# Rectangular Angle

Written by Jerry Ratzlaff on . Posted in Structural

• A rectangular angle is a structural shape used in construction.

## formulas that use area of a Rectangular Angle

 $$\large{ A = t \; \left( w + d \right) }$$

### Where:

$$\large{ A }$$ = area

$$\large{ d }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

## formulas that use Distance from Centroid of a Rectangular Angle

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

### Where:

$$\large{ C }$$ = distance from centroid

$$\large{ d }$$ = height

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ c }$$ = width

$$\large{ w }$$ = width

## formulas that use Elastic Section Modulus of a Rectangular Angle

 $$\large{ S_x = \frac{ I_x }{ C_y } }$$ $$\large{ S_y = \frac{ I_y }{ C_x } }$$

### Where:

$$\large{ S }$$ = elastic section modulus

$$\large{ C }$$ = distance from centroid

$$\large{ I }$$ = moment of inertia

## formulas that use Perimeter of a Rectangular Angle

 $$\large{ P = 2 \; \left( w + l \right) }$$

### Where:

$$\large{ P }$$ = perimeter

$$\large{ l }$$ = height

$$\large{ w }$$ = width

## formulas that use Polar Moment of Inertia of a Rectangular Angle

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

### Where:

$$\large{ J }$$ = torsional constant

$$\large{ I }$$ = moment of inertia

## formulas that use Radius of Gyration of a Rectangular Angle

 $$\large{ k_x = \frac{ t\;y^3 \;+\; w \; \left( l \;-\; y \right)^3 \;-\; \left( w \;-\; t \right) \; \left( l \;-\; y \;-\; t \right)^3 }{ 3\;t \;\; \left( w \;+\; l \;-\; t \right) } }$$ $$\large{ k_y = \frac{ t\;z^3 \;+\; l \; \left( w \;-\; z \right)^3 \;-\; \left( l \;-\; t \right) \; \left( w \;-\; z \;-\; t \right)^3 }{ 3\;t \;\; \left( w \;+\; l \;-\; t \right) } }$$ $$\large{ k_z = \sqrt{ k_{x}{^2} + k_{y}{^2} } }$$ $$\large{ k_{x1} = \sqrt{ \frac { I_{x1} }{ A } } }$$ $$\large{ k_{y1} = \sqrt{ \frac { I_{y1} }{ A } } }$$ $$\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }$$

### 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

## formulas that use Second Moment of Area of a Rectangular Angle

 $$\large{ I_x = \frac{ t\;y^3 \;+\; w \; \left( l \;-\; y \right)^3 \;-\; \left( w \;-\; t \right) \; \left( l \;-\; y \;-\; t \right)^3 }{3} }$$ $$\large{ I_y = \frac{ t\;z^3 \;+\; l \; \left( w \;-\; z \right)^3 \;-\; \left( l \;-\; t \right) \; \left( w \;-\; z \;-\; t \right)^3 }{3} }$$ $$\large{ I_{x1} = I_x + A\; C_{y}{^2} }$$ $$\large{ I_{y1} = I_y + A \;C_{x}{^2} }$$

### 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

## formulas that use Tortional Constant of a Rectangular Angle

 $$\large{ J = \frac{ \left[ d \;-\; \left( \frac{t}{2} \right) \right] \;+\; \left[ w \;-\; \left( \frac{t}{2} \right) \right] \; t^3 }{ 3 } }$$

### Where:

$$\large{ J }$$ = torsional constant

$$\large{ d }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width