, b }\) = side
Polar Moment of Inertia of a Rotated Rectangle formula
| \(\large{ J_{z} = \frac{b\;a}{3} \; \left( b^2 \;+\; a^2 \right) }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ a, b }\) = side
Radius of Gyration of a Rotated Rectangle formula
| \(\large{ k_{x} = \sqrt{ \frac{ a^2 \;cos^2 \; \left( b^2 \; sin^2 \; \theta \;+\; \theta \right) }{ 2\; \sqrt{3} } } }\) |
Where:
\(\large{ k }\) = radius of gyration
\(\large{ a, b }\) = side
Second Moment of Area of a Rotated Rectangle formula
| \(\large{ I_{x} = \frac{ba}{12} \; \left( a^2 \; cos^2 \; \theta + b^2 \; sin^2 \; \theta \right) }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ a, b }\) = side
Side of a Rotated Rectangle formulas
| \( \large{ a = \frac{P}{2} - b }\) | |
| \( \large{ b = \frac{P}{2} - a }\) |
Where:
\(\large{ a, b }\) = side
\(\large{ P }\) = perimeter
Tags: Equations for Inertia Equations for Structural Steel Equations for Modulus