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.

area of a Zed formula

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

Where:

$$\large{ A }$$ = area

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

Distance from Centroid of a Zed formula

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

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

Where:

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

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

Elastic Section Modulus of a Zed 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 Zed formula

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

Where:

$$\large{ P }$$ = perimeter

$$\large{ l }$$ = height

$$\large{ t }$$ = thickness

$$\large{ w }$$ = width

Polar Moment of Inertia of a Zed 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 Zed formula

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

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

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

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

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

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

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

Second Moment of Area of a Zed formula

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

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

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

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

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