Tees Split From I Section

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Tees split from Universal Columns (UC) are T-shaped sections created by cutting a UC section longitudinally. Used for truss chords or stiffeners.

Calculations

Description

Symbol Name

Value

Unit

Comment

Tees (T) Split from UC

Geometry Input

Section breadth

b_{t}

253.00

mm

Section depth

h_{t}

338.90

mm

Web thickness

t_{w}

11.70

mm

Flange thickness

t_{f}

16.20

mm

Root radius

r_{t}

15.20

mm

Material Properties

Young's modulus

E_{t}

210000

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

Poisson's ratio

v_{t}

0.30000

-

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

A_{flange}

4098.60

{mm}^{2}

A_{flange} = b_{t} \cdot t_{f} = 253.00 \cdot 16.20

A_{root}

49.58

{mm}^{2}

A_{root} = {r_{t}}^{2} \cdot (1 - \frac{π}{4}) = {15.20}^{2} \cdot (1 - \frac{π}{4})

A_{web}

3775.59

{mm}^{2}

A_{web} = (h_{t} - t_{f}) \cdot t_{w} = (338.90 - 16.20) \cdot 11.70

Section area

A_{t}

7973.35

{mm}^{2}

A_{t} = A_{web} + A_{flange} + 2 \cdot A_{root} = 3775.59 + 4098.60 + 2 \cdot 49.58

Mass per metre length

m_{m}

62.59

\frac{kg}{m}

m_{m} = \frac{A_{t}}{10^{6}} \cdot ρ_{t} = \frac{7973.35}{10^{6}} \cdot 7850.00

Web local buckling ratio

\frac{c_{w}}{t_{w}}

28.97

-

\frac{c_{w}}{t_{w}} = \frac{h_{t}}{t_{w}} = \frac{338.90}{11.70}

Flange local buckling ratio

\frac{c_{f}}{t_{f}}

6.51

-

\frac{c_{f}}{t_{f}} = \frac{(\frac{(b_{t} - t_{w})}{2} - r_{t})}{t_{f}} = \frac{(\frac{(253.00 - 11.70)}{2} - 15.20)}{16.20}

y_{flange}

8.10

mm

y_{flange} = \frac{t_{f}}{2} = \frac{16.20}{2}

y_{root}

19.60

mm

y_{root} = t_{f} + r_{t} - \frac{2 \cdot r_{t}}{(3 \cdot (4 - π))} = 16.20 + 15.20 - \frac{2 \cdot 15.20}{(3 \cdot (4 - π))}

y_{web}

177.55

mm

y_{web} = t_{f} + \frac{(h_{t} - t_{f})}{2} = 16.20 + \frac{(338.90 - 16.20)}{2}

Distance from the centroid to the extreme fiber of the section

C_{y}

88.48

mm

C_{y} = \frac{(A_{flange} \cdot y_{flange} + 2 \cdot A_{root} \cdot y_{root} + A_{web} \cdot y_{web})}{A_{t}} = \frac{(4098.60 \cdot 8.10 + 2 \cdot 49.58 \cdot 19.60 + 3775.59 \cdot 177.55)}{7973.35}

Distance from the bottom of the section to the centroid

C_{y,bot}

250.42

mm

C_{y,bot} = h_{t} - C_{y} = 338.90 - 88.48

I_{flange,web}

(8.929e+7)

{mm}^{4}

I_{flange,web} = \frac{A_{flange} \cdot {t_{f}}^{2}}{12} + A_{flange} \cdot {(y_{flange} - C_{y})}^{2} + \frac{A_{web} \cdot {(h_{t} - t_{f})}^{2}}{12} + A_{web} \cdot {(y_{web} - C_{y})}^{2} = \frac{4098.60 \cdot {16.20}^{2}}{12} + 4098.60 \cdot {(8.10 - 88.48)}^{2} + \frac{3775.59 \cdot {(338.90 - 16.20)}^{2}}{12} + 3775.59 \cdot {(177.55 - 88.48)}^{2}

I_{root}

238213

{mm}^{4}

I_{root} = (\frac{π}{16} - \frac{4}{(9 \cdot π)}) \cdot {r_{t}}^{4} + A_{root} \cdot {(y_{root} - C_{y})}^{2} = (\frac{π}{16} - \frac{4}{(9 \cdot π)}) \cdot {15.20}^{4} + 49.58 \cdot {(19.60 - 88.48)}^{2}

Second moment of area about axis y-y

I_{yy}

(8.953e+7)

{mm}^{4}

I_{yy} = I_{flange,web} + I_{root} = (8.929e+7) + 238213

Second moment of area about axis z-z

I_{zz}

(2.191e+7)

{mm}^{4}

I_{zz} = \frac{t_{f} \cdot {b_{t}}^{3}}{12} + \frac{(h_{t} - t_{f}) \cdot {t_{w}}^{3}}{12} + 2 \cdot {r_{t}}^{4} \cdot (\frac{π}{16} - \frac{4}{(9 \cdot π)}) = \frac{16.20 \cdot {253.00}^{3}}{12} + \frac{(338.90 - 16.20) \cdot {11.70}^{3}}{12} + 2 \cdot {15.20}^{4} \cdot (\frac{π}{16} - \frac{4}{(9 \cdot π)})

