Square Diamond

Written by Jerry Ratzlaff on . Posted in Plane Geometry

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

Area of a Square Diamond formula

(Eq. 1)  \( \large{ A = a^2 }\)

Perimeter of a Square Diamond formula

(Eq. 2)  \(\large{ P= 4\;a  }\)

Side of a Square Diamond formula

(Eq. 3)  \(\large{ a= \sqrt  { A  }   }\)

Distance from Centroid of a Square Diamond formula

(Eq. 4)  \(\large{ C_x =  \frac { a }  { 2 }   }\)

(Eq. 4)  \(\large{ C_y =  \frac { a }  { 2}   }\)

Elastic Section Modulus of a Square Diamond formula

(Eq. 5)  \(\large{ S =  \frac { a^3 }  { 6\; \sqrt {2}  }  }\)

Plastic Section Modulus of a Square Diamond formula

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

Polar Moment of Inertia of a Square Diamond formula

(Eq. 7)  \(\large{ J_{z} = \frac {a^4}{6}  }\)

(Eq. 8)  \(\large{ J_{z1} =  \frac {2\;a^4}{3}  }\)

Radius of Gyration of a Square Diamond formula

(Eq. 9)  \(\large{ k_{x} =    \frac { a }  {  2 \; \sqrt 3  }    }\)

(Eq. 9)  \(\large{ k_{y} =   \frac { a }  {  2 \; \sqrt 3  }  }\)

(Eq. 10)  \(\large{ k_{z} =   \frac { a }  {  \sqrt 6  }  }\)

(Eq. 11)  \(\large{ k_{x1} =   \frac { a }  {  \sqrt 3  }  }\)

(Eq. 11)  \(\large{ k_{y1} =   \frac { a }  {   \sqrt 3  }  }\)

(Eq. 12)  \(\large{ k_{z1} =   \sqrt {  \frac {2}{3} \;a    }   }\)

Second Moment of Area of a Square Diamond formula

(Eq. 13)  \(\large{ I_{x} =  \frac {a^4}{12}  }\)

(Eq. 13)  \(\large{ I_{y} = \frac {a^4}{12}  }\)

(Eq. 14)  \(\large{ I_{x1} =   \frac {a^4}{3}  }\)

(Eq. 14)  \(\large{ I_{y1} =  \frac {a^4}{3}  }\)

Torsional Constant of a Square Diamond formula

(Eq. 15)  \(\large{ J  =  2.25  \;  \left(   \frac {  a  } {  2  } \right)  ^4  }\)

 

Where:

\(\large{ A }\) = area

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

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

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

\(\large{ P }\) = perimeter

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

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

\(\large{ a }\) = side

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

 

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