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Square

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The square structural shape is a solid, continuous form defined by four equal-length sides meeting at right angles. Unlike hollow or tubular profiles, this square is completely filled throughout—imagine a solid block of material, such as concrete, with no voids or inner cavities. Its uniform geometry makes it easy to manufacture and calculate, offering consistent strength in both vertical and horizontal directions. The shape provides strong resistance to compressive forces, making it ideal for load-bearing columns, piers, or foundational supports in construction. Its simplicity and stability allow it to transfer loads evenly, and when made from dense materials like concrete, it also offers good resistance to bending and buckling under pressure.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Square

Side length

a_{t}

50.00

mm

Area

A_{t}

2500.00

{mm}^{2}

A_{t}

=

{a_{t}}^{2}

=

{50.00}^{2}

Perimeter

P_{t}

200.00

mm

P_{t}

=

4 \cdot a_{t}

=

4 \cdot 50.00

Distance to centroid (x-axis)

C_{x}

25.00

mm

C_{x}

=

\frac{a_{t}}{2}

=

\frac{50.00}{2}

Distance to centroid (y-axis)

C_{y}

25.00

mm

C_{y}

=

C_{x}

=

25.00

Second moment of area about x-axis

I_{x}

520833

{mm}^{4}

I_{x}

=

\frac{{a_{t}}^{4}}{12}

=

\frac{{50.00}^{4}}{12}

Second moment of area about y-axis

I_{y}

520833

{mm}^{4}

I_{y}

=

I_{x}

=

520833

Polar moment of inertia about centre

J_{z}

(1.042e+6)

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

520833 + 520833

Second moment of area about x1-axis

I_{x_{1}}

(2.083e+6)

{mm}^{4}

I_{x_{1}}

=

\frac{{a_{t}}^{4}}{3}

=

\frac{{50.00}^{4}}{3}

Second moment of area about y1-axis

I_{y_{1}}

(2.083e+6)

{mm}^{4}

I_{y_{1}}

=

I_{x_{1}}

=

(2.083e+6)

Polar moment of inertia about vertex

J_{z_{1}}

(4.167e+6)

{mm}^{4}

J_{z_{1}}

=

I_{x_{1}} + I_{y_{1}}

=

(2.083e+6) + (2.083e+6)

Radius of gyration about x-axis

K_{x}

14.43

mm

K_{x}

=

\sqrt{\frac{I_{x}}{A_{t}}}

=

\sqrt{\frac{520833}{2500.00}}

Radius of gyration about y-axis

K_{y}

14.43

mm

K_{y}

=

\sqrt{\frac{I_{y}}{A_{t}}}

=

\sqrt{\frac{520833}{2500.00}}

Radius of gyration in z-axis

K_{z}

20.41

mm

K_{z}

=

\sqrt{{K_{x}}^{2} + {K_{y}}^{2}}

=

\sqrt{{14.43}^{2} + {14.43}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

28.87

mm

K_{x_{1}}

=

\sqrt{\frac{I_{x_{1}}}{A_{t}}}

=

\sqrt{\frac{(2.083e+6)}{2500.00}}

Radius of gyration about y1-axis

K_{y_{1}}

28.87

mm

K_{y_{1}}

=

\sqrt{\frac{I_{y_{1}}}{A_{t}}}

=

\sqrt{\frac{(2.083e+6)}{2500.00}}

Radius of gyration about z1-axis

K_{z_{1}}

40.82

mm

K_{z_{1}}

=

\sqrt{{K_{x_{1}}}^{2} + {K_{y_{1}}}^{2}}

=

\sqrt{{28.87}^{2} + {28.87}^{2}}

Elastic section modulus

S

20833.3

{mm}^{3}

S

=

\frac{I_{x}}{C_{y}}

=

\frac{520833}{25.00}

Plastic section modulus

Z

31250.0

{mm}^{3}

Z

=

\frac{{a_{t}}^{3}}{4}

=

\frac{{50.00}^{3}}{4}