Parallel Flange Channels

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Parallel Flange Channels (PFC) are C-shaped sections with parallel inner and outer flange surfaces, simplifying connections. Used for columns, lintels, and beams.

Calculations

Description

Symbol Name

Value

Unit

Comment

Parallel Flange Channels (PFC)

Geometry Input

Section depth

h_{t}

430.00

mm

Section width

b_{t}

100.00

mm

Web thickness

t_{w}

11.00

mm

Flange thickness

t_{f}

19.00

mm

Root radius

r_{t}

15.00

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}}

Section Properties

Depth of web

h_{w}

392.00

mm

h_{w} = h_{t} - 2 \cdot t_{f} = 430.00 - 2 \cdot 19.00

Depth between fillets

d_{t}

362.00

mm

d_{t} = h_{t} - 2 \cdot t_{f} - 2 \cdot r_{t} = 430.00 - 2 \cdot 19.00 - 2 \cdot 15.00

Distance from major axis to flange centroid

h_{f}

205.50

mm

h_{f} = \frac{h_{t}}{2} - \frac{t_{f}}{2} = \frac{430.00}{2} - \frac{19.00}{2}

Cross-sectional area (1)

A_{I}

8112.00

{mm}^{2}

A_{I} = 2 \cdot b_{t} \cdot t_{f} + h_{w} \cdot t_{w} = 2 \cdot 100.00 \cdot 19.00 + 392.00 \cdot 11.00

Cross-sectional area (2)

A_{II}

96.57

{mm}^{2}

A_{II} = 2 \cdot {r_{t}}^{2} \cdot (1 - \frac{π}{4}) = 2 \cdot {15.00}^{2} \cdot (1 - \frac{π}{4})

Cross-sectional area

A_{t}

8208.57

{mm}^{2}

A_{t} = A_{I} + A_{II} = 8112.00 + 96.57

Distance to centroid in the z-z axis

C_{z}

215.00

mm

C_{z} = \frac{h_{t}}{2} = \frac{430.00}{2}

Distance to centroid in the y-y axis

C_{y}

26.35

mm

C_{y} = \frac{(2 \cdot {b_{t}}^{2} \cdot t_{f} + h_{w} \cdot {t_{w}}^{2})}{(2 \cdot b_{t} \cdot h_{t} - 2 \cdot h_{w} \cdot (b_{t} - t_{w}))} = \frac{(2 \cdot {100.00}^{2} \cdot 19.00 + 392.00 \cdot {11.00}^{2})}{(2 \cdot 100.00 \cdot 430.00 - 2 \cdot 392.00 \cdot (100.00 - 11.00))}

Mass per metre length

m_{m}

64.44

\frac{kg}{m}

m_{m} = \frac{A_{t} \cdot ρ_{t}}{1000000} = \frac{8208.57 \cdot 7850.00}{1000000}

Second moment of area about major axis (1)

I_{{yy}_{1}}

(2.158e+8)

{mm}^{4}

I_{{yy}_{1}} = \frac{b_{t} \cdot {h_{t}}^{3}}{12} - \frac{(b_{t} - t_{w}) \cdot {(h_{t} - 2 \cdot t_{f})}^{3}}{12} = \frac{100.00 \cdot {430.00}^{3}}{12} - \frac{(100.00 - 11.00) \cdot {(430.00 - 2 \cdot 19.00)}^{3}}{12}

Second moment of area about major axis (2)

I_{{yy}_{2}}

(3.584e+6)

{mm}^{4}

I_{{yy}_{2}} = 2 \cdot {r_{t}}^{2} \cdot (1 - \frac{π}{4}) \cdot {(\frac{d_{t}}{2} + 0.7766 \cdot r_{t})}^{2} = 2 \cdot {15.00}^{2} \cdot (1 - \frac{π}{4}) \cdot {(\frac{362.00}{2} + 0.7766 \cdot 15.00)}^{2}

Second moment of area about major axis

I_{yy}

(2.194e+8)

{mm}^{4}

I_{yy} = I_{{yy}_{1}} + I_{{yy}_{2}} = (2.158e+8) + (3.584e+6)

Second moment of area about minor axis (1)

I_{{zz}_{1}}

(7.210e+6)

{mm}^{4}

I_{{zz}_{1}} = \frac{{t_{w}}^{3} \cdot h_{w}}{12} + t_{w} \cdot h_{w} \cdot {(C_{y} - \frac{t_{w}}{2})}^{2} + \frac{2 \cdot {b_{t}}^{3} \cdot t_{f}}{12} + 2 \cdot b_{t} \cdot t_{f} \cdot {(C_{y} - \frac{b_{t}}{2})}^{2} = \frac{{11.00}^{3} \cdot 392.00}{12} + 11.00 \cdot 392.00 \cdot {(26.35 - \frac{11.00}{2})}^{2} + \frac{2 \cdot {100.00}^{3} \cdot 19.00}{12} + 2 \cdot 100.00 \cdot 19.00 \cdot {(26.35 - \frac{100.00}{2})}^{2}

