Hollow Rectangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • hollow rectangle 2A two-dimensional figure that is a quadrilateral with two pair of parallel edges.
  • A hollow 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 Hollow Rectangle formula

\( \large{ A = b\;a - b_1\;a_1   }\)

Where:

\(\large{ A }\) = area

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

Distance from Centroid of a Hollow Rectangle formula

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

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

Where:

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

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

Elastic Section Modulus of a Hollow Rectangle formula

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

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

Where:

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

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

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

Perimeter of a Hollow Rectangle formula

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

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

Where:

\(\large{ P }\) = perimeter

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

Polar Moment of Inertia of a Hollow Rectangle formula

\(\large{ J_{z} =  I_x + I_y   }\)

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

Where:

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

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

Radius of Gyration of a Hollow Rectangle formula

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

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

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

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

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

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

Where:

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

\(\large{ A }\) = area

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

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

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

Second Moment of Area of a Hollow Rectangle formula

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

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

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

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

Where:

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

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

Side of a Hollow Rectangle formula

\( \large{ a = \frac{P}{2} - b   }\)

\( \large{ b = \frac{P}{2} - a  }\)

Where:

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

\(\large{ P }\) = perimeter

 

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