# Zed

on . Posted in Plane Geometry

Zed beam, also called known as a "Z-shaped" or "Z-section" beam, is a variation of the letter "Z," which reflects the shape of the cross-sectional profile of the beam.  A Zed beam, or Z-section beam, has a cross-sectional shape resembling the letter "Z," with flanges (horizontal top and bottom parts) that are parallel and connected by a vertical web.  The flanges are usually smaller in width than those of an I-beam, and they extend outward from the web at the top and bottom.  The web connects the two flanges and provides vertical rigidity to the beam. ## area of a Zed formula

$$\large{ A = t \; \left[ l + 2 \; \left( w - t \right) \right] }$$
Symbol English Metric
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ l }$$ = height  $$\large{ in }$$  $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Distance from Centroid of a Zed formulas

$$\large{ C_x = \frac{ 2\;w \;-\; t }{ 2 } }$$

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

Symbol English Metric
$$\large{ C }$$ = distance from centroid  $$\large{ in }$$  $$\large{ mm }$$
$$\large{ l }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Elastic Section Modulus of a Zed formulas

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

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

Symbol English Metric
$$\large{ S }$$ = elastic section modulus $$\large{ in^3 }$$ $$\large{ mm^3 }$$
$$\large{ C }$$ = distance from centroid $$\large{ in }$$ $$\large{ mm }$$
$$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{ mm^4 }$$ ## Perimeter of a Zed formula

$$\large{ P = 2 \; \left( w + l \right) - t }$$
Symbol English Metric
$$\large{ P }$$ = perimeter  $$\large{ in }$$  $$\large{ mm }$$
$$\large{ l }$$ = height  $$\large{ in }$$  $$\large{ mm }$$
$$\large{ t }$$ = thickness  $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Polar Moment of Inertia of a Zed formulas

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

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

Symbol English Metric
$$\large{ J }$$ = torsional constant $$\large{ in^4 }$$ $$\large{ mm^4 }$$
$$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{ mm^4 }$$ ## Radius of Gyration of a Zed formulas

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

$$\large{ k_{y} = \frac{ l \; \left( w \;+\; c \right)^3 \;-\; 2c^3 \;h \;-\; 6\;w^2\; c\;h }{ 12\;t \; \left[ l \;+\; 2 \; \left( w \;-\; t \right) \right] } }$$

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

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

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

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

Symbol English Metric
$$\large{ k }$$ = radius of gyration $$\large{ in }$$ $$\large{ mm }$$
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ l }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{ mm^4 }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ c }$$ = width $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ ## Second Moment of Area of a Zed formulas

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

$$\large{ I_{y} = \frac{ l \; \left( w \;+\; c \right)^3 \;-\; 2\;c^3\; h \;-\; 6\;w^2 \;c\;h }{12} }$$

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

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

Symbol English Metric
$$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{ mm^4 }$$
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ C }$$ = distance from centroid $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ l }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{ mm }$$
$$\large{ c }$$ = width $$\large{ in }$$ $$\large{ mm }$$
$$\large{ w }$$ = width $$\large{ in }$$ $$\large{ mm }$$ 