Hot Formed I Sections

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Hot-formed I-sections are structural steel shapes produced by hot rolling, giving them an “I” shaped cross-section with parallel flanges and a central web, optimised for carrying bending and shear in buildings and civil works.

Calculations

Description

Symbol Name

Value

Unit

Comment

Geometry Input

Section depth

h_{t}

1056.00

mm

Section width

b_{t}

314.00

mm

Web thickness

t_{w}

36.00

mm

Flange thickness

t_{f}

64.00

mm

Root radius

r_{t}

30.00

mm

Material Properties

Young's modulus

E_{t}

210000

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

Poisson's ratio

v_{t}

0.30000

-

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))}

Density

ρ_{t}

7850.00

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

Calculated geometry parameters

Depth of web

h_{w}

928.00

mm

h_{w} = h_{t} - 2 \cdot t_{f} = 1056.00 - 2 \cdot 64.00

Depth between fillets

d_{t}

868.00

mm

d_{t} = h_{t} - 2 \cdot t_{f} - 2 \cdot r_{t} = 1056.00 - 2 \cdot 64.00 - 2 \cdot 30.00

Distance from major axis to flange centroid

h_{f}

496.00

mm

h_{f} = \frac{h_{t}}{2} - \frac{t_{f}}{2} = \frac{1056.00}{2} - \frac{64.00}{2}

Distance to centroid in the y-y axis

C_{y}

157.00

mm

C_{y} = \frac{b_{t}}{2} = \frac{314.00}{2}

Distance to centroid in the z-z axis

C_{z}

528.00

mm

C_{z} = \frac{h_{t}}{2} = \frac{1056.00}{2}

Cross-sectional area (1)

A_{I}

73600.0

{mm}^{2}

A_{I} = 2 \cdot b_{t} \cdot t_{f} + h_{w} \cdot t_{w} = 2 \cdot 314.00 \cdot 64.00 + 928.00 \cdot 36.00

A_{flange}

20096.0

{mm}^{2}

A_{flange} = b_{t} \cdot t_{f} = 314.00 \cdot 64.00

A_{web}

33408.0

{mm}^{2}

A_{web} = h_{w} \cdot t_{w} = 928.00 \cdot 36.00

Cross-sectional area (2)

A_{root}

193.14

{mm}^{2}

A_{root} = {r_{t}}^{2} \cdot (1 - \frac{π}{4}) = {30.00}^{2} \cdot (1 - \frac{π}{4})

Cross-sectional area

A_{t}

74372.6

{mm}^{2}

A_{t} = A_{web} + 2 \cdot A_{flange} + 4 \cdot A_{root} = 33408.0 + 2 \cdot 20096.0 + 4 \cdot 193.14

Mass per metre length

m_{m}

583.82

\frac{kg}{m}

m_{m} = \frac{A_{t} \cdot ρ_{t}}{1000000} = \frac{74372.6 \cdot 7850.00}{1000000}

c_{w} \div t_{w}

24.11

c_{w} \div t_{w} = \frac{(h_{t} - 2 \cdot (t_{f} + r_{t}))}{t_{w}} = \frac{(1056.00 - 2 \cdot (64.00 + 30.00))}{36.00}

c_{f} \div t_{f}

1.70

c_{f} \div t_{f} = \frac{0.5 \cdot (b_{t} - (t_{w} + 2 \cdot r_{t}))}{t_{f}} = \frac{0.5 \cdot (314.00 - (36.00 + 2 \cdot 30.00))}{64.00}

C_{end,clearance}

20.00

mm

C_{end,clearance} = round (\frac{t_{w}}{2} + 2) = round (\frac{36.00}{2} + 2)

N_{notch}

150.00

mm

N_{notch} = ceil ((\frac{(b_{t} - t_{w})}{2} + 10) \cdot 0.5) \cdot 2 = ceil ((\frac{(314.00 - 36.00)}{2} + 10) \cdot 0.5) \cdot 2

n_{notch}

94.00

n_{notch} = ceil (\frac{(h_{t} - d_{t})}{2} \cdot 0.5) \cdot 2 = ceil (\frac{(1056.00 - 868.00)}{2} \cdot 0.5) \cdot 2

