Square Diamond

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Square Diamond - Geometric Properties

• Square ( $$SQ$$ ) is a quadrilateral with four parallel edges.
• Interior angles are 90°.
• Exterior angles are 90°.
• 2 diagonals
• 4 edges
• 4 vertexs

Area of a Square Diamond formula

$$\large{ A = a^2 }$$

Perimeter of a Square Diamond formula

$$\large{ P= 4a }$$

Side of a Square Diamond formula

$$\large{ a= \sqrt { A } }$$

Distance from Centroid of a Square Diamond formula

$$\large{ C_x = \frac { a } { 2 } }$$

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

Elastic Section Modulus of a Square Diamond formula

$$\large{ S = \frac { a^3 } { 6 \sqrt {2} } }$$

Plastic Section Modulus of a Square Diamond formula

$$\large{ Z = \frac { a^3 \sqrt {2} } { 6 } }$$

Polar Moment of Inertia of a Square Diamond formula

$$\large{ J_{z} = \frac {a^4}{6} }$$

$$\large{ J_{z1} = \frac {2a^4}{3} }$$

Radius of Gyration of a Square Diamond formula

$$\large{ k_{x} = \frac { a } { 2 \sqrt 3 } }$$

$$\large{ k_{y} = \frac { a } { 2 \sqrt 3 } }$$

$$\large{ k_{z} = \frac { a } { \sqrt 6 } }$$

$$\large{ k_{x1} = \frac { a } { \sqrt 3 } }$$

$$\large{ k_{y1} = \frac { a } { \sqrt 3 } }$$

$$\large{ k_{z1} = \sqrt { \frac {2}{3} a } }$$

Second Moment of Area of a Square Diamond formula

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

$$\large{ I_{y} = \frac {a^4}{12} }$$

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

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

Torsional Constant of a Square Diamond formula

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

Where:

$$\large{ A }$$ = area

$$\large{ a }$$ = side

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

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

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

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

$$\large{ P }$$ = perimeter

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

$$\large{ Z }$$ = plastic section modulus