Rectangle Angle

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The rectangle angle section, or L-section with unequal leg lengths, features two perpendicular legs of different dimensions. This asymmetry provides different section properties about its principal axes, allowing for more tailored strength characteristics compared to equal angles. Common applications include bracing, connecting members, frames for light structures, shelf supports, and situations where directional stiffness is a key design consideration.

Calculations

Description

Symbol Name

Value

Unit

Comment

Rectangular Angle

Section depth

h_{t}

100.00

mm

Section breadth

b_{t}

50.00

mm

Thickness

t_{t}

11.00

mm

No web breadth

c_{t}

39.00

mm

c_{t} = b_{t} - t_{t} = 50.00 - 11.00

Web depth

L_{t}

89.00

mm

L_{t} = h_{t} - t_{t} = 100.00 - 11.00

Area

A_{t}

1529.00

{mm}^{2}

A_{t} = t_{t} \cdot (b_{t} + L_{t}) = 11.00 \cdot (50.00 + 89.00)

Perimeter

P_{t}

300.00

mm

P_{t} = 2 \cdot (b_{t} + h_{t}) = 2 \cdot (50.00 + 100.00)

Distance to centroid (x-axis)

C_{x}

12.51

mm

C_{x} = \frac{1}{A_{t}} \cdot (\frac{t_{t}}{2} \cdot ({b_{t}}^{2} + h_{t} \cdot t_{t} - {t_{t}}^{2})) = \frac{1}{1529.00} \cdot (\frac{11.00}{2} \cdot ({50.00}^{2} + 100.00 \cdot 11.00 - {11.00}^{2}))

Distance to centroid (y-axis)

C_{y}

37.51

mm

C_{y} = \frac{(t_{t} \cdot (2 \cdot L_{t} + b_{t}) + {L_{t}}^{2})}{(2 \cdot (L_{t} + b_{t}))} = \frac{(11.00 \cdot (2 \cdot 89.00 + 50.00) + {89.00}^{2})}{(2 \cdot (89.00 + 50.00))}

Distance from top to centroid

y_{t}

62.49

mm

y_{t} = h_{t} - C_{y} = 100.00 - 37.51

Distance from right-end to centroid

z_{t}

37.49

mm

z_{t} = b_{t} - C_{x} = 50.00 - 12.51

Second moment of area about x-axis

I_{x}

(1.532e+6)

{mm}^{4}

I_{x} = \frac{(t_{t} \cdot {y_{t}}^{3} + b_{t} \cdot {(h_{t} - y_{t})}^{3} - (b_{t} - t_{t}) \cdot {(h_{t} - y_{t} - t_{t})}^{3})}{3} = \frac{(11.00 \cdot {62.49}^{3} + 50.00 \cdot {(100.00 - 62.49)}^{3} - (50.00 - 11.00) \cdot {(100.00 - 62.49 - 11.00)}^{3})}{3}

Second moment of area about y-axis

I_{y}

258363

{mm}^{4}

I_{y} = \frac{(t_{t} \cdot {z_{t}}^{3} + h_{t} \cdot {(b_{t} - z_{t})}^{3} - (h_{t} - t_{t}) \cdot {(b_{t} - z_{t} - t_{t})}^{3})}{3} = \frac{(11.00 \cdot {37.49}^{3} + 100.00 \cdot {(50.00 - 37.49)}^{3} - (100.00 - 11.00) \cdot {(50.00 - 37.49 - 11.00)}^{3})}{3}

Second moment of area about x1-axis

I_{x_{1}}

(3.684e+6)

{mm}^{4}

I_{x_{1}} = I_{x} + A_{t} \cdot {C_{y}}^{2} = (1.532e+6) + 1529.00 \cdot {37.51}^{2}

Second moment of area about y1-axis

I_{y_{1}}

497820

{mm}^{4}

I_{y_{1}} = I_{y} + A_{t} \cdot {C_{x}}^{2} = 258363 + 1529.00 \cdot {12.51}^{2}

Polar moment of inertia about centre

J_{z}

(1.791e+6)

{mm}^{4}

J_{z} = I_{x} + I_{y} = (1.532e+6) + 258363

Polar moment of inertia about vertex

J_{z_{1}}

(4.182e+6)

