# Tapered T Beam

Written by Jerry Ratzlaff on . Posted in Structural

• A tapered T beam is a structural shape used in construction.
• See Geometric Properties of Structural Shapes

### area of a Tapered T Beam formula

$$\large{ A = w\;s + \frac{ h \; \left(T + t \right) }{2} }$$

### Perimeter of a Tapered T Beam formula

$$\large{ P = 2\;w + 2\;s \;-\; T + t + 2\; \sqrt{ \left( \frac{1}{2} \right)^2 + \left( \frac{T}{2} \right)^2 } }$$

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

$$\large{ C_x = 0 }$$

$$\large{ C_y = l \;-\; \frac{1}{6\;A} \; \left[ 3\;w\;s^2 + 3\;h\;t \; \left( l + s \right) + h \; \left( T \;-\; t \right) \; \left( h + 3\;s \right) \right] }$$

### Elastic section Modulus of a Tapered T Beam formula

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

### Radius of Gyration of a Tapered T Beam formula

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

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

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

$$\large{ I_{x} = \frac { \left[ 4\;w\;s^2 \;+\; h^3 \; \left( 3\;t \;+\; T \right) \right] \;-\; A \; \left( l \;-\; C_y \;-\; s \right)^2 } {12} }$$

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

Where:

$$\large{ A }$$ = area

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

$$\large{ d }$$ = distance from principle axis

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

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

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

$$\large{ P }$$ = perimeter

$$\large{ p }$$ = principal axis

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