Second moment of area about minor axis (2)

I_{{zz}_{2}}

13893.8

{mm}^{4}

I_{{zz}_{2}} = 2 \cdot {r_{t}}^{2} \cdot (1 - \frac{π}{4}) \cdot {(C_{y} - t_{w} - 0.2234 \cdot r_{t})}^{2} = 2 \cdot {15.00}^{2} \cdot (1 - \frac{π}{4}) \cdot {(26.35 - 11.00 - 0.2234 \cdot 15.00)}^{2}

Second moment of area about minor axis

I_{zz}

(7.224e+6)

{mm}^{4}

I_{zz} = I_{{zz}_{1}} + I_{{zz}_{2}} = (7.210e+6) + 13893.8

Web local buckling ratio

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

32.91

-

\frac{c_{w}}{t_{w}} = \frac{d_{t}}{t_{w}} = \frac{362.00}{11.00}

Flange local buckling ratio

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

3.89

-

\frac{c_{f}}{t_{f}} = \frac{(b_{t} - t_{w} - r_{t})}{(t_{f})} = \frac{(100.00 - 11.00 - 15.00)}{(19.00)}

Radius of gyration about major axis

K_{yy}

163.48

mm

K_{yy} = \sqrt{\frac{I_{yy}}{A_{t}}} = \sqrt{\frac{(2.194e+8)}{8208.57}}

Radius of gyration about minor axis

K_{zz}

29.67

mm

K_{zz} = \sqrt{\frac{I_{zz}}{A_{t}}} = \sqrt{\frac{(7.224e+6)}{8208.57}}

Elastic section modulus about the major axis

S_{yy}

(1.020e+6)

{mm}^{3}

S_{yy} = \frac{I_{yy}}{C_{z}} = \frac{(2.194e+8)}{215.00}

Elastic section modulus about the minor axis

S_{zz}

98079.6

{mm}^{3}

S_{zz} = \frac{I_{zz}}{(b_{t} - C_{y})} = \frac{(7.224e+6)}{(100.00 - 26.35)}

Plastic section modulus about major axis (1)

Z_{yy,1}

(1.203e+6)

{mm}^{3}

Z_{yy,1} = \frac{b_{t} \cdot {h_{t}}^{2}}{4} - \frac{(b_{t} - t_{w}) \cdot {h_{w}}^{2}}{4} = \frac{100.00 \cdot {430.00}^{2}}{4} - \frac{(100.00 - 11.00) \cdot {392.00}^{2}}{4}

Plastic section modulus about major axis (2)

Z_{yy,2}

18604.3

{mm}^{3}

Z_{yy,2} = 2 \cdot {r_{t}}^{2} \cdot (1 - \frac{π}{4}) \cdot (\frac{d_{t}}{2} + 0.7766 \cdot r_{t}) = 2 \cdot {15.00}^{2} \cdot (1 - \frac{π}{4}) \cdot (\frac{362.00}{2} + 0.7766 \cdot 15.00)

Plastic section modulus about major axis

Z_{yy}

(1.222e+6)

{mm}^{3}

Z_{yy} = Z_{yy,1} + Z_{yy,2} = (1.203e+6) + 18604.3

Plastic neutral axis location - pna is inside the web

y_{pna,1}

9.54

mm

y_{pna,1} = \frac{A_{t}}{(2 \cdot h_{t})} = \frac{8208.57}{(2 \cdot 430.00)}

Plastic neutral axis location - pna is outside the web

y_{pna,2}

-8.01

mm

y_{pna,2} = t_{w} + \frac{(\frac{A_{t}}{2} - t_{w} \cdot h_{t} - 2 \cdot {r_{t}}^{2} \cdot (1 - \frac{π}{4}))}{(2 \cdot t_{f})} = 11.00 + \frac{(\frac{8208.57}{2} - 11.00 \cdot 430.00 - 2 \cdot {15.00}^{2} \cdot (1 - \frac{π}{4}))}{(2 \cdot 19.00)}

Moment of Total Area about Rear

Z_{total}

215102

{mm}^{3}

Z_{total} = \frac{h_{t} \cdot {t_{w}}^{2}}{2} + t_{f} \cdot ({b_{t}}^{2} - {t_{w}}^{2}) + 2 \cdot {r_{t}}^{2} \cdot (1 - \frac{π}{4}) \cdot (t_{w} + 0.2234 \cdot r_{t}) = \frac{430.00 \cdot {11.00}^{2}}{2} + 19.00 \cdot ({100.00}^{2} - {11.00}^{2}) + 2 \cdot {15.00}^{2} \cdot (1 - \frac{π}{4}) \cdot (11.00 + 0.2234 \cdot 15.00)