{mm}^{4}

J_{z_{1}} = I_{x_{1}} + I_{y_{1}} = (3.684e+6) + 497820

Radius of gyration about x-axis

K_{x}

31.66

mm

K_{x} = \sqrt{\frac{I_{x}}{A_{t}}} = \sqrt{\frac{(1.532e+6)}{1529.00}}

Radius of gyration abouty-axis

K_{y}

13.00

mm

K_{y} = \sqrt{\frac{I_{y}}{A_{t}}} = \sqrt{\frac{258363}{1529.00}}

Radius of gyration about z-axis

K_{z}

34.22

mm

K_{z} = \sqrt{{K_{x}}^{2} + {K_{y}}^{2}} = \sqrt{{31.66}^{2} + {13.00}^{2}}

Radius of gyration about x1-axis

K_{x_{1}}

49.09

mm

K_{x_{1}} = \sqrt{\frac{I_{x_{1}}}{A_{t}}} = \sqrt{\frac{(3.684e+6)}{1529.00}}

Radius of gyration about y-axis

K_{y_{1}}

18.04

mm

K_{y_{1}} = \sqrt{\frac{I_{y_{1}}}{A_{t}}} = \sqrt{\frac{497820}{1529.00}}

Radius of gyration about z1-axis

K_{z_{1}}

52.30

mm

K_{z_{1}} = \sqrt{{K_{x_{1}}}^{2} + {K_{y_{1}}}^{2}} = \sqrt{{49.09}^{2} + {18.04}^{2}}

Elastic section modulus about x-axis

S_{x}

24520.3

{mm}^{3}

Minimum value at the tip

S_{x} = \frac{I_{x}}{(h_{t} - C_{y})} = \frac{(1.532e+6)}{(100.00 - 37.51)}

Elastic section modulus about y-axis

S_{y}

6892.33

{mm}^{3}

Minimum value at the tip

S_{y} = \frac{I_{y}}{(b_{t} - C_{x})} = \frac{258363}{(50.00 - 12.51)}

Z_{x, 1}

42407.8

{mm}^{3}

Z_{x, 1} = t_{t} \cdot (\frac{({(h_{t} - t_{t})}^{2} - {b_{t}}^{2} + 2 \cdot h_{t} \cdot b_{t})}{4}) = 11.00 \cdot (\frac{({(100.00 - 11.00)}^{2} - {50.00}^{2} + 2 \cdot 100.00 \cdot 50.00)}{4})

Z_{x, 2}

45670.3

{mm}^{3}

Z_{x, 2} = \frac{b_{t} \cdot {t_{t}}^{2}}{4} + \frac{h_{t} \cdot t_{t} \cdot (h_{t} - t_{t})}{2} - \frac{{t_{t}}^{2} \cdot {(h_{t} - t_{t})}^{2}}{(4 \cdot b_{t})} = \frac{50.00 \cdot {11.00}^{2}}{4} + \frac{100.00 \cdot 11.00 \cdot (100.00 - 11.00)}{2} - \frac{{11.00}^{2} \cdot {(100.00 - 11.00)}^{2}}{(4 \cdot 50.00)}

Z_{x}

42407.8

{mm}^{3}

Z_{x} = {\begin{cases} Z_{x, 2} & if t_{t} > \frac{A_{t}}{(2 \cdot b_{t})} \\ Z_{x, 1} & otherwise. \end{cases} = {\begin{cases} 45670.3 & if 11.00 > \frac{1529.00}{(2 \cdot 50.00)} \\ 42407.8 & otherwise. \end{cases}

Z_{y, 1}

4182.75

{mm}^{2}

Z_{y, 1} = \frac{t_{t} \cdot ({(b_{t} - t_{t})}^{2} - {h_{t}}^{2} + 2 \cdot h_{t} \cdot b_{t})}{4} = \frac{11.00 \cdot ({(50.00 - 11.00)}^{2} - {100.00}^{2} + 2 \cdot 100.00 \cdot 50.00)}{4}

Z_{y, 2}

13289.9

{mm}^{3}

Z_{y, 2} = \frac{h_{t} \cdot {t_{t}}^{2}}{4} + \frac{b_{t} \cdot t_{t} \cdot (b_{t} - t_{t})}{2} - \frac{{t_{t}}^{2} \cdot {(b_{t} - t_{t})}^{2}}{(4 \cdot h_{t})} = \frac{100.00 \cdot {11.00}^{2}}{4} + \frac{50.00 \cdot 11.00 \cdot (50.00 - 11.00)}{2} - \frac{{11.00}^{2} \cdot {(50.00 - 11.00)}^{2}}{(4 \cdot 100.00)}

Z_{y}

13289.9

{mm}^{3}

Z_{y} = {\begin{cases} Z_{y, 2} & if t_{t} > \frac{A_{t}}{(2 \cdot h_{t})} \\ Z_{y, 1} & otherwise. \end{cases} = {\begin{cases} 13289.9 & if 11.00 > \frac{1529.00}{(2 \cdot 100.00)} \\ 4182.75 & otherwise. \end{cases}