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Rectangle

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The solid rectangular structural shape is defined by four sides with opposite sides being equal in length, meeting at right angles, and a completely filled cross-section. Its primary advantage lies in its differing bending strengths about its major and minor axes, allowing for optimised orientation based on load direction. It offers good compressive strength and is commonly used for beams (when oriented to maximise moment resistance), columns, lintels, and other load-bearing elements in construction.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Rectangle

figure wim70244253f7

Depth

a_{t}

5.00

mm

Breadth

b_{t}

10.00

mm

Area

A_{t}

50.00

{mm}^{2}

A_{t}

=

a_{t} \cdot b_{t}

=

5.00 \cdot 10.00

Perimeter

P_{t}

30.00

mm

P_{t}

=

2 \cdot (a_{t} + b_{t})

=

2 \cdot (5.00 + 10.00)

Distance to centroid (x-axis)

C_{x}

5.00

mm

C_{x}

=

\frac{b_{t}}{2}

=

\frac{10.00}{2}

Distance to centroid (y-axis)

C_{y}

2.50

mm

C_{y}

=

\frac{a_{t}}{2}

=

\frac{5.00}{2}

Second moment of area about x-axis

I_{x}

104.17

{mm}^{4}

I_{x}

=

\frac{{a_{t}}^{3} \cdot b_{t}}{12}

=

\frac{{5.00}^{3} \cdot 10.00}{12}

Second moment of area about y-axis

I_{y}

416.67

{mm}^{4}

I_{y}

=

\frac{a_{t} \cdot {b_{t}}^{3}}{12}

=

\frac{5.00 \cdot {10.00}^{3}}{12}

Second moment of area about x1-axis

I_{x_{1}}

416.67

{mm}^{4}

I_{x_{1}}

=

\frac{{a_{t}}^{3} \cdot b_{t}}{3}

=

\frac{{5.00}^{3} \cdot 10.00}{3}

Second moment of area about y1-axis

I_{y_{1}}

1666.67

{mm}^{4}

I_{y_{1}}

=

\frac{a_{t} \cdot {b_{t}}^{3}}{3}

=

\frac{5.00 \cdot {10.00}^{3}}{3}

Polar moment of inertia about centre

J_{z}

520.83

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

104.17 + 416.67

Polar moment of inertia about vertex

J_{z_{1}}

2083.33

{mm}^{4}

J_{z_{1}}

=

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

=

416.67 + 1666.67

Radius of gyration about x-axis

K_{x}

1.44

mm

K_{x}

=

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

=

\sqrt{\frac{104.17}{50.00}}

Radius of gyration about y-axis

K_{y}

2.89

mm

K_{y}

=

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

=

\sqrt{\frac{416.67}{50.00}}

Radius of gyration about z-axis

K_{z}

3.23

mm

K_{z}

=

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

=

\sqrt{{1.44}^{2} + {2.89}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

2.89

mm

K_{x_{1}}

=

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

=

\sqrt{\frac{416.67}{50.00}}

Radius of gyration about y1-axis

K_{y_{1}}

5.77

mm

K_{y_{1}}

=

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

=

\sqrt{\frac{1666.67}{50.00}}

Radius of gyration about z1-axis

K_{z_{1}}

6.45

mm

K_{z_{1}}

=

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

=

\sqrt{{2.89}^{2} + {5.77}^{2}}

Elastic section modulus about x-axis

S_{x}

41.67

{mm}^{3}

S_{x}

=

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

=

\frac{104.17}{2.50}

Elastic section modulus about y-axis

S_{y}

83.33

{mm}^{3}

S_{y}

=

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

=

\frac{416.67}{5.00}

Plastic section modulus about x-axis

Z_{x}

62.50

{mm}^{3}

Z_{x}

=

\frac{{a_{t}}^{2} \cdot b_{t}}{4}

=

\frac{{5.00}^{2} \cdot 10.00}{4}

Elastic section modulus about y-axis

Z_{y}

125.00

{mm}^{3}

Z_{y}

=

\frac{a_{t} \cdot {b_{t}}^{2}}{4}

=

\frac{5.00 \cdot {10.00}^{2}}{4}