# Square Angle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Two rectangles that intersect at a 90° angle at one end each.
• A square angle is a structural shape used in construction.

## formulas that use area of a Square Angle

 $$\large{ A = t \; \left( 2\;w - t \right) }$$

### Where:

$$\large{ A }$$ = area

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

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

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

### Where:

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

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

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

 $$\large{ P = 4\;w }$$

### Where:

$$\large{ P }$$ = perimeter

$$\large{ w }$$ = width

## formulas that use Polar Moment of Inertia of a Square 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 Principal Axis of a Square Angle

 $$\large{ d = \frac{ w^2 \;+\; w\;t \;-\; t^2 }{ 2 \; \left( 2\;w \;-\; t \right) \; cos\; 45^\circ } }$$

### Where:

$$\large{ d }$$ = distance from principle axis

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

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

 $$\large{ k_{x} = \sqrt{ \frac { I_{x} }{ A } } }$$ $$\large{ k_{y} = \sqrt{ \frac { I_{y} }{ A } } }$$ $$\large{ k_{z} = \sqrt{ k_{x}{^2} + k_{y}{^2} } }$$ $$\large{ k_{x1} = \sqrt{ \frac { I_{x1} }{ A } } }$$ $$\large{ k_{y1} = \sqrt{ \frac { I_{y1} }{ A } } }$$ $$\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }$$

### Where:

$$\large{ k }$$ = radius of gyration

$$\large{ A }$$ = area

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

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

 $$\large{ I_{x} = \frac{ t \; \left( w \;-\; C_y \right)^3 \;+\; w \; \left[ w \;-\; \left( w \;-\; C_y \right) \right]^3 \;-\; \left( w \;-\; t \right) \; \left[ w \;-\; \left( w \;-\; C_y \right) \;-\; t \right]^3 }{3} }$$ $$\large{ I_{x} = \frac{ t \; \left( w \;-\; C_y \right)^3 \;+\; w \; \left[ w \;-\; \left( w \;-\; C_y \right) \right]^3 \;-\; \left( w \;-\; t \right) \; \left[ w \;-\; \left( w \;-\; C_y \right) \;-\; t \right]^3 }{3} }$$ $$\large{ I_{x1} = I_{x} + A\; C_{y} }$$ $$\large{ I_{y1} = I_{y} + A\; C_{x} }$$

### Where:

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

$$\large{ A }$$ = area

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

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

## formulas that use Tortional Constant of a Square Angle

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

### Where:

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

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width