A 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
- See Article - Geometric Properties of Structural Shapes
Area of a Thin Wall Rectangle formula |
||
| \( A \;=\; 2\cdot t \cdot \left( b + a \right) \) | ||
| 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 |
||
|
\( C_x \;=\; \dfrac{ b }{ 2 }\) \( C_y \;=\; \dfrac{ a }{ 2 }\) |
||
| Symbol | English | Metric |
| \( C \) = distance from centroid | \(in \) | \(mm \) |
| \( a, b \) = edge | \(in \) | \(mm \) |
Elastic Section Modulus of a Thin Wall Rectangle formulas |
||
|
\( S_x \;=\; \dfrac{ 2\cdot a\cdot b\cdot t }{ 3 }\) \( S_y \;=\; \dfrac{ 2\cdot a\cdot b\cdot t }{ 3 }\) |
||
| 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 |
||
|
\( P_o \;=\; 2\cdot \left( a + b \right) \) (Outside) \( P_i \;=\; 2\cdot \left( a + b - 4\cdot t \right) \) (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 |
||
|
\( Z_x \;=\; 2 \cdot [ \; b\cdot t \cdot \left( \dfrac{ a}{2} - \dfrac{ t}{2 } \right) + t \cdot \left( \dfrac{ a}{2} - t \right)^2 ] \) \( Z_y \;=\; 2\cdot t \cdot \left( \dfrac{ a}{2} - t \right) \cdot \left( \dfrac{ b}{2} - t \right) + 2\cdot b\cdot t \cdot \left( \dfrac{ b}{2} - \dfrac{ t}{2} \right) \) |
||
| 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 |
||
|
\( J_{z} \;=\; \dfrac{ a\cdot b\cdot t}{3 } \cdot ( a + b ) \) \( J_{z1} \;=\; \left( \dfrac{1}{2} \cdot ( b^3 + a^3 ) + \dfrac{5}{6} \cdot b\cdot a \cdot ( b + a ) \right) \cdot t \) |
||
| 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 |
||
|
\( k_{x} \;=\; \left( \sqrt{ \dfrac{ b }{ 6 \cdot ( b + a ) } } \right) \cdot a \) \( k_{y} \;=\; \left( \sqrt{ \dfrac{ a }{ 6 \cdot ( b + a ) } } \right) \cdot b \) \( k_{z} \;=\; \sqrt{ \dfrac{ a\cdot b }{ 6 } } \) \( k_{x1} \;=\; \left( \sqrt{ \dfrac{ 5\cdot b + 3\cdot a }{ 12 \cdot ( b + a ) } } \right) \cdot a \) \( k_{y1} \;=\; \left( \sqrt{ \dfrac{ 3\cdot b + 5\cdot a }{ 12 \cdot ( b + a ) } } \right) \cdot b \) \( k_{z1} \;=\; \sqrt{ \dfrac{ 3 \cdot ( b^3 + a^3 ) + 5\cdot b\cdot a \cdot ( b + a ) }{ 12 \cdot ( b + a ) } } \) |
||
| Symbol | English | Metric |
| \( k \) = radius of gyration | \(in \) | \(mm \) |
| \( a, b \) = edge | \(in \) | \(mm \) |
Second Moment of Area of a Thin Wall Rectangle formulas |
||
|
\( I_{x} \;=\; \dfrac{1}{3} \cdot b\cdot a^2\cdot t \) \( I_{y} \;=\ \dfrac{1}{3} \cdot b^2\cdot a\cdot t \) \( I_{x1} \;=\; \left( \; \dfrac{5}{6} \cdot b + \dfrac{1}{2} \cdot a \right) \cdot a^2\cdot t \) \( I_{y1} \;=\; \left( \dfrac{1}{2} \cdot b + \dfrac{5}{6} \cdot a \right) \cdot b^2\cdot t \) |
||
| 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 |
||
|
\( a \;=\; \dfrac{ P}{2} - b \) \( b \;=\; \dfrac{ P}{2} - a \) |
||
| Symbol | English | Metric |
| \( a, b \) = edge | \(in \) | \(mm \) |
| \(\large{ P }\) = perimeter | \(in \) | \(mm \) |
Torsional Constant of a Thin Wall Rectangle formula |
||
| \( J \;=\; \dfrac{ 2\cdot t^2 \cdot ( b - 2 )^2 \cdot ( a - t )^2 }{ a\cdot t + b\cdot t - 2\cdot t^2 }\) | ||
| Symbol | English | Metric |
| \( J \) = tortional constant | \(in^4 \) | \(mm^4 \) |
| \( a, b \) = edge | \(in \) | \(mm \) |
| \( t \) = thickness | \(in \) | \(mm \) |
