# Rectangular Angle

on . Posted in Structural Engineering

Rectangular angle, also called angle or angle iron, is a L-shaped structural member with rectangular legs.  An angle iron has an L-shaped cross-section formed by bending a piece  of steel at a 90-degree angle.  This type of angle iron has unequal length sides forming a 90-degree corner.  It's commonly used as a structural component in various construction and engineering applications due to its rigidity and load-bearing capacity. ## area of a Rectangular Angle formula

$$\large{ A = t \; \left( w + d \right) }$$
Symbol English Metric
$$\large{ A }$$ = area $$\large{ in^2 }$$  $$\large{ mm^2 }$$
$$\large{ d }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Distance from Centroid of a Rectangular Angle formulas

$$\large{ C_x = \frac{ t \; \left( 2\;c \;+\; l \right) \;+\; c^2 }{ 2 \; \left( c \;+\; l \right) } }$$

$$\large{ C_y = \frac{ t \; \left( 2\;d \;+\; w \right) \;+\; d^2 }{ 2 \; \left( d \;+\; w \right) } }$$

Symbol English Metric
$$\large{ C }$$ = distance from centroid $$\large{ in }$$  $$\large{ mm }$$
$$\large{ d }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ l }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ c }$$ = width $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Elastic Section Modulus of a Rectangular Angle formulas

$$\large{ S_x = \frac{ I_x }{ C_y } }$$

$$\large{ S_y = \frac{ I_y }{ C_x } }$$

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 Rectangular Angle formula

$$\large{ P = 2 \; \left( w + l \right) }$$
Symbol English Metric
$$\large{ P }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ l }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Polar Moment of Inertia of a Rectangular Angle formulas

$$\large{ J_z = I_x + I_y }$$

$$\large{ J_{z1} = I_{x1} + I_{y1} }$$

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 Rectangular Angle formulas

$$\large{ k_x = \frac{ t\;y^3 \;+\; w \; \left( l \;-\; y \right)^3 \;-\; \left( w \;-\; t \right) \; \left( l \;-\; y \;-\; t \right)^3 }{ 3\;t \;\; \left( w \;+\; l \;-\; t \right) } }$$

$$\large{ k_y = \frac{ t\;z^3 \;+\; l \; \left( w \;-\; z \right)^3 \;-\; \left( l \;-\; t \right) \; \left( w \;-\; z \;-\; t \right)^3 }{ 3\;t \;\; \left( w \;+\; l \;-\; t \right) } }$$

$$\large{ k_z = \sqrt{ k_{x}{^2} + k_{y}{^2} } }$$

$$\large{ k_{x1} = \sqrt{ \frac { I_{x1} }{ A } } }$$

$$\large{ k_{y1} = \sqrt{ \frac { I_{y1} }{ A } } }$$

$$\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }$$

Symbol English Metric
$$\large{ k }$$ = radius of gyration $$\large{ in }$$ $$\large{ mm }$$
$$\large{ l }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ y }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{ mm^4 }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$
$$\large{ z }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Second Moment of Area of a Rectangular Angle formulas

$$\large{ I_x = \frac{ t\;y^3 \;+\; w \; \left( l \;-\; y \right)^3 \;-\; \left( w \;-\; t \right) \; \left( l \;-\; y \;-\; t \right)^3 }{3} }$$

$$\large{ I_y = \frac{ t\;z^3 \;+\; l \; \left( w \;-\; z \right)^3 \;-\; \left( l \;-\; t \right) \; \left( w \;-\; z \;-\; t \right)^3 }{3} }$$

$$\large{ I_{x1} = I_x + A\; C_{y}{^2} }$$

$$\large{ I_{y1} = I_y + A \;C_{x}{^2} }$$

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 $$\large{ in }$$ $$\large{ mm }$$
$$\large{ y }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$
$$\large{ z }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Tortional Constant of a Rectangular Angle formula

$$\large{ J = \frac{ \left[ d \;-\; \left( \frac{t}{2} \right) \right] \;+\; \left[ w \;-\; \left( \frac{t}{2} \right) \right] \; t^3 }{ 3 } }$$
Symbol English Metric
$$\large{ J }$$ = torsional constant $$\large{ in^4 }$$ $$\large{ mm^4 }$$
$$\large{ d }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ 