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Zed Beam

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The zed-beam (Z-section) has a Z-shaped profile, consisting of a web and two flanges that extend in opposite directions from the web. This point-symmetric shape offers advantages in certain applications, such as purlins, where they can be lapped at supports to create a continuous line. They are designed to resist bending and are commonly used in cold-formed steel construction for roof and wall support systems.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Zed Beam

figure wim28cd395692

Section depth

d_{t}

100.00

mm

Flange breadth

b_{t}

50.00

mm

Thickness

t_{t}

10.00

mm

Web depth

d_{w}

80.00

mm

d_{w}

=

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

=

100.00 - 2 \cdot 10.00

Inner flange breadth

c_{t}

40.00

mm

c_{t}

=

b_{t} - t_{t}

=

50.00 - 10.00

Area

A_{t}

1800.00

{mm}^{2}

A_{t}

=

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

=

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

Perimeter

P_{t}

290.00

mm

P_{t}

=

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

=

2 \cdot (50.00 + 100.00) - 10.00

Distance to centroid (x-axis)

C_{x}

45.00

mm

C_{x}

=

\frac{(2 \cdot b_{t} - t_{t})}{2}

=

\frac{(2 \cdot 50.00 - 10.00)}{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} - c_{t} \cdot {(d_{t} - 2 \cdot t_{t})}^{3})}{12}

=

\frac{(50.00 \cdot {100.00}^{3} - 40.00 \cdot {(100.00 - 2 \cdot 10.00)}^{3})}{12}

Second moment of area about y-axis

I_{y}

615000

{mm}^{4}

I_{y}

=

\frac{(b_{t} - t_{t}) \cdot t_{t} \cdot {b_{t}}^{2}}{2} + \frac{t_{t} \cdot {(b_{t} - t_{t})}^{3}}{6} + \frac{d_{t} \cdot {t_{t}}^{3}}{12}

=

\frac{(50.00 - 10.00) \cdot 10.00 \cdot {50.00}^{2}}{2} + \frac{10.00 \cdot {(50.00 - 10.00)}^{3}}{6} + \frac{100.00 \cdot {10.00}^{3}}{12}

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}}

(4.260e+6)

{mm}^{4}

I_{y_{1}}

=

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

=

615000 + 1800.00 \cdot {45.00}^{2}

Polar moment of inertia about centre

J_{z}

(3.075e+6)

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

(2.460e+6) + 615000

Polar moment of inertia about vertex

J_{z_{1}}

(1.122e+7)

{mm}^{4}

J_{z_{1}}

=

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

=

(6.960e+6) + (4.260e+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}

18.48

mm

K_{y}

=

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

=

\sqrt{\frac{615000}{1800.00}}

Radius of gyration about z-axis

K_{z}

41.33

mm

K_{z}

=

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

=

\sqrt{{36.97}^{2} + {18.48}^{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}}

48.65

mm

K_{y_{1}}

=

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

=

\sqrt{\frac{(4.260e+6)}{1800.00}}

Radius of gyration about z1-axis

K_{z_{1}}

78.95

mm

K_{z_{1}}

=

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

=

\sqrt{{62.18}^{2} + {48.65}^{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}

13666.7

{mm}^{3}

S_{y}

=

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

=

\frac{615000}{45.00}

Plastic section modulus about the x-axis

Z_{x}

61000.0

{mm}^{3}

Since the top and bottom flanges are equal, PNA can only be located in the web

Z_{x}

=

b_{t} \cdot t_{t} \cdot (d_{t} - t_{t}) + \frac{t_{t} \cdot {d_{w}}^{2}}{4}

=

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

Plastic section modulus about the y-axis

Z_{y}

22500.0

{mm}^{3}

Z_{y}

=

\frac{2 \cdot b_{t} \cdot t_{t} \cdot (b_{t} - 0.5 \cdot t_{t})}{2}

=

\frac{2 \cdot 50.00 \cdot 10.00 \cdot (50.00 - 0.5 \cdot 10.00)}{2}