Surface Area per Metre

A_{m}

3244.50

{mm}^{2}

A_{m} = 2 \cdot h_{t} + 4 \cdot b_{t} + 2 \cdot π \cdot r_{t} - 8 \cdot r_{t} - 2 \cdot t_{w} = 2 \cdot 1056.00 + 4 \cdot 314.00 + 2 \cdot π \cdot 30.00 - 8 \cdot 30.00 - 2 \cdot 36.00

Surface Area per Tonne

A_{m} \div m_{m}

5.56

\frac{{mm}^{2}}{t}

A_{m} \div m_{m} = \frac{A_{m}}{m_{m}} = \frac{3244.50}{583.82}

Second moment of area

Second moment of area about major axis (1)

I_{{yy}_{1}}

(1.230e+10)

{mm}^{4}

I_{{yy}_{1}} = \frac{2 \cdot A_{flange} \cdot {t_{f}}^{2}}{12} + 2 \cdot A_{flange} \cdot {h_{f}}^{2} + \frac{A_{web} \cdot {h_{w}}^{2}}{12} = \frac{2 \cdot 20096.0 \cdot {64.00}^{2}}{12} + 2 \cdot 20096.0 \cdot {496.00}^{2} + \frac{33408.0 \cdot {928.00}^{2}}{12}

Second moment of area about major axis (1)

I_{{yy}_{2}}

(1.616e+8)

{mm}^{4}

I_{{yy}_{2}} = 4 \cdot A_{root} \cdot {(\frac{d_{t}}{2} + 0.7766 \cdot r_{t})}^{2} = 4 \cdot 193.14 \cdot {(\frac{868.00}{2} + 0.7766 \cdot 30.00)}^{2}

Second moment of area about major axis

I_{yy}

(1.246e+10)

{mm}^{4}

I_{yy} = I_{{yy}_{1}} + I_{{yy}_{2}} = (1.230e+10) + (1.616e+8)

Second moment of area about minor axis

I_{zz}

(3.343e+8)

{mm}^{4}

I_{zz} = \frac{2 \cdot A_{flange} \cdot {b_{t}}^{2}}{12} + \frac{A_{web} \cdot {t_{w}}^{2}}{12} + 4 \cdot A_{root} \cdot {(\frac{t_{w}}{2} + 0.2234 \cdot r_{t})}^{2} = \frac{2 \cdot 20096.0 \cdot {314.00}^{2}}{12} + \frac{33408.0 \cdot {36.00}^{2}}{12} + 4 \cdot 193.14 \cdot {(\frac{36.00}{2} + 0.2234 \cdot 30.00)}^{2}

Other parameters

Radius of gyration about major axis

K_{yy}

409.32

mm

K_{yy} = \sqrt{\frac{I_{yy}}{A_{t}}} = \sqrt{\frac{(1.246e+10)}{74372.6}}

Radius of gyration about minor axis

K_{zz}

67.05

mm

K_{zz} = \sqrt{\frac{I_{zz}}{A_{t}}} = \sqrt{\frac{(3.343e+8)}{74372.6}}

Elastic section modulus about the major axis

S_{yy}

(2.360e+7)

{mm}^{3}

S_{yy} = \frac{I_{yy}}{C_{z}} = \frac{(1.246e+10)}{528.00}

Elastic section modulus about the minor axis

S_{zz}

(2.129e+6)

{mm}^{3}

S_{zz} = \frac{I_{zz}}{C_{y}} = \frac{(3.343e+8)}{157.00}

Plastic section modulus about major axis (1)

Z_{{Pyy}_{1}}

(2.769e+7)

{mm}^{3}

Z_{{Pyy}_{1}} = 2 \cdot A_{flange} \cdot h_{f} + \frac{A_{web} \cdot h_{w}}{4} = 2 \cdot 20096.0 \cdot 496.00 + \frac{33408.0 \cdot 928.00}{4}

Plastic section modulus about major axis (2)

Z_{{Pyy}_{2}}

353293

{mm}^{3}

Z_{{Pyy}_{2}} = 4 \cdot A_{root} \cdot (\frac{d_{t}}{2} + 0.7766 \cdot r_{t}) = 4 \cdot 193.14 \cdot (\frac{868.00}{2} + 0.7766 \cdot 30.00)

Plastic section modulus about major axis

Z_{Pyy}

(2.804e+7)