Radius of gyration about axis y-y

K_{yy}

105.96

mm

K_{yy} = \sqrt{\frac{I_{yy}}{A_{t}}} = \sqrt{\frac{(8.953e+7)}{7973.35}}

Radius of gyration about axis z-z

K_{zz}

52.42

mm

K_{zz} = \sqrt{\frac{I_{zz}}{A_{t}}} = \sqrt{\frac{(2.191e+7)}{7973.35}}

Elastic section modulus of the flange about axis y-y

S_{yy,flange}

(1.012e+6)

{mm}^{3}

S_{yy,flange} = \frac{I_{yy}}{C_{y}} = \frac{(8.953e+7)}{88.48}

Elastic section modulus of the toe about axis y-y

S_{yy,toe}

357508

{mm}^{3}

S_{yy,toe} = \frac{I_{yy}}{C_{y,bot}} = \frac{(8.953e+7)}{250.42}

Elastic section modulus about axis z-z

S_{zz}

173211

{mm}^{3}

S_{zz} = \frac{I_{zz}}{(\frac{b_{t}}{2})} = \frac{(2.191e+7)}{(\frac{253.00}{2})}

y_{pna,web}

-1.84

mm

y_{pna,web} = h_{t} - \frac{A_{t}}{(2 \cdot t_{w})} = 338.90 - \frac{7973.35}{(2 \cdot 11.70)}

Distance from the top of the flange to the PNA

y_{pna,flange}

15.76

mm

y_{pna,flange} = \frac{A_{t}}{(2 \cdot b_{t})} = \frac{7973.35}{(2 \cdot 253.00)}

Plastic section modulus about axis y-y

Z_{yy,flange,1}

642297

{mm}^{3}

Z_{yy,flange,1} = \frac{0.5 \cdot A_{t} \cdot y_{pna,flange}}{2} + \frac{b_{t} \cdot {(t_{f} - y_{pna,flange})}^{2}}{2} + A_{web} \cdot ((t_{f} - y_{pna,flange}) + \frac{(h_{t} - t_{f})}{2}) = \frac{0.5 \cdot 7973.35 \cdot 15.76}{2} + \frac{253.00 \cdot {(16.20 - 15.76)}^{2}}{2} + 3775.59 \cdot ((16.20 - 15.76) + \frac{(338.90 - 16.20)}{2})

Z_{yy,flange,2}

380.59

mm

Z_{yy,flange,2} = 2 \cdot A_{root} \cdot (t_{f} - y_{pna,flange} + 0.2234 \cdot r_{t}) = 2 \cdot 49.58 \cdot (16.20 - 15.76 + 0.2234 \cdot 15.20)

Total plastic section modulus the about axis z-z

Z_{yy,flange}

642677

{mm}^{3}

Z_{yy,flange} = Z_{yy,flange,1} + Z_{yy,flange,2} = 642297 + 380.59

Z_{yy,web,1}

640371

Z_{yy,web,1} = \frac{A_{t} \cdot (h_{t} - y_{pna,web})}{4} + A_{flange} \cdot (y_{pna,web} - \frac{t_{f}}{2}) + (A_{web} - \frac{A_{t}}{2}) \cdot 0.5 \cdot (y_{pna,web} - t_{f}) = \frac{7973.35 \cdot (338.90 - -1.84)}{4} + 4098.60 \cdot (-1.84 - \frac{16.20}{2}) + (3775.59 - \frac{7973.35}{2}) \cdot 0.5 \cdot (-1.84 - 16.20)

Z_{yy,web,2}

-2125.79

{mm}^{3}

Z_{yy,web,2} = 2 \cdot A_{root} \cdot (y_{pna,web} - t_{f} - 0.2234 \cdot r_{t}) = 2 \cdot 49.58 \cdot (-1.84 - 16.20 - 0.2234 \cdot 15.20)

Z_{yy,web}

638245

{mm}^{3}

Z_{yy,web} = Z_{yy,web,1} + Z_{yy,web,2} = 640371 + -2125.79

Z_{yy}

642677

{mm}^{3}

Z_{yy} = {\begin{cases} Z_{yy,web} & if t_{f} \leq \frac{A_{t}}{(2 \cdot b_{t})} \\ Z_{yy,flange} & otherwise. \end{cases} = {\begin{cases} 638245 & if 16.20 \leq \frac{7973.35}{(2 \cdot 253.00)} \\ 642677 & otherwise. \end{cases}

