Square Diamond

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • square diamond 2A square diamond is a structural shape used in construction.
  • Abbreviated as SQ
  • Interior angles are 90°.
  • Exterior angles are 90°.
  • 2 diagonals
  • 4 edges
  • 4 vertexs

Structural Shapes

Area of a Square Diamond formula

\( \large{ A = a^2 }\)

Where:

\(\large{ A }\) = area

\(\large{ a }\) = side

Distance from Centroid of a Square Diamond formula

\(\large{ C_x =  \frac{ a }{ 2 }   }\)

\(\large{ C_y =  \frac{ a }{ 2}   }\)

Where:

\(\large{ C }\) = distance from centroid

\(\large{ a }\) = side

Elastic Section Modulus of a Square Diamond formula

\(\large{ S =  \frac { a^3 }  { 6\; \sqrt {2}  }  }\)

Where:

\(\large{ S }\) = elastic section modulus

\(\large{ a }\) = side

Perimeter of a Square Diamond formula

\(\large{ P= 4\;a  }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ a }\) = side

Plastic Section Modulus of a Square Diamond formula

\(\large{ Z =  \frac { a^3\; \sqrt {2} }  { 6  }  }\)

Where:

\(\large{ Z }\) = plastic section modulus

\(\large{ a }\) = side

Polar Moment of Inertia of a Square Diamond formula

\(\large{ J_{z} = \frac{a^4}{6}  }\)

\(\large{ J_{z1} =  \frac{2\;a^4}{3}  }\)

Where:

\(\large{ J }\) = torsional constant

\(\large{ a }\) = side

Radius of Gyration of a Square Diamond formula

\(\large{ k_{x} =    \frac{ a }{  2 \; \sqrt{3}  }    }\)

\(\large{ k_{y} =   \frac{ a }{  2 \; \sqrt{3}  }  }\)

\(\large{ k_{z} =   \frac{ a }{  \sqrt{6}  }  }\)

\(\large{ k_{x1} =   \frac{ a }{  \sqrt{3}  }  }\)

\(\large{ k_{y1} =   \frac{ a }{   \sqrt{3}  }  }\)

\(\large{ k_{z1} =   \sqrt{  \frac{2}{3} \;a }   }\)

Where:

\(\large{ k }\) = radius of gyration

\(\large{ a }\) = side

Second Moment of Area of a Square Diamond formula

\(\large{ I_{x} =  \frac{a^4}{12}  }\)

\(\large{ I_{y} = \frac{a^4}{12}  }\)

\(\large{ I_{x1} =   \frac{a^4}{3}  }\)

\(\large{ I_{y1} =  \frac{a^4}{3}  }\)

Where:

\(\large{ I }\) = moment of inertia

\(\large{ a }\) = side

Side of a Square Diamond formula

\(\large{ a= \sqrt{A}   }\)

Where:

\(\large{ a }\) = side

\(\large{ A }\) = area

Torsional Constant of a Square Diamond formula

\(\large{ J  =  2.25  \;  \left(\frac{a}{2}\right)^4  }\)

Where:

\(\large{ J }\) = torsional constant

\(\large{ a }\) = side

 

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