Hollow Rectangle

Written by Jerry Ratzlaff on . Posted in Geometry

Hollow Rectangle - Geometric Propertieshollow rectangle 2

  • Rectangle is a quadrilateral with two pair of parallel edges.
  • Interior angles are 90°
  • Exterior angles are 90°
  • Angle \(\;A = B = C = D\)
  • 2 diagonals
  • 4 edges
  • 4 vertexs

Area of a Hollow Rectangle formula

\( \large{ A = ba - b_1a_1   }\)

Perimeter of a Hollow Rectangle formula

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

\( \large{ P= 2 \left( a_1 + b_2     \right)  }\)   ( Inside )

Side of a Hollow Rectangle formula

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

\( \large{ b = \frac {P} {2} - a  }\)

Distance from Centroid of a Hollow Rectangle formula

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

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

Elastic Section Modulus of a Hollow Rectangle formula

\( \large{ S_x =  \frac { I_x }  { C_y  }  }\)

\( \large{ S_y =  \frac { I_y }  { C_x  }  }\)

Polar Moment of Inertia of a Hollow Rectangle formula

\(\large{ J_{z} =  I_x + I_y   }\)

\(\large{ J_{z1} =  I_{x1} + I_{y1}   }\)

Radius of Gyration of a Hollow Rectangle formula

\(\large{ k_{x} =   \sqrt{      \frac {  b a^3  - b_1 a_{1}{^3}  }  {  12  \left(  ba - b_1 a_1  \right)   }    }    }\)

\(\large{ k_{y} =    \sqrt{      \frac {  b^3 a  - b_{1}{^3}  a_1  }  {  12  \left(  ba - b_1 a_1  \right)   }    }    }\)

\(\large{ k_{z} =   \sqrt {   k_{x}{^2}  +  k_{y}{^2}   } }\)

\(\large{ k_{x1} =   \sqrt{   \frac { I_{x1} }  {  A  }  }    }\)

\(\large{ k_{y1} =  \sqrt{   \frac { I_{y1} }  {  A  }  }    }\)

\(\large{ k_{z1} =   \sqrt {   k_{x1}{^2}  +  k_{y1}{^2}   }   }\)

Second Moment of Area of a Hollow Rectangle formula

\(\large{ I_{x} =  \frac { b a^3 - b_1 a_{1}{^3} }  {12}     }\)

\(\large{ I_{y} = \frac { b^3 a - b_{1}{^3} a_1 }  {12}      }\)

\(\large{ I_{x1} =   \frac { b a^3 }  {3}  -  \frac { b_1  a_1   \left(  a_{1}{^2}  + 3a^2   \right)     }    {12}     }\)

\(\large{ I_{y1} =  \frac { b^3 a }  {3}  -   \frac { b_1  a_1   \left(  b_{1}{^2}  + 3b^2   \right)     }    {12}       }\)

 

Where:

\(\large{ A }\) = area

\(\large{ a, b, a_1, b_1 }\) = side

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

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

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

\(\large{ P }\) = perimeter

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

 

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