Plastic section modulus about minor axis (2)

Z_{zz,2,temp}

26320.2

{mm}^{3}

Z_{zz,2,temp} = \frac{h_{t} \cdot {t_{w}}^{2}}{2} + 2 \cdot {r_{t}}^{2} \cdot (1 - \frac{π}{4}) \cdot (t_{w} + 0.2234 \cdot r_{t}) + t_{f} \cdot ({y_{pna,2}}^{2} - {t_{w}}^{2}) = \frac{430.00 \cdot {11.00}^{2}}{2} + 2 \cdot {15.00}^{2} \cdot (1 - \frac{π}{4}) \cdot (11.00 + 0.2234 \cdot 15.00) + 19.00 \cdot ({-8.01}^{2} - {11.00}^{2})

Plastic section modulus about minor axis

Z_{zz}

175927

{mm}^{3}

Z_{zz} = {\begin{cases} Z_{total} - h_{t} \cdot {y_{pna,1}}^{2} & if 0.5 \cdot A_{t} \leq h_{t} \cdot t_{w} \\ Z_{total} - 2 \cdot Z_{zz,2,temp} & otherwise. \end{cases} = {\begin{cases} 215102 - 430.00 \cdot {9.54}^{2} & if 0.5 \cdot 8208.57 \leq 430.00 \cdot 11.00 \\ 215102 - 2 \cdot 26320.2 & otherwise. \end{cases}

Warping constant

I_{w}

(2.177e+11)

{mm}^{6}

I_{w} = \frac{{(h_{t} - t_{f})}^{2}}{4} \cdot (I_{zz} - (A_{t} \cdot {(C_{y} - \frac{t_{w}}{2})}^{2} \cdot (\frac{{(h_{t} - t_{f})}^{2} \cdot A_{t}}{(4 \cdot I_{yy})} - 1))) = \frac{{(430.00 - 19.00)}^{2}}{4} \cdot ((7.224e+6) - (8208.57 \cdot {(26.35 - \frac{11.00}{2})}^{2} \cdot (\frac{{(430.00 - 19.00)}^{2} \cdot 8208.57}{(4 \cdot (2.194e+8))} - 1)))

Geometric coefficient

α_{1}

0.09208

-

α_{1} = \frac{0.2621 \cdot t_{w}}{t_{f}} - 0.0908 + \frac{0.1231 \cdot r_{t}}{t_{f}} - \frac{0.0752 \cdot r_{t} \cdot t_{w}}{{t_{f}}^{2}} - \frac{0.0945 \cdot {t_{w}}^{2}}{{t_{f}}^{2}} = \frac{0.2621 \cdot 11.00}{19.00} - 0.0908 + \frac{0.1231 \cdot 15.00}{19.00} - \frac{0.0752 \cdot 15.00 \cdot 11.00}{{19.00}^{2}} - \frac{0.0945 \cdot {11.00}^{2}}{{19.00}^{2}}

Geometric coefficient

D_{1}

23.22

mm

D_{1} = 2 \cdot ((3 \cdot r_{t} + t_{w} + t_{f}) - \sqrt{2 \cdot (2 \cdot r_{t} + t_{w}) \cdot (2 \cdot r_{t} + t_{f})}) = 2 \cdot ((3 \cdot 15.00 + 11.00 + 19.00) - \sqrt{2 \cdot (2 \cdot 15.00 + 11.00) \cdot (2 \cdot 15.00 + 19.00)})

Torsional constant

I_{T}

630028

{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 100.00 \cdot {19.00}^{3} + \frac{1}{3} \cdot (430.00 - 2 \cdot 19.00) \cdot {11.00}^{3} + 2 \cdot 0.09208 \cdot {23.22}^{4} - 0.42 \cdot {19.00}^{4}

Torsional index

X

22.44

-

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 8208.57 \cdot (2.177e+11))}{(20 \cdot 80769.2 \cdot 630028 \cdot (7.224e+6))}}

Geometric coefficient

g

0.98340

-

g = \sqrt{1 - \frac{I_{zz}}{I_{yy}}} = \sqrt{1 - \frac{(7.224e+6)}{(2.194e+8)}}

Buckling parameter

U

0.91836

-

U = {(\frac{Z_{yy} \cdot g}{A_{t}})}^{0.5} \cdot {(\frac{I_{zz}}{I_{w}})}^{0.25} = {(\frac{(1.222e+6) \cdot 0.98340}{8208.57})}^{0.5} \cdot {(\frac{(7.224e+6)}{(2.177e+11)})}^{0.25}