# Tapered I Beam

Written by Jerry Ratzlaff on . Posted in Structural

• A tapered I beam is a structural shape used in construction.

### area of a Tapered I Beam formula

$$\large{ A = l\;t + 2\;a \;\left( s + n \right) }$$

Where:

$$\large{ A }$$ = area

$$\large{ l }$$ = height

$$\large{ n }$$ = thickness

$$\large{ s }$$ = thickness

$$\large{ t }$$ = thickness

$$\large{ a }$$ = width

### Distance from Centroid of a Tapered I Beam formula

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

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

Where:

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

$$\large{ l }$$ = height

$$\large{ w }$$ = width

### Elastic Section Modulus of a Tapered 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 Tapered I Beam formula

$$\large{ P = 2\;w + 4\;s + 2\;L + 4 \; \sqrt{ \left( \frac{w \;-\; a}{2} \; \right)^2 + \left( s + n \right)^2 } }$$

Where:

$$\large{ P }$$ = perimeter

$$\large{ L }$$ = height

$$\large{ n }$$ = thickness

$$\large{ s }$$ = thickness

$$\large{ a }$$ = width

$$\large{ w }$$ = width

### Polar Moment of Inertia of a Tapered I Beam 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 Tapered I Beam formula

$$\large{ k_x = \sqrt{ \frac{ \frac{1}{12} \; \left[ w\;l^3 \;-\; \frac{1}{4\;g} \; \left( h^4 \;-\; L^4 \right) \right] }{ l\;t \;+\; 2\;a \; \left( s \;+\; n \right) } } }$$

$$\large{ k_y = \sqrt{ \frac{ \frac{1}{3} \; \left[ w^3 \; \left( l \;-\; h \right) \;+\; L\;t^3 \;+\; \frac{g}{4} \; \left( w^4 \;-\; t^4 \right) \right] }{ lt \;+\; 2\;a \; \left( s \;+\; n \right) } } }$$

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

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

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

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

Where:

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

$$\large{ A }$$ = area

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

$$\large{ h }$$ = height

$$\large{ l }$$ = height

$$\large{ L }$$ = height

$$\large{ n }$$ = thickness

$$\large{ s }$$ = thickness

$$\large{ t }$$ = thickness

$$\large{ a }$$ = width

$$\large{ w }$$ = width

### Second Moment of Area of a Tapered I Beam formula

$$\large{ I_x = \frac{1}{12} \; \left[ w\;l^3 \;-\; \frac{1}{4\;g} \; \left( h^4 \;-\; L^4 \right) \right] }$$

$$\large{ I_y = \frac{1}{3} \; \left[ w^3 \; \left( l \;-\; h \right) + L\;t^3 + \frac{g}{4} \; \left( w^4 \;-\; t^4 \right) \right] }$$

$$\large{ I_{x1} = l_{x} + A\;C_{y}{^2} }$$

$$\large{ I_{y1} = l_{y} + A\;C_{x}{^2} }$$

Where:

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

$$\large{ A }$$ = area

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

$$\large{ h }$$ = height

$$\large{ l }$$ = height

$$\large{ L }$$ = height

$$\large{ g }$$ = slope of taper

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

### Slope of Flange of a Tapered I Beam formula

$$\large{ g = \frac{ h \;-\; L }{ w \;-\; t } }$$

Where:

$$\large{ g }$$ = slope of taper

$$\large{ h }$$ = height

$$\large{ L }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width