- See Article - Geometric Properties of Structural Shapes
Area of a Rectangle formula |
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| \( A_{area} \;=\; a \cdot b \) | ||
| Symbol | English | Metric |
| \( A_{area} \) = area | \( in^2 \) | \( mm^2 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Rectangle (a two-dimensional figure) is a quadrilateral with two pair of parallel edges.- Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
- Diagonal is a line from one vertices to another that is non adjacent.
Circumcircle Radius of a Rectangle formulas |
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\( R \;=\; \dfrac{ D' }{2 } \) \( R \;=\; \dfrac{\sqrt{ a^2 + b^2 } }{ 2 }\) |
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| Symbol | English | Metric |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( D' \) = diagonal | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
- Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
- Quadrilateral (a two-dimensional figure) is a polygon with four sides.
- a ∥ c
- b ∥ d
- a = c
- b = d
Diagonal of a Rectangle formula |
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| \( D' \;=\; \sqrt {a^2 + b^2 } \) | ||
| Symbol | English | Metric |
| \( D' \) = diagonal | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
- ∠A = ∠B = ∠C = ∠D = 360°
- 4 interior angles are 90°
- 2 diagonals
- 4 edges
- 4 vertexs
Distance from Centroid of a Rectangle formulas |
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\( C_x \;=\; \dfrac{ b }{ 2 } \) \( C_y \;=\; \dfrac{ a }{ 2 } \) |
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| Symbol | English | Metric |
| \( C \) = distance from centroid | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Elastic Section Modulus of a Rectangle formulas |
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\( S_x \;=\; \dfrac{ a^2\cdot b }{ 6 }\) \( S_y \;=\; \dfrac{ a \cdot b^2 }{ 6 }\) |
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| Symbol | English | Metric |
| \( S \) = elastic section modulus | \( in^3 \) | \( mm^3 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Perimeter of a Rectangle formulas |
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\( P \;=\; 2 \cdot a + 2 \cdot b \) \( P \;=\; 2 \cdot ( a + b) \) |
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| Symbol | English | Metric |
| \( P \) = perimeter | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Plastic Section Modulus of a Rectangle formulas |
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\( Z_x \;=\; \dfrac{ a^2 \cdot b }{ 4 } \) \( Z_y \;=\; \dfrac{ a \cdot b^2 }{ 4 } \) |
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| Symbol | English | Metric |
| \( Z \) = plastic section modulus | \( in^3 \) | \( mm^3 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Polar Moment of Inertia of a Rectangle formulas |
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\( J_{z} \;=\; \dfrac{ a \cdot b }{ 12 } \cdot ( a^2 + b^2 ) \) \( J_{z1} \;=\; \dfrac{ a \cdot b }{ 3 } \cdot ( a^2 + b^2 ) \) |
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| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \( mm^4 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Radius of Gyration of a Rectangle formulas |
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\( k_{x} \;=\; \dfrac{ a }{ 2 \cdot \sqrt{3} } \) \( k_{y} \;=\; \dfrac{ b }{ 2 \cdot \sqrt{3} } \) \( k_{z} \;=\; \sqrt{ \dfrac{ a^2 + b^2 }{ 2 \cdot \sqrt{3} } } \) \( k_{x1} \;=\; \dfrac{ a }{ \sqrt{3} }\) \( k_{y1} \;=\; \dfrac{ b }{ \sqrt{3} } \) \( k_{z1} \;=\; \sqrt{ \dfrac{ a^2 + b^2 }{ \sqrt{3} } } \) |
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| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Second Moment of Area of a Rectangle formulas |
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\( I_{x} \;=\; \dfrac{ a^3\cdot b}{12 }\) \( I_{y} \;=\; \dfrac{ a\cdot b^3}{12 }\) \( I_{x1} \;=\; \dfrac{ a^3 \cdot b}{3 }\) \( I_{y1} \;=\; \dfrac{ a\cdot b^3}{3 }\) |
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| Symbol | English | Metric |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Side of a Rectangle formulas |
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\( a \;=\; \dfrac{ P}{2 } - b \) \( b \;=\; \dfrac{P}{2} - a \) |
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| Symbol | English | Metric |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( P \) = perimeter | \( in \) | \( mm \) |
Torsional Constant of a Rectangle formula |
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| \( J \;=\; a^3 \cdot b \cdot \left( \dfrac{1}{3} - \dfrac{ 0.21 \cdot a }{ b } \cdot \left( 1 - \left( \dfrac{ a^4 }{ 12 \cdot b^4 } \right) \right) \right) \) | ||
| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \( mm^4 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |