# Square Channel

Written by Jerry Ratzlaff on . Posted in Structural

## Square Channel - Geometric Properties

### area formula

$$\large{ A = wl - h \left( w - t \right) }$$

### Perimeter formula

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

### Distance from Centroid Axis formula

$$\large{ C_x = \frac { 2w^2 s + ht^2 } { 2 wl - 2h \left( w - t \right) } }$$

$$\large{ C_y = \frac { l } { 2} }$$

### Elastic Section Modulus formula

$$\large{ S_{x} = \frac { I_{x} } { C_{y} } }$$

$$\large{ S_{y} = \frac { I_{y} } { C_{x} } }$$

### Moment of Inertia about Axis formula

$$\large{ I_{x} = \frac { wl^2 - h^3 \left( w - t \right) } { 12 } }$$

$$\large{ I_{y} = \frac { 2 sw^3 + ht^3 } { 3 } - A C_{x}{^2} }$$

$$\large{ I_{x1} = I_{x} + A C_y }$$

$$\large{ I_{y1} = I_{y} + A C_x }$$

### Polar Moment of Inertia about Axis formula

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

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

$$\large{ k_{x} = \sqrt { \frac { wl^2 - h^3 \left( w - t \right) } { 12 \left[ wl^2 - h^3 \left( w - t \right) \right] } } }$$

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

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

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

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

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

### Torsional Constant formula

$$\large{ J = \frac { 2 \left( w - \frac {t}{2} \right) s^3 \left( l - s \right) t^3 } { 3 } }$$

Where:

$$A$$ = area

$$C$$ = distance from centroid

$$I$$ = moment of inertia

$$J$$ = torsional constant

$$k$$ = radius of gyration

$$P$$ = perimeter

$$S$$ = elastic section modulus