7/27/2019 Design of Burlin - C Shape 10x100 Board

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JOB NO.: Sign Board 10mx100m REV. NO: 0 Prepared by: a.shaban

Client: Hesham Date: 18-Jul-10 Checked by: M.Akh

Purlin Span = 6000 mm

Unsupported Length For Comp. Falnge = 1000 mm

Design Loads

Applied Uniform Dead Load = 14.10 KG/m'

Applied Uniform Wind Load = 66.8 KG/m'

Dimension

Length H = 100 mm

Width B = 80 mm

Thickness t = 3 mm

Inside bend radius r = 3 mm

Lip length BL = 20 mm

Material Properties

Yielding strength = 235 N/mm2

Ultimate Strength = 340 N/mm2

Elastic Modulus = 200000 N/mm2

Poisson's ration of steel μ = 0.30

Shear Modulus G = 76923 N/mm2 E/2/(1+poisson ratio)

Flat width to thickness consideration

Ratio of Unstiffned Flange b/t = 24.7 <60 Unstiffned element according to AISI B1.1

Ratio of stiffned Web h/t = 29.3 <200 stiffned element according to AISI B1.2

Shear lag effect L/WF = 77.9 >30 No shear lag effect according to AISI B1.1.C

Effective dime nsion consideration

For Compression Lip According AISI Clause B.3.1

d = 14 mm

t/d = 0.214

K = 0.43

Fcr = 3569 N/mm2

f = 235 N/mm2

λ = 0.26

p = 1.00 Full flange can be utilized

Effective Lip width d's = 14 mm d's=P x W

For Compression Flange According AISI Clause B.4.2

W = 68 mm

t/w = 0.044

w/t = 22.66667

s = 37.34

Ia = 701.976 mm4

n = 0.430247

d = 14 mm

d's = 14 mm check according to B.3.2

Is = 686.0 mm4

R1 = 1.0 mm4

D/w = 0.294118

K = 3.75 For 40° < θ < 140°

Fcr = 1318 N/mm2

f = 235 N/mm2

λ = 0.42

p = 1.00 Full flange can be utilized

Effective Flange width b = 68 mm b=P x W

b1 = 33.226 mm

b2 = 34.774 mm

 A.S.M 

Design Of Purlin According to AISI 2001 & Aashto

7/27/2019 Design of Burlin - C Shape 10x100 Board

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ds = 13.681 mm

For Web (assuming web under compression as conserative) According AISI Clause B.2.1

W = 88 mm

t / W = 0.034

K = 4

Poisson's ration of steel μ = 0.3

Fcr = 840 N/mm2

f = 235 N/mm2

λ = 0.53

p = 1.00 Full web can be utilized

Effective Web width b = 88 mm b=P x W

Effective Section Properties

Outside bend radius R = 6 mm

Left flange width B1 = 34.00 mm

Right flange width B2 = 34.00 mm

Left top web width B3 = 44.00 mm

Right top web width B4 = 44.00 mm

Left bottom web width B5 = 34.00 mm

Right bottom web width B6 = 34.00 mm

Left lip width B7 = 14.00 mm

Right lip width B8 = 14.00 mm

ItemArea

(mm2)

X dist.

(mm)

Y dist.

(mm)

X * area

(mm3)

Y * area

(mm3)

Ix

(mm4)

IY

(mm4)

