Rectangular Angle
A rectangular angle is a structural shape used in construction.
Structural Shapes
area of a Rectangular Angle formula
| \(\large{ A = t \; \left( w + d \right) }\) |
Where:
\(\large{ A }\) = area
\(\large{ d }\) = height
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Distance from Centroid of a Rectangular Angle formulas
| \(\large{ C_x = \frac{ t \; \left( 2\;c \;+\; l \right) \;+\; c^2 }{ 2 \; \left( c \;+\; l \right) } }\) | |
| \(\large{ C_y = \frac{ t \; \left( 2\;d \;+\; w \right) \;+\; d^2 }{ 2 \; \left( d \;+\; w \right) } }\) |
Where:
\(\large{ C }\) = distance from centroid
\(\large{ d }\) = height
\(\large{ l }\) = height
\(\large{ t }\) = thickness
\(\large{ c }\) = width
\(\large{ w }\) = width
Elastic Section Modulus of a Rectangular 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 Rectangular Angle formula
| \(\large{ P = 2 \; \left( w + l \right) }\) |
Where:
\(\large{ P }\) = perimeter
\(\large{ l }\) = height
\(\large{ w }\) = width
Polar Moment of Inertia of a Rectangular 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
Radius of Gyration of a Rectangular Angle formulas
| \(\large{ k_x = \frac{ t\;y^3 \;+\; w \; \left( l \;-\; y \right)^3 \;-\; \left( w \;-\; t \right) \; \left( l \;-\; y \;-\; t \right)^3 }{ 3\;t \;\; \left( w \;+\; l \;-\; t \right) } }\) | |
| \(\large{ k_y = \frac{ t\;z^3 \;+\; l \; \left( w \;-\; z \right)^3 \;-\; \left( l \;-\; t \right) \; \left( w \;-\; z \;-\; t \right)^3 }{ 3\;t \;\; \left( w \;+\; l \;-\; t \right) } }\) | |
| \(\large{ k_z = \sqrt{ k_{x}{^2} + k_{y}{^2} } }\) | |
| \(\large{ k_{x1} = \sqrt{ \frac { I_{x1} }{ A } } }\) | |
| \(\large{ k_{y1} = \sqrt{ \frac { I_{y1} }{ A } } }\) | |
| \(\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }\) |
Where:
\(\large{ k }\) = radius of gyration
\(\large{ I }\) = moment of inertia
\(\large{ l }\) = height
\(\large{ y }\) = height
\(\large{ t }\) = thickness
\(\large{ w }\) = width
\(\large{ z }\) = width
Second Moment of Area of a Rectangular Angle formulas
| \(\large{ I_x = \frac{ t\;y^3 \;+\; w \; \left( l \;-\; y \right)^3 \;-\; \left( w \;-\; t \right) \; \left( l \;-\; y \;-\; t \right)^3 }{3} }\) | |
| \(\large{ I_y = \frac{ t\;z^3 \;+\; l \; \left( w \;-\; z \right)^3 \;-\; \left( l \;-\; t \right) \; \left( w \;-\; z \;-\; t \right)^3 }{3} }\) | |
| \(\large{ I_{x1} = I_x + A\; C_{y}{^2} }\) | |
| \(\large{ I_{y1} = I_y + A \;C_{x}{^2} }\) |
Where:
\(\large{ I }\) = moment of inertia
\(\large{ A }\) = area
\(\large{ C }\) = distance from centroid
\(\large{ l }\) = height
\(\large{ y }\) = height
\(\large{ t }\) = thickness
\(\large{ w }\) = width
\(\large{ z }\) = width
Tortional Constant of a Rectangular Angle formula
| \(\large{ J = \frac{ \left[ d \;-\; \left( \frac{t}{2} \right) \right] \;+\; \left[ w \;-\; \left( \frac{t}{2} \right) \right] \; t^3 }{ 3 } }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ d }\) = height
\(\large{ t }\) = thickness
\(\large{ w }\) = width
Tags: Equations for Inertia Equations for Structural Steel Equations for Modulus