# Square Diamond

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• A 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