Cross
Cross is a type of structural beam with a cross shaped cross-sectional profile. The cross has a central vertical web and horizontal flanges at the center of the vertical web. The web and flange can have varying dimensions and thicknesses, depending on the specific load bearing requirements and design considerations of the structure.
- See Article Link - Geometric Properties of Structural Shapes
- Tags: Structural Steel
Cross Index
- Area of a Cross
- Distance from Centroid of a Cross
- Elastic Section Modulus of a Cross
- Perimeter of a Cross
- Polar Moment of Inertia of a Cross
- Radius of Gyration of a Cross
- Second Moment of Area of a Cross
area of a Cross formula |
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| \(\large{ A = l\;t + s \; \left( w - t \right) }\) | ||
| Symbol | English | Metric |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ l }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ s }\) = thickness | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ w }\) = width | \(\large{ in }\) | \(\large{ mm }\) |
Elastic Section Modulus of a Cross formulas |
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\(\large{ S_{x} = \frac{ I_{x} }{ C_{y} } }\) \(\large{ S_{y} = \frac{ I_{y} }{ C_{x} } }\) |
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| Symbol | English | Metric |
| \(\large{ S }\) = elastic section modulus | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ C }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ I }\) = moment of inertia | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
Perimeter of a Cross formula |
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| \(\large{ A = 2 \; \left( w + l \right) }\) | ||
| Symbol | English | Metric |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ l }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ w }\) = width | \(\large{ in }\) | \(\large{ mm }\) |
Polar Moment of Inertia of a Cross formulas |
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\(\large{ J_{z} = I_{x} + I_{y} }\) \(\large{ J_{z1} = I_{x1} + I_{y1} }\) |
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| Symbol | English | Metric |
| \(\large{ J }\) = torsional constant | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
| \(\large{ I }\) = moment of inertia | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
Radius of Gyration of a Cross formulas |
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\(\large{ k_{x} = \sqrt{ \frac{ t\;l^3 \;+\; s^3 \; \left( w \;-\; t \right) }{ 12 \; \left[ l\;t \;+\; s \; \left( w \;-\; t \right) \right] } } }\) \(\large{ k_{y} = \sqrt{ \frac{ s\;w^3 \;+\; t^3 \; \left( l \;-\; s \right) }{ 12 \; \left[ l\;t \;+\; s \; \left( w \;-\; t \right) \right] } } }\) \(\large{ k_{z} = \sqrt{ k_{x}{^2} + k_{y}{^2} } }\) \(\large{ k_{x1} = \sqrt{ \frac { I_{x1} }{ A } } }\) \(\large{ k_{y1} = \sqrt{ \frac { I_{y1} }{ A } } }\) \(\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }\) |
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| Symbol | English | Metric |
| \(\large{ k }\) = radius of gyration | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ l }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ s }\) = thickness | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ w }\) = width | \(\large{ in }\) | \(\large{ mm }\) |
Second Moment of Area of a Cross formulas |
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\(\large{ I_{x} = \frac{ t\;l^3 \;+\; s^3 \; \left( w \;-\; t \right) }{12} }\) \(\large{ I_{y} = \frac{ s\;w^3 \;+\; t^3 \; \left( l \;-\; s \right) }{12} }\) \(\large{ I_{x1} = I_{x} + A\;C_{y}{^2} }\) \(\large{ I_{y1} = I_{y} + A\;C_{x}{^2} }\) |
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| Symbol | English | Metric |
| \(\large{ I }\) = moment of inertia | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
| \(\large{ A }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ C }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ l }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ s }\) = thickness | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ t }\) = thickness | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ w }\) = width | \(\large{ in }\) | \(\large{ mm }\) |
Tags: Structural Steel