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Back To Back Equal Angles

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Back-to-Back Equal Angles consist of two equal leg angles connected together to form a T-shape or star-shape profile, improving stability for compression members.

Calculations

Description

Symbol Name

Value

Unit

Comment

0

Back To Back Equal Angles

1

figure wim2023d268f0

2

Geometry Input

3

Side length

h_{t}

65.00

mm

4

Section thickness

t_{t}

7.00

r_{toe}

5

Root radius

r_{r o o t}

9.00

mm

6

Toe radius

r_{toe}

4.50

mm

7

Space between angles

s_{t}

0

mm

8

Material Properties

9

Poisson's ratio

v_{t}

0.30000

-

10

Young's modulus

E_{t}

210000

\frac{N}{{mm}^{2}}

11

Density

ρ_{t}

7850.00

\frac{kg}{m^{3}}

12

Shear modulus

G_{t}

80769.2

\frac{N}{{mm}^{2}}

G_{t} = \frac{E_{t}}{(2 \cdot (1 + v_{t}))} = \frac{210000}{(2 \cdot (1 + 0.30000))}

13

Section Properties

14

Overall bredth

b_{total}

130.00

mm

b_{total} = 2 \cdot h_{t} + s_{t} = 2 \cdot 65.00 + 0

15

A_{web}

406.00

{mm}^{2}

A_{web} = (h_{t} - t_{t}) \cdot t_{t} = (65.00 - 7.00) \cdot 7.00

16

A_{flange}

455.00

{mm}^{2}

A_{flange} = h_{t} \cdot t_{t} = 65.00 \cdot 7.00

17

A_{root}

17.38

{mm}^{2}

A_{root} = (1 - \frac{π}{4}) \cdot {r_{r o o t}}^{2} = (1 - \frac{π}{4}) \cdot {9.00}^{2}

18

A_{toe}

-4.35

{mm}^{2}

A_{toe} = - 1 \cdot (1 - \frac{π}{4}) \cdot {r_{toe}}^{2} = - 1 \cdot (1 - \frac{π}{4}) \cdot {4.50}^{2}

19

Total section area

A_{t}

1739.38

{mm}^{2}

A_{t} = 2 \cdot (A_{web} + A_{flange} + A_{root} + 2 \cdot A_{toe}) = 2 \cdot (406.00 + 455.00 + 17.38 + 2 \cdot -4.35)

20

Mass per metre length

m_{m}

13.65

\frac{kg}{m}

m_{m} = \frac{(A_{t} \cdot ρ_{t})}{10^{6}} = \frac{(1739.38 \cdot 7850.00)}{10^{6}}

21

y_{web}

29.00

mm

y_{web} = \frac{(h_{t} - t_{t})}{2} = \frac{(65.00 - 7.00)}{2}

22

y_{flange}

61.50

mm

y_{flange} = h_{t} - \frac{t_{t}}{2} = 65.00 - \frac{7.00}{2}

23

y_{root}

55.99

mm

y_{root} = h_{t} - t_{t} - r_{r o o t} + \frac{2 \cdot r_{r o o t}}{(3 \cdot (4 - π))} = 65.00 - 7.00 - 9.00 + \frac{2 \cdot 9.00}{(3 \cdot (4 - π))}

24

y_{toe,f}

59.01

mm

y_{toe,f} = h_{t} - t_{t} + r_{toe} - \frac{2 \cdot r_{toe}}{(3 \cdot (4 - π))} = 65.00 - 7.00 + 4.50 - \frac{2 \cdot 4.50}{(3 \cdot (4 - π))}

25

y_{toe,w}

1.01

mm

y_{toe,w} = r_{toe} - \frac{2 \cdot r_{toe}}{(3 \cdot (4 - π))} = 4.50 - \frac{2 \cdot 4.50}{(3 \cdot (4 - π))}

