Rotated Rectangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • rotated rectangle 2Rectangle 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

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 formula

\( \large{ C_x =  \frac {  b \; cos  \; \theta   \;+\;  a \; sin  \; \theta           }  { 2 }   }\)

\( \large{ C_y =  \frac {  a \; cos  \; \theta  \;+\;  b \; sin  \; \theta           }  { 2 }    }\)

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 formula

\( \large{ a = \frac{P}{2} - b   }\)

\( \large{ b = \frac{P}{2} - a  }\)

Where:

\(\large{ a, b }\) = side

\(\large{ P }\) = perimeter

 

Tags: Equations for Moment of Inertia Equations for Structural Steel Equations for Modulus