{mm}^{3}

Z_{Pyy} = Z_{{Pyy}_{1}} + Z_{{Pyy}_{2}} = (2.769e+7) + 353293

Plastic section modulus about minor axis

Z_{Pzz}

(3.475e+6)

{mm}^{3}

Z_{Pzz} = 2 \cdot A_{flange} \cdot (\frac{b_{t}}{4}) + A_{web} \cdot (\frac{t_{w}}{4}) + 4 \cdot A_{root} \cdot (\frac{t_{w}}{2} + 0.2234 \cdot r_{t}) = 2 \cdot 20096.0 \cdot (\frac{314.00}{4}) + 33408.0 \cdot (\frac{36.00}{4}) + 4 \cdot 193.14 \cdot (\frac{36.00}{2} + 0.2234 \cdot 30.00)

Warping constant

I_{w}

(8.225e+13)

{mm}^{6}

I_{w} = \frac{I_{zz} \cdot {(h_{t} - t_{f})}^{2}}{4} = \frac{(3.343e+8) \cdot {(1056.00 - 64.00)}^{2}}{4}

Geometric coefficient

α_{1}

0.09974

-

α_{1} = \frac{0.2204 \cdot t_{w}}{t_{f}} - 0.042 + \frac{0.1355 \cdot r_{t}}{t_{f}} - \frac{0.0865 \cdot r_{t} \cdot t_{w}}{{t_{f}}^{2}} - \frac{0.0725 \cdot {t_{w}}^{2}}{{t_{f}}^{2}} = \frac{0.2204 \cdot 36.00}{64.00} - 0.042 + \frac{0.1355 \cdot 30.00}{64.00} - \frac{0.0865 \cdot 30.00 \cdot 36.00}{{64.00}^{2}} - \frac{0.0725 \cdot {36.00}^{2}}{{64.00}^{2}}

Geometric coefficient

D_{1}

82.58

mm

D_{1} = \frac{{(t_{f} + r_{t})}^{2}}{(2 \cdot r_{t} + t_{f})} + \frac{(r_{t} + 0.25 \cdot t_{w}) \cdot t_{w}}{(2 \cdot r_{t} + t_{f})} = \frac{{(64.00 + 30.00)}^{2}}{(2 \cdot 30.00 + 64.00)} + \frac{(30.00 + 0.25 \cdot 36.00) \cdot 36.00}{(2 \cdot 30.00 + 64.00)}

Torsional constant

I_{T}

(7.154e+7)

{mm}^{4}

I_{T} = \frac{2}{3} \cdot b_{t} \cdot {t_{f}}^{3} + \frac{1}{3} \cdot (h_{t} - 2 \cdot t_{f}) \cdot {t_{w}}^{3} + 2 \cdot α_{1} \cdot {D_{1}}^{4} - 0.42 \cdot {t_{f}}^{4} = \frac{2}{3} \cdot 314.00 \cdot {64.00}^{3} + \frac{1}{3} \cdot (1056.00 - 2 \cdot 64.00) \cdot {36.00}^{3} + 2 \cdot 0.09974 \cdot {82.58}^{4} - 0.42 \cdot {64.00}^{4}

Torsional index

X

18.12

-

X = \sqrt{\frac{(π^{2} \cdot E_{t} \cdot A_{t} \cdot I_{w})}{(20 \cdot G_{t} \cdot I_{T} \cdot I_{zz})}} = \sqrt{\frac{(π^{2} \cdot 210000 \cdot 74372.6 \cdot (8.225e+13))}{(20 \cdot 80769.2 \cdot (7.154e+7) \cdot (3.343e+8))}}

Geometric coefficient

g

0.98649

-

g = \sqrt{1 - \frac{I_{zz}}{I_{yy}}} = \sqrt{1 - \frac{(3.343e+8)}{(1.246e+10)}}

Buckling parameter

U

0.86593

-

U = {(\frac{Z_{Pyy} \cdot g}{A_{t}})}^{0.5} \cdot {(\frac{I_{zz}}{I_{w}})}^{0.25} = {(\frac{(2.804e+7) \cdot 0.98649}{74372.6})}^{0.5} \cdot {(\frac{(3.343e+8)}{(8.225e+13)})}^{0.25}