# Square Angle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

### area of a Square Angle formula

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

Where:

$$\large{ A }$$ = area

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

### Perimeter of a Square Angle formula

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

Where:

$$\large{ A }$$ = area

$$\large{ w }$$ = width

### Distance from Centroid of a Square Angle formula

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

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

Where:

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

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

### Elastic Section Modulus of a Square Angle formula

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

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

Where:

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

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

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

### 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

### Polar Moment of Inertia of a Square Angle formula

$$\large{ J_{z} = I_{x} + I_{y} }$$

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

Where:

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

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

### Radius of Gyration of a Square Angle formula

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

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

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

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

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

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

Where:

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

$$\large{ A }$$ = area

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

### Second Moment of Area of a Square Angle formula

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

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

$$\large{ I_{x1} = I_{x} + A\; C_{y} }$$

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

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