Square Angle
Two rectangles that intersect at a 90° angle at one end each.- A square angle is a structural shape used in construction.
Structural Shapes
area of a Square Angle formula
| \(\large{ A = t \; \left( 2\;w - t \right) }\) |
Where:
\(\large{ A }\) = area
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Distance from Centroid of a Square Angle formulas
| \(\large{ C_x = \frac{ w^2 \;+\; w\;t \;-\; t^2 }{ 2 \; \left( 2\;w \;-\; t \right) } }\) | |
| \(\large{ C_y = \frac{ w^2 \;+\; w\;t \;-\; t^2 }{ 2 \; \left( 2\;w \;-\; t \right) } }\) |
Where:
\(\large{ C }\) = distance from centroid
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Elastic Section Modulus of a Square Angle 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 Square Angle formula
| \(\large{ P = 4\;w }\) |
Where:
\(\large{ P }\) = perimeter
\(\large{ w }\) = width
Polar Moment of Inertia of a Square Angle 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
Principal Axis of a Square Angle formula
| \(\large{ d = \frac{ w^2 \;+\; w\;t \;-\; t^2 }{ 2 \; \left( 2\;w \;-\; t \right) \; cos\; 45^\circ } }\) |
Where:
\(\large{ d }\) = distance from principle axis
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Radius of Gyration of a Square Angle formulas
| \(\large{ k_{x} = \sqrt{ \frac { I_{x} }{ A } } }\) | |
| \(\large{ k_{y} = \sqrt{ \frac { I_{y} }{ A } } }\) | |
| \(\large{ k_{z} = \sqrt{ k_{x}{^2} + k_{y}{^2} } }\) | |
| \(\large{ k_{x1} = \sqrt{ \frac { I_{x1} }{ A } } }\) | |
| \(\large{ k_{y1} = \sqrt{ \frac { I_{y1} }{ A } } }\) | |
| \(\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }\) |
Where:
\(\large{ k }\) = radius of gyration
\(\large{ A }\) = area
\(\large{ I }\) = moment of inertia
Second Moment of Area of a Square Angle formulas
| \(\large{ I_{x} = \frac{ t \; \left( w \;-\; C_y \right)^3 \;+\; w \; \left[ w \;-\; \left( w \;-\; C_y \right) \right]^3 \;-\; \left( w \;-\; t \right) \; \left[ w \;-\; \left( w \;-\; C_y \right) \;-\; t \right]^3 }{3} }\) | |
| \(\large{ I_{x} = \frac{ t \; \left( w \;-\; C_y \right)^3 \;+\; w \; \left[ w \;-\; \left( w \;-\; C_y \right) \right]^3 \;-\; \left( w \;-\; t \right) \; \left[ w \;-\; \left( w \;-\; C_y \right) \;-\; t \right]^3 }{3} }\) | |
| \(\large{ I_{x1} = I_{x} + A\; C_{y} }\) | |
| \(\large{ I_{y1} = I_{y} + A\; C_{x} }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ A }\) = area
\(\large{ C }\) = distance from centroid
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Tortional Constant of a Square Angle formula
| \(\large{ J = \frac{ \left[ w \;-\; \left( \frac {t}{2} \right) \right] \;+\; \left[ w \;-\; \left( \frac {t}{2} \right) \right] \; t^3 }{3} }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Tags: Equations for Inertia Equations for Structural Steel Equations for Modulus