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Hollow Rectangle

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

Hollow Rectangle Index

 

Area of a Hollow Rectangle formula
\( A = b\;a - b_1\;a_1   \) 
Symbol English Metric
\( A \) = area \( in^2 \) \( mm^2 \)
\( a, b, a_1, b_1 \) = edge \( in \) \( mm \)

 

Distance from Centroid of a Hollow Rectangle formulas

\( C_x =  \frac{ b }{ 2 }  \)

\( C_y =  \frac{ a }{ 2}   \) 
Symbol English Metric
\( C \) = distance from centroid \( in \) \( mm \)
\( a, b, a_1, b_1 \) = edge \( in \) \( mm \)

  

Elastic Section Modulus of a Hollow Rectangle formulas

\( S_x =  \frac{ I_x }{ C_y  }  \) 

\( S_y =  \frac{ I_y }{ C_x  }  \) 
Symbol English Metric
\( S \) = elastic section modulus \( in^3 \) \( mm^3 \)
\( C \) = distance from centroid \( in \) \( mm \)
\( I \) = moment of inertia \( in^4 \) \( mm^4 \)

 

Perimeter of a Hollow Rectangle formulas

\( P_o = 2\; \left( a + b   \right)  \)     (outside) 

\( P_i = 2\; \left( a_1 + b_2  \right)  \)     (inside) 
Symbol English Metric
\( P \) = perimeter \( in \) \( mm \)
\( a, b, a_1, b_1 \) = edge \( in \) \( mm \)

     

Polar Moment of Inertia of a Hollow Rectangle formulas

\( J_{z} =  I_x + I_y   \) 

\( J_{z1} =  I_{x1} + I_{y1}   \) 
Symbol English Metric
\( J \) = torsional constant \( in^4 \) \( mm^4 \)
\( I \) = moment of inertia \( in^4 \) \( mm^4 \)

   

Radius of Gyration of a Hollow Rectangle formulas

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

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

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

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

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

\( k_{z1} =   \sqrt{   k_{x1}{^2}  +  k_{y1}{^2}   }   \)
Symbol English Metric
\( k \) = radius of gyration \( in \) \( mm \)
\( A \) = area \( in^2 \) \( mm^2 \)
\( a, b, a_1, b_1 \) = edge \( in \) \( mm \)
\( I \) = moment of inertia \( in^4 \) \( mm^4 \)

    

Second Moment of Area of a Hollow Rectangle formulas

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

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

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

\( I_{y1} =  \frac{ b^3 \;a }{3}  -   \frac { b_1 \; a_1 \;  \left(  b_{1}{^2}  \;+\; 3\;b^2   \right)     }{12}   \)
Symbol English Metric
\( I \) = moment of inertia \( in^4 \) \( mm^4 \)
\( a, b, a_1, b_1 \) = edge \( in \) \( mm \)

   

Side of a Hollow Rectangle formulas

\( a = \frac{P}{2} - b   \) 

\( b = \frac{P}{2} - a  \) 
Symbol English Metric
\( a, b, a_1, b_1 \) = edge \( in \) \( mm \)
\( P \) = perimeter \( in \) \( mm \)

 

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Tags: Structural Steel

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