Cross
Two rectangles that intersect perpendicular at a center point.- A cross is a structural shape used in construction.
Structural Shapes
area of a Cross formula
| \(\large{ A = l\;t + s \; \left( w - t \right) }\) |
Where:
\(\large{ A }\) = area
\(\large{ l }\) = height
\(\large{ s }\) = thickness
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Distance from Centroid of a Cross formulas
| \(\large{ C_x = \frac{ w }{ 2 } }\) | |
| \(\large{ C_y = \frac{ l }{ 2 } }\) |
Where:
\(\large{ C }\) = distance from centroid
\(\large{ l }\) = height
\(\large{ w }\) = width
Elastic Section Modulus of a Cross formulas
| \(\large{ S_{x} = \frac{ I_{x} }{ C_{y} } }\) | |
| \(\large{ S_{y} = \frac{ I_{y} }{ C_{x} } }\) |
Where:
\(\large{ S }\) = elastic section modulus
\(\large{ C }\) = distance from centroid
\(\large{ I }\) = moment of inertia
Perimeter of a Cross formula
| \(\large{ A = 2 \; \left( w + l \right) }\) |
Where:
\(\large{ A }\) = area
\(\large{ l }\) = height
\(\large{ w }\) = width
Polar Moment of Inertia of a Cross formulas
| \(\large{ J_{z} = I_{x} + I_{y} }\) | |
| \(\large{ J_{z1} = I_{x1} + I_{y1} }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ I }\) = moment of inertia
Radius of Gyration of a Cross formulas
| \(\large{ k_{x} = \sqrt{ \frac{ t\;l^3 \;+\; s^3 \; \left( w \;-\; t \right) }{ 12 \; \left[ l\;t \;+\; s \; \left( w \;-\; t \right) \right] } } }\) | |
| \(\large{ k_{y} = \sqrt{ \frac{ s\;w^3 \;+\; t^3 \; \left( l \;-\; s \right) }{ 12 \; \left[ l\;t \;+\; s \; \left( w \;-\; t \right) \right] } } }\) | |
| \(\large{ k_{z} = \sqrt{ k_{x}{^2} + k_{y}{^2} } }\) | |
| \(\large{ k_{x1} = \sqrt{ \frac { I_{x1} }{ A } } }\) | |
| \(\large{ k_{y1} = \sqrt{ \frac { I_{y1} }{ A } } }\) | |
| \(\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }\) |
Where:
\(\large{ k }\) = radius of gyration
\(\large{ A }\) = area
\(\large{ l }\) = height
\(\large{ s }\) = thickness
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Second Moment of Area of a Cross formulas
| \(\large{ I_{x} = \frac{ t\;l^3 \;+\; s^3 \; \left( w \;-\; t \right) }{12} }\) | |
| \(\large{ I_{y} = \frac{ s\;w^3 \;+\; t^3 \; \left( l \;-\; s \right) }{12} }\) | |
| \(\large{ I_{x1} = I_{x} + A\;C_{y}{^2} }\) | |
| \(\large{ I_{y1} = I_{y} + A\;C_{x}{^2} }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ A }\) = area
\(\large{ C }\) = distance from centroid
\(\large{ l }\) = height
\(\large{ s }\) = thickness
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Tags: Equations for Inertia Equations for Structural Steel Equations for Modulus