Rectangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Rectangle - Geometric Propertiesrectangle 2Arectangle 1A

  • Rectangle is a quadrilateral with two pair of parallel edges.
  • 4 interior angles are 90°
  • 2 diagonals
  • 4 edges
  • 4 vertexs

Area of a Rectangle formula

\( \large{ A_{area} = ab  }\)

Circumcircle of a Rectangle formula

The radius of a circumcircle (outer) of a square if given side of diagonal \(( R )\).

\( \large{ R =  \frac {D'}{2}    }\)

\( \large{ R =  \frac  {  \sqrt { a^2 \;+\; b^2 }  }  { 2 }   }\)

Diagonal of a Rectangle formula

\( \large{ D' = \sqrt { a^2 \;+\; b^2 }   }\)

Perimeter of a Rectangle formula

\( \large{ P= 2a \;+\; 2b  }\)

\( \large{ P= 2 \left( a \;+\; b     \right)  }\)

Side of a Rectangle formula

\( \large{ a = \frac {P} {2} \;-\; b   }\)

\( \large{ b = \frac {P} {2} \;-\; a  }\)

Distance from Centroid of a Rectangle formula

\( \large{ C_x =  \frac { b }  { 2 }  }\)

\( \large{ C_y =  \frac { a }  { 2}  }\)  

Elastic Section Modulus of a Rectangle formula

\( \large{ S_x =  \frac { a^2b }  { 6  }  }\)

\( \large{ S_y =  \frac { ab^2 }  { 6  }  }\)

Plastic Section Modulus of a Rectangle formula

\( \large{ Z_x =  \frac { a^2b }  { 4  }   }\)

\( \large{ Z_y =  \frac { ab^2 }  { 4  }   }\)

Polar Moment of Inertia of a Rectangle formula

\(\large{ J_{z} = \frac {ab}{12}  \left( a^2 \;+\; b^2  \right)  }\)

\(\large{ J_{z1} = \frac {ab}{3}  \left( a^2 \;+\; b^2  \right)  }\)

Radius of Gyration of a Rectangle formula

\(\large{ k_{x} =    \frac { a }  {  2  \sqrt 3  }    }\)

\(\large{ k_{y} =   \frac { b }  {  2  \sqrt 3  }  }\)

\(\large{ k_{z} =   \sqrt    \frac { a^2 \;+\; b^2 }  {  2  \sqrt 3  }  }\)

\(\large{ k_{x1} =   \frac { a }  {  \sqrt 3  }  }\)

\(\large{ k_{y1} =  \frac { b }  {  \sqrt 3  }  }\)

\(\large{ k_{z1} =  \sqrt    \frac { a^2 \;+\; b^2 }  {  \sqrt 3  }  }\)

Second Moment of Area of a Rectangle formula

\(\large{ I_{x} =  \frac {a^3b}{12}  }\)

\(\large{ I_{y} = \frac {ab^3}{12}  }\)

\(\large{ I_{x1} =   \frac {a^3b}{3}  }\)

\(\large{ I_{y1} =  \frac {ab^3}{3}  }\)

Torsional Constant of a Rectangle formula

\(\large{ J  =  a^3 b \left[  \frac {16}{3} \;-\; \frac {3.36a}{b}  \left(  1 \;-\; \frac {  a^4  } {  12b^4  } \right)    \right]    }\)

 

Where:

\(\large{ A_{area} }\) = area

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

\(\large{ A, B, C, D }\) = vertex

\(\large{ C }\) = distance from centroid

\(\large{ D' }\) = diagonal

\(\large{ I }\) = moment of inertia

\(\large{ J }\) = torsional constant

\(\large{ k }\) = radius of gyration

\(\large{ P }\) = perimeter

\(\large{ r }\) = incircle

\(\large{ R }\) = outcircle

\(\large{ S }\) = elastic section modulus

\(\large{ Z }\) = plastic section modulus

 

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