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I Beam

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I-sections consist of two parallel flanges connected by a central web, providing high efficiency in resisting bending about its strong axis and shear forces through the web. The flanges and web can be of different sizes, depending on the application and requirements for the strength and stiffness in the minor and major axis.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Squared I-beam

figure wim350e3728bc

Section depth

d_{t}

100.00

mm

Section breadth

b_{t}

50.00

mm

Flange thickness

s_{t}

10.00

mm

Web thickness

t_{t}

10.00

mm

Web depth

h_{t}

80.00

mm

h_{t}

=

d_{t} - 2 \cdot s_{t}

=

100.00 - 2 \cdot 10.00

Area

A_{t}

1800.00

{mm}^{2}

A_{t}

=

b_{t} \cdot d_{t} - h_{t} \cdot (b_{t} - t_{t})

=

50.00 \cdot 100.00 - 80.00 \cdot (50.00 - 10.00)

Perimeter

P_{t}

380.00

mm

P_{t}

=

2 \cdot (2 \cdot b_{t} + d_{t} - t_{t})

=

2 \cdot (2 \cdot 50.00 + 100.00 - 10.00)

Distance to centroid (x-axis)

C_{x}

25.00

mm

C_{x}

=

\frac{b_{t}}{2}

=

\frac{50.00}{2}

Distance to centroid (y-axis)

C_{y}

50.00

mm

C_{y}

=

\frac{d_{t}}{2}

=

\frac{100.00}{2}

Second moment of area about x-axis

I_{x}

(2.460e+6)

{mm}^{4}

I_{x}

=

\frac{(b_{t} \cdot {d_{t}}^{3} - {h_{t}}^{3} \cdot (b_{t} - t_{t}))}{12}

=

\frac{(50.00 \cdot {100.00}^{3} - {80.00}^{3} \cdot (50.00 - 10.00))}{12}

Second moment of area about y-axis

I_{y}

215000

{mm}^{4}

I_{y}

=

\frac{(2 \cdot s_{t} \cdot {b_{t}}^{3} + h_{t} \cdot {t_{t}}^{3})}{12}

=

\frac{(2 \cdot 10.00 \cdot {50.00}^{3} + 80.00 \cdot {10.00}^{3})}{12}

Polar moment of inertia about centre

J_{z}

(2.675e+6)

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

(2.460e+6) + 215000

Second moment of area about x1-axis

I_{x_{1}}

(6.960e+6)

{mm}^{4}

I_{x_{1}}

=

I_{x} + A_{t} \cdot {C_{y}}^{2}

=

(2.460e+6) + 1800.00 \cdot {50.00}^{2}

Second moment of area about y1-axis

I_{y_{1}}

(1.340e+6)

{mm}^{4}

I_{y_{1}}

=

I_{y} + A_{t} \cdot {C_{x}}^{2}

=

215000 + 1800.00 \cdot {25.00}^{2}

Polar moment of inertia about centre

J_{z_{1}}

(8.300e+6)

{mm}^{4}

J_{z_{1}}

=

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

=

(6.960e+6) + (1.340e+6)

Radius of gyration about x-axis

K_{x}

36.97

mm

K_{x}

=

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

=

\sqrt{\frac{(2.460e+6)}{1800.00}}

Radius of gyration about y-axis

K_{y}

10.93

mm

K_{y}

=

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

=

\sqrt{\frac{215000}{1800.00}}

Radius of gyration about z-axis

K_{z}

38.55

mm

K_{z}

=

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

=

\sqrt{{36.97}^{2} + {10.93}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

62.18

mm

K_{x_{1}}

=

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

=

\sqrt{\frac{(6.960e+6)}{1800.00}}

Radius of gyration about y1-axis

K_{y_{1}}

27.28

mm

K_{y_{1}}

=

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

=

\sqrt{\frac{(1.340e+6)}{1800.00}}

Radius of gyration about z1-axis

K_{z_{1}}

67.91

mm

K_{z_{1}}

=

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

=

\sqrt{{62.18}^{2} + {27.28}^{2}}

Elastic section modulus about x-axis

S_{x}

49200.0

{mm}^{3}

S_{x}

=

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

=

\frac{(2.460e+6)}{50.00}

Elastic section modulus about y-axis

S_{y}

8600.00

{mm}^{3}

S_{y}

=

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

=

\frac{215000}{25.00}

Plastic section modulus around x-axis

Z_{x}

61000.0

{mm}^{3}

Z_{x}

=

\frac{1}{4} \cdot b_{t} \cdot {d_{t}}^{2} - \frac{1}{4} \cdot (b_{t} - t_{t}) \cdot {h_{t}}^{2}

=

\frac{1}{4} \cdot 50.00 \cdot {100.00}^{2} - \frac{1}{4} \cdot (50.00 - 10.00) \cdot {80.00}^{2}

Plastic section modulus around y-axis

Z_{y}

14500.0

{mm}^{3}

Z_{y}

=

\frac{1}{4} \cdot h_{t} \cdot {t_{t}}^{2} + \frac{1}{2} \cdot s_{t} \cdot {b_{t}}^{2}

=

\frac{1}{4} \cdot 80.00 \cdot {10.00}^{2} + \frac{1}{2} \cdot 10.00 \cdot {50.00}^{2}