Zed

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Three rectangles, two that intersect at a 90° angle to the third one at end each at different directions.
• A zed is a structural shape used in construction.

formulas that use area of a Zed

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

Where:

$$\large{ A }$$ = area

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

formulas that use Distance from Centroid of a Zed

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

Where:

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

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

formulas that use Elastic Section Modulus of a Zed

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

Where:

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

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

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

formulas that use Perimeter of a Zed formula

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

Where:

$$\large{ P }$$ = perimeter

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

formulas that use Polar Moment of Inertia of a Zed

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

Where:

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

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

formulas that use Radius of Gyration of a Zed

 $$\large{ k_{x} = \sqrt{ \frac { w\;l^3 \;-\; c \; \left( l \;-\; 2\;t \right)^3 }{ 12\;t \; \left[ l \;+\; 2 \; \left( w \;-\; t \right) \right] } } }$$ $$\large{ k_{y} = \frac{ l \; \left( w \;+\; c \right)^3 \;-\; 2c^3 \;h \;-\; 6\;w^2\; c\;h }{ 12\;t \; \left[ l \;+\; 2 \; \left( w \;-\; t \right) \right] } }$$ $$\large{ k_{z} = \sqrt{ k_{x}{^2} + k_{y}{^2} } }$$ $$\large{ k_{x1} = \sqrt{ \frac{ I_{x1} }{ A } } }$$ $$\large{ k_{y1} = \sqrt{ \frac{ I_{y1} }{ A } } }$$ $$\large{ k_{z1} = \sqrt{ k_{x1}{^2} + k_{y1}{^2} } }$$

Where:

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

$$\large{ A }$$ = area

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

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

$$\large{ h }$$ = height

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ c }$$ = width

$$\large{ w }$$ = width

formulas that use Second Moment of Area of a Zed

 $$\large{ I_{x} = \frac{ w\;l^3 \;-\; c \; \left( l \;-\; 2\;t \right)^3 }{12} }$$ $$\large{ I_{y} = \frac{ l \; \left( w \;+\; c \right)^3 \;-\; 2\;c^3\; h \;-\; 6\;w^2 \;c\;h }{12} }$$ $$\large{ I_{x1} = I_{x} + A\;C_{y}{^2} }$$ $$\large{ I_{y1} = I_{y} + A\;C_{x}{^2} }$$

Where:

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

$$\large{ A }$$ = area

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

$$\large{ h }$$ = height

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ c }$$ = width

$$\large{ w }$$ = width