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Thin Wall Rectangle

on . Posted in Plane Geometry

  • hollow thin wall rectangle 3A two-dimensional figure that is a quadrilateral with two pair of parallel edges.
  • A thin wall 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

Thin Wall Rectangle Index

 

Area of a Thin Wall Rectangle formula
\( A = 2\;t \; \left(  b + a \right)    \) 
Symbol English Metric
\( A \) = area \(in^2 \) \(mm^2 \)
\( a, b \) = edge \(in \) \(mm \)
\( t \) = thickness \(in \) \(mm \)

 

Distance from Centroid of a Thin Wall Rectangle formulas

\( C_x =  b \;/\; 2   \) 

\( C_y =  a \;/\; 2  \)
Symbol English Metric
\( C \) = distance from centroid \(in \) \(mm \)
\( a, b \) = edge \(in \) \(mm \)

 

Elastic Section Modulus of a Thin Wall Rectangle formulas

\(  S_x =   2\;a\;b\;t \;/\; 3  \) 

\(  S_y =   2\;a\;b\;t \;/\; 3 \) 
Symbol English Metric
\( S \) = elastic section modulus \(in^3 \) \(mm^3 \)
\( a, b \) = edge \(in \) \(mm \)
\( t \) = thickness \(in \) \(mm \)

  

Perimeter of a Thin Wall Rectangle formulas

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

\(  P_i = 2\; \left( a + b  - 4\;t  \right)  \)     (inside) 
Symbol English Metric
\( P \) = perimeter \(in \) \(mm \)
\( a, b \) = edge \(in \) \(mm \)
\( t \) = thickness \(in \) \(mm \)

 

Plastic Section Modulus of a Thin Wall Rectangle formulas

\(  Z_x =  2 \; [ \; b\;t  \; [\; (a\;/\;2) - (t\;/\;2 ) \;]  + t  \; [\; (a\;/\;2) - t \;]^2 \; ]  \) 

\(  Z_y =  2\;t  \; [ \; (a\;/\;2) - t \;]  \;  [ \;(b\;/\;2) - t\; ]  + 2\;b\;t \; [ \;(b\;/\;2) - ( t\;/\;2) \;]  \) 
Symbol English Metric
\( Z \) = elastic section modulus \(in^3 \) \(mm^3 \)
\( a, b \) = edge \(in \) \(mm \)
\( t \) = thickness \(in \) \(mm \)

 

Polar Moment of Inertia of a Thin Wall Rectangle formulas

\( J_{z} =  ( a\;b\;t\;/\;3 )  \; ( a + b )  \) 

\( J_{z1} =  [  \;  \frac{1}{2} \; (  b^3 + a^3 )  + \frac{5}{6} \; b\;a \; ( b + a )  \;] \; t    \) 
Symbol English Metric
\( J \) = tortional constant \(in^4 \) \(mm^4 \)
\( a, b \) = edge \(in \) \(mm \)
\( t \) = thickness \(in \) \(mm \)

 

Radius of Gyration of a Thin Wall Rectangle formulas

\( k_{x} =  [\; \sqrt{  b\;/\;6 \; (  b + a )  }\; ] \; a   \) 

\( k_{y} =   [\; \sqrt{  a\;/\;6 \; (  b + a ) } \;] \; b   \) 

\( k_{z} =  \sqrt{ a\;b\;/\;6 }  \) 

\( k_{x1} = [\; \sqrt{  5\;b + 3\;a \;/\;12 \; (  b + a )  }\; ] \;  \;a   \)

\( k_{y1} = [\; \sqrt{  3\;b + 5\;a \;/\; 12 \; (  b + a )  }\; ] \; \;b   \)

\( k_{z1} =   \sqrt{ 3 \; ( b^3 + a^3 ) + 5\;b\;a \; ( b + a )  \;/\;  12 \; (  b + a )   }  \)
Symbol English Metric
\( k \) = radius of gyration \(in \) \(mm \)
\( a, b \) = edge \(in \) \(mm \)

 

Second Moment of Area of a Thin Wall Rectangle formulas

\( I_{x} =  \frac{1}{3}  \;  b\;a^2\; t  \) 

\( I_{y} =  \frac{1}{3}  \;  b^2\; a\;t  \)

\( I_{x1} =  ( \; \frac{5}{6} \; b  +  \frac{1}{2} \; a \; )  \;  a^2\; t   \) 

\( I_{y1} =  ( \; \frac{1}{2} \; b  +  \frac{5}{6} \; a \; )  \;  b^2\; t    \)
Symbol English Metric
\( I \) = moment of inertia \(in^4 \) \(mm^4 \)
\( a, b \) = edge \(in \) \(mm \)
\( t \) = thickness \(in \) \(mm \)

 

Side of a Thin Wall Rectangle formulas

\( a = (P\;/\;2) - b  \) 

\( b = (P\;/\;2) - a  \) 
Symbol English Metric
\( a, b \) = edge \(in \) \(mm \)
\(\large{ P }\) = perimeter \(in \) \(mm \)

 

Torsional Constant of a Thin Wall Rectangle formula
\( J =  2\;t^2 \; ( b - 2 )^2 \; (  a - t )^2 \;/\; a\;t + b\;t - 2\;t^2   \) 
Symbol English Metric
\( J \) = tortional constant \(in^4 \) \(mm^4 \)
\( a, b \) = edge \(in \) \(mm \)
\( t \) = thickness \(in \) \(mm \)

 

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Tags: Inertia Structural Steel Modulus

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