Plastic section modulus about axis z-z

Z_{zz}

271197

{mm}^{3}

Z_{zz} = 2 \cdot (\frac{A_{flange}}{2} \cdot (\frac{b_{t}}{4}) + \frac{A_{web}}{2} \cdot (\frac{t_{w}}{4}) + A_{root} \cdot (\frac{t_{w}}{2} + 0.2234 \cdot r_{t})) = 2 \cdot (\frac{4098.60}{2} \cdot (\frac{253.00}{4}) + \frac{3775.59}{2} \cdot (\frac{11.70}{4}) + 49.58 \cdot (\frac{11.70}{2} + 0.2234 \cdot 15.20))

Buckling parameter

U_{t}

0.64295

U_{t} = {(\frac{4 \cdot {Z_{yy}}^{2} \cdot (1 - \frac{I_{zz}}{I_{yy}})}{({A_{t}}^{2} \cdot {h_{t}}^{2})})}^{0.25} = {(\frac{4 \cdot 642677^{2} \cdot (1 - \frac{(2.191e+7)}{(8.953e+7)})}{({7973.35}^{2} \cdot {338.90}^{2})})}^{0.25}

Warping constant

I_{w}

(2.089e+9)

{mm}^{6}

I_{w} = \frac{1}{144} \cdot {t_{f}}^{3} \cdot {b_{t}}^{3} + \frac{1}{36} \cdot {(h_{t} - \frac{t_{f}}{2})}^{3} \cdot {t_{w}}^{3} = \frac{1}{144} \cdot {16.20}^{3} \cdot {253.00}^{3} + \frac{1}{36} \cdot {(338.90 - \frac{16.20}{2})}^{3} \cdot {11.70}^{3}

Distance from the outside of the flange to the side of the web

z_{0}

80.38

mm

z_{0} = C_{y} - \frac{t_{f}}{2} = 88.48 - \frac{16.20}{2}

Parameter required for monosymmetric index

x

(-7.537e+9)

{mm}^{3}

x = \frac{z_{0} \cdot {b_{t}}^{3} \cdot t_{f}}{12} + b_{t} \cdot t_{f} \cdot {z_{0}}^{3} + (\frac{t_{w}}{4}) \cdot ({(C_{y} - t_{f})}^{4} - {(h_{t} - C_{y})}^{4}) = \frac{80.38 \cdot {253.00}^{3} \cdot 16.20}{12} + 253.00 \cdot 16.20 \cdot {80.38}^{3} + (\frac{11.70}{4}) \cdot ({(88.48 - 16.20)}^{4} - {(338.90 - 88.48)}^{4})

Monosymmetry index

ψ_{a}

0.74047

-

ψ_{a} = (2 \cdot (C_{y} - \frac{t_{f}}{2}) - \frac{x}{I_{yy}}) \cdot (\frac{1}{(h_{t} - \frac{t_{f}}{2})}) = (2 \cdot (88.48 - \frac{16.20}{2}) - \frac{(-7.537e+9)}{(8.953e+7)}) \cdot (\frac{1}{(338.90 - \frac{16.20}{2})})

Geometric coefficient

α_{1}

0.14788

-

α_{1} = \frac{0.2204 \cdot t_{w}}{t_{f}} + \frac{0.1355 \cdot r_{t}}{t_{f}} - \frac{0.0865 \cdot t_{w} \cdot r_{t}}{{t_{f}}^{2}} - \frac{0.0725 \cdot {t_{w}}^{2}}{{t_{f}}^{2}} - 0.042 = \frac{0.2204 \cdot 11.70}{16.20} + \frac{0.1355 \cdot 15.20}{16.20} - \frac{0.0865 \cdot 11.70 \cdot 15.20}{{16.20}^{2}} - \frac{0.0725 \cdot {11.70}^{2}}{{16.20}^{2}} - 0.042

Geometric coefficient

D_{1}

25.71

mm

D_{1} = \frac{({(t_{f} + r_{t})}^{2} + (r_{t} + 0.25 \cdot t_{w}) \cdot t_{w})}{(2 \cdot r_{t} + t_{f})} = \frac{({(16.20 + 15.20)}^{2} + (15.20 + 0.25 \cdot 11.70) \cdot 11.70)}{(2 \cdot 15.20 + 16.20)}

Torsional constant

I_{T}

578994

{mm}^{4}

I_{T} = \frac{1}{3} \cdot b_{t} \cdot {t_{f}}^{3} + \frac{1}{3} \cdot (h_{t} - t_{f}) \cdot {t_{w}}^{3} + α_{1} \cdot {D_{1}}^{4} - 0.21 \cdot {t_{f}}^{4} - 0.105 \cdot {t_{w}}^{4} = \frac{1}{3} \cdot 253.00 \cdot {16.20}^{3} + \frac{1}{3} \cdot (338.90 - 16.20) \cdot {11.70}^{3} + 0.14788 \cdot {25.71}^{4} - 0.21 \cdot {16.20}^{4} - 0.105 \cdot {11.70}^{4}

Torsional Index

X_{t}

22.51

X_{t} = 0.566 \cdot h_{t} \cdot {(\frac{A_{t}}{I_{T}})}^{0.5} = 0.566 \cdot 338.90 \cdot {(\frac{7973.35}{578994})}^{0.5}