26

Horizontal distance to centroid per single angle

C_{x}

46.53

mm

C_{x} = \frac{2 \cdot (A_{flange} \cdot y_{flange} + A_{web} \cdot y_{web} + A_{root} \cdot y_{root} + A_{toe} \cdot y_{toe,f} + A_{toe} \cdot y_{toe,w})}{A_{t}} = \frac{2 \cdot (455.00 \cdot 61.50 + 406.00 \cdot 29.00 + 17.38 \cdot 55.99 + -4.35 \cdot 59.01 + -4.35 \cdot 1.01)}{1739.38}

27

Vertical distance to centroid per single angle

C_{y}

46.53

mm

C_{y} = C_{x} = 46.53

28

Second moment of area of a single angle (1)

I_{web}

238616

{mm}^{4}

I_{web} = \frac{A_{web} \cdot {(h_{t} - t_{t})}^{2}}{12} + A_{web} \cdot {(y_{web} - C_{y})}^{2} = \frac{406.00 \cdot {(65.00 - 7.00)}^{2}}{12} + 406.00 \cdot {(29.00 - 46.53)}^{2}

29

Second moment of area of a single angle (2)

I_{flange}

103789

{mm}^{4}

I_{flange} = \frac{A_{flange} \cdot {t_{t}}^{2}}{12} + A_{flange} \cdot {(y_{flange} - C_{y})}^{2} = \frac{455.00 \cdot {7.00}^{2}}{12} + 455.00 \cdot {(61.50 - 46.53)}^{2}

30

γ_{yy,local}

0.05488

γ_{yy,local} = \frac{π}{16} - \frac{4}{(9 \cdot π)}

31

Single angle second moment of area about the x axis

I_{root}

1914.72

{mm}^{4}

I_{root} = γ_{yy,local} \cdot {r_{r o o t}}^{4} + A_{root} \cdot {(y_{root} - C_{y})}^{2} = 0.05488 \cdot {9.00}^{4} + 17.38 \cdot {(55.99 - 46.53)}^{2}

32

I_{toes}

-9728.55

I_{toes} = - 2 \cdot γ_{yy,local} \cdot {r_{toe}}^{4} + A_{toe} \cdot {(y_{toe,f} - C_{y})}^{2} + A_{toe} \cdot {(y_{toe,w} - C_{y})}^{2} = - 2 \cdot 0.05488 \cdot {4.50}^{4} + -4.35 \cdot {(59.01 - 46.53)}^{2} + -4.35 \cdot {(1.01 - 46.53)}^{2}

33

Second moment area about axis x-x

I_{xx}

669182

{mm}^{4}

I_{xx} = 2 \cdot (I_{web} + I_{flange} + I_{root} + I_{toes}) = 2 \cdot (238616 + 103789 + 1914.72 + -9728.55)

34

Perpendicular distance between single angle centroid and overall angle centroid

d_{x}

18.47

mm

d_{x} = h_{t} - C_{x} + \frac{s_{t}}{2} = 65.00 - 46.53 + \frac{0}{2}

35

Second moment of area about axis y-y

I_{yy}

(1.262e+6)

{mm}^{4}

I_{yy} = (I_{xx} + A_{t} \cdot {(d_{x})}^{2}) = (669182 + 1739.38 \cdot {(18.47)}^{2})

36

Radius of gyration about axis x-x

K_{x}

19.61

mm

K_{x} = \sqrt{\frac{I_{xx}}{A_{t}}} = \sqrt{\frac{669182}{1739.38}}

37

Radius of gyration about axis y-y

K_{y}

26.94

mm

K_{y} = \sqrt{\frac{I_{yy}}{A_{t}}} = \sqrt{\frac{(1.262e+6)}{1739.38}}

38

Elastic section modulus about axis x-x

S_{xx}

14380.9

{mm}^{3}

S_{xx} = \frac{I_{xx}}{(C_{x})} = \frac{669182}{(46.53)}

39

Elastic section modulus about axis y-y

S_{yy}

19421.4

{mm}^{3}

S_{yy} = \frac{I_{yy}}{(0.5 \cdot b_{total})} = \frac{(1.262e+6)}{(0.5 \cdot 130.00)}