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.

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Calculations

Description

Symbol Name

Value

Unit

Comment

Back To Back Equal Angles

Geometry Input

Side length

h_{t}

65.00

mm

Section thickness

t_{t}

7.00

mm

Root radius

r_{r o o t}

9.00

mm

Toe radius

r_{toe}

4.50

mm

Space between angles

s_{t}

mm

Material Properties

Poisson's ratio

v_{t}

0.30000

-

Young's modulus

E_{t}

210000

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

Density

ρ_{t}

7850.00

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

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))}

Section Properties

Overall bredth

b_{total}

130.00

mm

b_{total}

=

2 \cdot h_{t} + s_{t}

=

2 \cdot 65.00 + 0

A_{web}

406.00

{mm}^{2}

A_{web}

=

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

=

(65.00 - 7.00) \cdot 7.00

A_{flange}

455.00

{mm}^{2}

A_{flange}

=

h_{t} \cdot t_{t}

=

65.00 \cdot 7.00

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}

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}

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)

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}}

y_{web}

29.00

mm

y_{web}

=

\frac{(h_{t} - t_{t})}{2}

=

\frac{(65.00 - 7.00)}{2}

y_{flange}

61.50

mm

y_{flange}

=

h_{t} - \frac{t_{t}}{2}

=

65.00 - \frac{7.00}{2}

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))}

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))}

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))}

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}

Vertical distance to centroid per single angle

C_{y}

46.53

mm

C_{y}

=

C_{x}

=

46.53

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}

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}

γ_{yy,local}

0.05488

γ_{yy,local}

=

\frac{π}{16} - \frac{4}{(9 \cdot π)}

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}

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}

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)

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}

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})

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}}

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}}

Elastic section modulus about axis x-x

S_{xx}

14380.9

{mm}^{3}

S_{xx}

=

\frac{I_{xx}}{(C_{x})}

=

\frac{669182}{(46.53)}

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)}