Square

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Square - Geometric Propertiessquare 2Asquare 1A

  • Square ( \(SQ\) ) is a quadrilateral with four parallel edges.
  • 4 interior angles are 90°
  • 2 diagonals
  • 4 edges
  • 4 vertexs

Area of a Square formula

\( \large{ A_{area} = a^2 }\)

Circumcircle of a Square formula

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

\(\large{ R =  \frac  { a } {  \sqrt  { 2  }    }    }\)

\(\large{ R =  \frac  { d } { 2 }   }\)

Diagonal of a Square formula

\(\large{ D' = \sqrt {2} \;  a  }\)

Inscribed Circle of a Square formula

The radius of a inscribed circle (inner) of a square if given side \(( r )\).

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

Perimeter of a Square formula

\(\large{ P = 4a  }\)

Side of a Square formula

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

Distance from Centroid of a Square formula

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

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

Elastic Section Modulus of a Square formula

\(\large{ S =  \frac { a^3 }  { 6  }  }\)

Plastic Section Modulus of a Square formula

\(\large{ Z =  \frac { a^3 }  { 4  }  }\)

Polar Moment of Inertia of a Square formula

\(\large{ J_{z} = \frac {a^4}{6}  }\)

\(\large{ J_{z1} =  \frac {2a^4}{3}  }\)

Radius of Gyration of a Square formula

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

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

\(\large{ k_{z} =   \frac { a }  {  \sqrt 6  }  }\)

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

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

\(\large{ k_{z1} =   \sqrt {  \frac {2}{3} a    }   }\)

Second Moment of Area of a Square formula

\(\large{ I_{x} =  \frac {a^4}{12}  }\)

\(\large{ I_{y} = \frac {a^4}{12}  }\)

\(\large{ I_{x1} =   \frac {a^4}{3}  }\)

\(\large{ I_{y1} =  \frac {a^4}{3}  }\)

Torsional Constant of a Square formula

\(\large{ J  =  2.25    \left(   \frac {  a  } {  2  } \right)  ^4  }\)

 

Where:

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

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

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

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

\(\large{ r }\) = incircle

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

\(\large{ R }\) = outcircle

\(\large{ P }\) = perimeter

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

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

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

\(\large{ a }\) = side

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

 

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