Square I Beam

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Three rectangles, two that intersect at the center at 90° angles to the end of one rectangle.
• A square I beam is a structural shape used in construction.

area of a Square I Beam formula

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

Where:

$$\large{ A }$$ = area

$$\large{ h }$$ = height

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

Distance from Centroid of a Square I Beam formula

$$\large{ C_x = \frac{ w }{ 2 } }$$

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

Where:

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

$$\large{ l }$$ = height

$$\large{ s }$$ = thickness

$$\large{ w }$$ = width

Elastic Section Modulus of a Square I Beam 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

Perimeter of a Square I Beam formula

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

Where:

$$\large{ P }$$ = perimeter

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

Polar Moment of Inertia of a Square I Beam formula

$$\large{ J_{z} = I_{x} + I_{y}{^2} }$$

$$\large{ J_{z1} = I_{x1} + I_{y1}{^2} }$$

Where:

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

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

Radius of Gyration of a Square I Beam formula

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

$$\large{ k_{y} = \sqrt{ \frac{ 2\;s\;w^3 \;+\; h\;t^3 }{ 12 \; \left [ w\;l \;-\; h \; \left( w \;-\; t \right) \right ] } } }$$

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

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

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

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

Where:

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

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

$$\large{ h }$$ = height

$$\large{ l }$$ = height

$$\large{ s }$$ = thickness

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

Second Moment of Area of a Square I Beam formula

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

$$\large{ I_{y} = \frac{ 2\;s\;w^3 \;+\; h\;t^3 }{12} }$$

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

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

Where:

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

$$\large{ A }$$ = area

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

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

$$\large{ h }$$ = height

$$\large{ l }$$ = height

$$\large{ s }$$ = thickness

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

Torsional Constant of a Square I Beam formula

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

Where:

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

$$\large{ l }$$ = height

$$\large{ s }$$ = thickness

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width