Tapered I Beam
A tapered I beam is a structural shape used in construction.
Structural Steel
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 formulas
| \(\large{ C_x = \frac{ w }{ 2 } }\) | |
| \(\large{ C_y = \frac{ l }{ 2 } }\) |
Where:
\(\large{ C }\) = distance from centroid
\(\large{ l }\) = height
\(\large{ w }\) = width
Elastic Section Modulus of a Tapered I Beam formulas
| \(\large{ S_x = \frac{ I_x }{ C_y } }\) | |
| \(\large{ S_y = \frac{ I_y }{ C_x } }\) |
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 formulas
| \(\large{ J_z = I_x + I_y }\) | |
| \(\large{ J_{z1} = I_{x1} + I_{y1} }\) |
Where:
\(\large{ J }\) = torsional constant
\(\large{ I }\) = moment of inertia
Radius of Gyration of a Tapered I Beam formulas
| \(\large{ k_x = \sqrt{ \frac{ \frac{1}{12} \; \left[ w\;l^3 \;-\; \frac{1}{4\;g} \; \left( h^4 \;-\; L^4 \right) \right] }{ l\;t \;+\; 2\;a \; \left( s \;+\; n \right) } } }\) | |
| \(\large{ k_y = \sqrt{ \frac{ \frac{1}{3} \; \left[ w^3 \; \left( l \;-\; h \right) \;+\; L\;t^3 \;+\; \frac{g}{4} \; \left( w^4 \;-\; t^4 \right) \right] }{ lt \;+\; 2\;a \; \left( s \;+\; n \right) } } }\) | |
| \(\large{ k_z = \sqrt{ k_{x}{^2} + k_{y}{^2} } }\) | |
| \(\large{ k_{x1} = \sqrt{ \frac{ I_{x1} }{ A } } }\) | |
| \(\large{ k_{y1} = \sqrt{ \frac{ I_{y1} }{ A } } }\) | |
| \(\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }\) |
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 formulas
| \(\large{ I_x = \frac{1}{12} \; \left[ w\;l^3 \;-\; \frac{1}{4\;g} \; \left( h^4 \;-\; L^4 \right) \right] }\) | |
| \(\large{ I_y = \frac{1}{3} \; \left[ w^3 \; \left( l \;-\; h \right) + L\;t^3 + \frac{g}{4} \; \left( w^4 \;-\; t^4 \right) \right] }\) | |
| \(\large{ I_{x1} = l_{x} + A\;C_{y}{^2} }\) | |
| \(\large{ I_{y1} = l_{y} + A\;C_{x}{^2} }\) |
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
Tags: Inertia Equations Structural Steel Equations Modulus Equations