# Square Angle

on . Posted in Plane Geometry

Square angle is an angle iron with square legs, creating a right angle.  This type of angle iron has equal 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.  Square angles, like other angle iron profiles, come in various sizes, thicknesses, and materials to accommodate different load-bearing capacities and design requirements.  The cross-sectional properties of the angle, such as the moment of inertia and section modulus, determine its performance under different loading conditions.

## area of a Square Channel formula

$$\large{ A = t \; \left( 2\;w - t \right) }$$
Symbol English Metric
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$

## Distance from Centroid of a Square Angle formulas

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

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

Symbol English Metric
$$\large{ C }$$ = distance from centroid $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$

## Elastic Section Modulus of a Square 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 Square Angle formula

$$\large{ P = 4\;w }$$
Symbol English Metric
$$\large{ P }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$

## Polar Moment of Inertia of a Square 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 $$\large{ in^4 }$$ $$\large{ mm^4 }$$

## Principal Axis of a Square Angle formula

$$\large{ d = \frac{ w^2 \;+\; w\;t \;-\; t^2 }{ 2 \; \left( 2\;w \;-\; t \right) \; cos\; 45^\circ } }$$
Symbol English Metric
$$\large{ d }$$ = distance from principle axis $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$

## Radius of Gyration of a Square Angle formulas

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

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

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

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

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

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

Symbol English Metric
$$\large{ k }$$ = radius of gyration $$\large{ in }$$ $$\large{ mm }$$
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{ mm^4 }$$

## Second Moment of Area of a Square Angle formulas

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

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

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

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

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 $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$

## Tortional Constant of a Square Angle formula

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

Tags: Structural Steel