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The cross-sectional shape, resembling a plus sign (+), typically consists of four legs or plates radiating from a common central point, or formed by two intersecting members. This cruciform shape provides good biaxial bending resistance and is relatively stable against buckling when used as a compression member. Common applications include columns, stanchions, and compression elements in towers or lattice structures where load can come from multiple directions.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Cross

figure wim1428ccf9e8

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

Area

A_{t}

1400.00

{mm}^{2}

A_{t}

=

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

=

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

Perimeter

P_{t}

300.00

mm

P_{t}

=

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

=

2 \cdot (50.00 + 100.00)

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}

836667

{mm}^{4}

I_{x}

=

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

=

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

Second moment of area about y-axis

I_{y}

111667

{mm}^{4}

I_{y}

=

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

=

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

Second moment of area about x1-axis

I_{x_{1}}

(4.337e+6)

{mm}^{4}

I_{x_{1}}

=

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

=

836667 + 1400.00 \cdot {50.00}^{2}

Second moment of area about y1-axis

I_{y_{1}}

986667

{mm}^{4}

I_{y_{1}}

=

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

=

111667 + 1400.00 \cdot {25.00}^{2}

Polar moment of inertia about centre

J_{z}

948333

{mm}^{4}

J_{z}

=

I_{x} + I_{y}

=

836667 + 111667

Polar moment of inertia about vertex

J_{z_{1}}

(5.323e+6)

{mm}^{4}

J_{z_{1}}

=

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

=

(4.337e+6) + 986667

Radius of gyration about x-axis

K_{x}

24.45

mm

K_{x}

=

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

=

\sqrt{\frac{836667}{1400.00}}

Radius of gyration about y-axis

K_{y}

8.93

mm

K_{y}

=

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

=

\sqrt{\frac{111667}{1400.00}}

Radius of gyration about z-axis

K_{z}

26.03

mm

K_{z}

=

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

=

\sqrt{{24.45}^{2} + {8.93}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

55.66

mm

K_{x_{1}}

=

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

=

\sqrt{\frac{(4.337e+6)}{1400.00}}

Radius of gyration about y1-axis

K_{y_{1}}

26.55

mm

K_{y_{1}}

=

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

=

\sqrt{\frac{986667}{1400.00}}

Radius of gyration about z1-axis

K_{z_{1}}

61.66

mm

K_{z_{1}}

=

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

=

\sqrt{{55.66}^{2} + {26.55}^{2}}

Elastic section modulus about x-axis

S_{x}

16733.3

{mm}^{3}

S_{x}

=

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

=

\frac{836667}{50.00}

Elastic section modulus about y-axis

S_{y}

4466.67

{mm}^{3}

S_{y}

=

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

=

\frac{111667}{25.00}

Plastic section modulus about the x-axis

Z_{x}

26000.0

{mm}^{3}

Z_{x}

=

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

=

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

Plastic section modulus about the y-axis

Z_{y}

8500.00

{mm}^{3}

Z_{y}

=

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

=

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