Location OF Centre OF gravity B1 102.00 1.5 23.0 153.0 2346.0 17650 240006

Ẍ = 50.0 mm B2 102.00 98.5 23.0 10047.0 2346.0 17650 240006

Ẏ = 31.76 mm B3 132.00 28 1.5 3696.0 198.0 120952 85184

Effective Area A = 841 mm2 B4 132.00 72 1.5 9504.0 198.0 120952 85184

B5 102.00 1.5 57.0 153.0 5814.0 74816 240006

B6 102.00 98.5 57.0 10047.0 5814.0 74816 240006

B7 42.00 13 78.5 546.0 3297.0 91793 58184

B8 42.00 87 78.5 3654.0 3297.0 91793 58184

CornerL-Bot 21.21 6 74.0 127.2 1569.2 38077.7 41292.9

CornerR-Bot 21.21 94 74.0 1993.3 1569.2 38077.7 41292.9

Radius OF gyration CornerL-Top 21.21 6 6.0 127.2 127.2 14308.1 41292.9

rX = 29.16 mm CornerR-Top 21.21 94 6.0 1993.3 127.2 14308.1 41292.9

rY = 40.98 mm Sumation 840.8 - - 42041.2 26702.9 715193 1411932

Effective Section Elastic Modulus

Sxtop = 22520 mm

3

Sxbot = 14825 mm

3

SYleft = 28239 mm

3

SYright = 28239 mm

3

Gross Section Properties

Outside bend radius R = 6 mm

Left flange width B1 = 34.00 mm

Right flange width B2 = 34.00 mm

Left top web width B3 = 44.00 mm

Right top web width B4 = 44.00 mm

Left bottom web width B5 = 34.00 mm

Right bottom web width B6 = 34.00 mm

Left lip width B7 = 14.00 mm

Right lip width B8 = 14.00 mm

ItemArea

(mm2)

X dist.

(mm)

Y dist.

(mm)

X * area

(mm3)

Y * area

(mm3)

Ix

(mm4)

IY

(mm4)

Location OF Centre OF gravity B1 102 1.5 23.0 153.0 2346.0 17650 240006

Ẍ = 50.0 mm B2 102 98.5 23.0 10047.0 2346.0 17650 240006

7/27/2019 Design of Burlin - C Shape 10x100 Board

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Ẏ = 31.76 mm B3 132 28 1.5 3696.0 198.0 120952 85184

Gross Area A = 841 mm2 B4 132 72 1.5 9504.0 198.0 120952 85184

B5 102.00 1.5 57.0 153.0 5814.0 74816 240006

B6 102.00 98.5 57.0 10047.0 5814.0 74816 240006

B7 42.00 13 78.5 546.0 3297.0 91793 58184

B8 42.00 87 78.5 3654.0 3297.0 91793 58184

CornerL-Bot 21.21 6 74.0 127.2 1569.2 38077.7 41292.9

CornerR-Bot 21.21 94 74.0 1993.3 1569.2 38077.7 41292.9

Radius OF gyration CornerL-Top 21.21 6 6.0 127.2 127.2 14308.1 41292.9

rX = 19.81 mm CornerR-Top 21.21 94 6.0 1993.3 127.2 14308.1 41292.9

rY = 63.70 mm Sumation 840.8 - - 42041.2 26702.9 330072 ############

S aint venant tosion c on J = 25 22 .4 69 mm4

b = 77 mm d = 97 mm Bl = 18.5 mm

t = 3 mm Ix = 3412265 mm4

Shear Centre Offset m = 40.94 mm From Gregory J . Hancock Cold-Formed Steel Structures (Page 161)

Warping Constant Cw = 1.9E+09 mm6 From Gregory J. Hancock Cold-Formed Steel Structures (Page 16 1)

Gross Section Elastic Modulus

Sxtop = 10393 mm

3

Sxbot = 6842 mm

3

SYleft = 68245 mm

3

SYright = 68245 mm

3

Lateral Torsional buckling strength For Strong Axis

Lt = 1000 mm Torsional Length

KLx/rx = 50.5

xo = -72.70 mm

σey = 774.9 N/mm2

ro = 98.67 mm

σt = 473.40 N/mm2

Cb = 1.299 Eq. C3.1.2-11

Sf  = 68245 mm3

Fe = 956.4685 N/mm2 (Eq. C3.1.2-5)

2.78 Fy = 653.3 N/mm2

0.56 Fy = 131.6 N/mm2

Fc = 235 N/mm2 Fy Eq. C3.1.2-2

Mn = 6636078 N.mm

Max Allowable Bending Capacity = 5285021 N.mm Eq. C3.1.2.1-1

Moment Capacity For bending about weak axis

Mn = 3483907 N.mm

Max Al lowable Bending Capacity = 2774609 N.mm Eq. C3.1.1-1

Applied Bending Moment

Mx = 634520.7 N.mm = 0.63 KN.m

My = 3005794 N.mm = 3.01 KN.m

Interaction Equation

U.F = = 0.80 < 1.0 Safe section