Zed

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • Zed beam 1Three 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.

Structural Shapes

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

 

Tags: Equations for Moment of Inertia Equations for Structural Steel Equations for Modulus