Purlin Check - Member Properties

C PURLIN DESIGN CALCULATION SIMPLE SPAN Member Properties Purlin Size Purlin span, L Purlin spacing, Pitch angle Thickness, t Depth, D

= = = = = =

YCP 1716 8.65 1 7 1.6 175

m m degree mm mm

Design strength, p y

=

450

N/mm

Yield strength, Ys

=

450

N/mm3

Elastic modulus, Zx-x

=

29.85

x 103 mm3

Elastic modulus, Zy-y Ix-x

=

7.1

x 10 mm

=

2.588

x 106 mm4

Support condition Coefficient for bending Coefficient for deflection

= = =

1 0.125 0.01302

Load Data Dead load, DL

=

0.15

kN/m2

Live Load, LL

=

0.25

kN/m2

Load Combination 1.4DL+1.6LL

=

0.61

kN/m2

= =

0.61 0.61

x kN/m

Design ultimate load, W

4.27 kg/m

2

3

3

(1 = simply support, 2 = double span, 3 = continuos)

1

Bending Stress Calculation Max. Bending Moment, Mx

= =

(Wx L²) x 5.66

0.125 x cos kNm

7 °

Max. Bending Moment, My

= =

(Wx L²) x 0.69

0.125 x sin kNm

7 °

Bending stress (x-x)

= =

Mx/Zx 189.71

N/mm2

= =

My/Zy 97.88

N/mm2

=

1     D  Ys  2    py 1.13  0.0019  t  280      

=

389.95

N/mm2

= =

389.95 1.36

/ (My/Zy) + (Mx/Zx)

Bending stress (y-y)

Allowable bending stress

Factor of safety

BS 5950 : 5 CL 5.2.2.2

OK

Deflection Check Deflection, D

=

for serviceability dead load

=

20.61

mm

for serviceability live load

=

34.35

mm

Allowable deflection

= =

L/150 57.67

mm

= =

57.67 1.05

Factor of safety

No. 1 2 3 4

0.01302

WL4/EIx

x

/

54.96 OK

Table of Coefficient Support Condition Bending simply-supported 0.12500 double span 0.12500 continuos span 0.08330 cantilever 0.50000

Deflection 0.01302 0.00540 0.00607 0.12500

Bolt Shear Capacity No of bolts =

2

nos

Diameter of bolts =

12

mm

Bolt Grade =

4.6

Shear Area, As =

84.3

N/mm

Shear Strength, ps =

160

N/mm

Shear Capacity per bolts =

13.49

kN

Shear Capacity of Purlin Cleat Bolts =

26.98

kN

2 2

Section Identification YCP 1016 YCP 1020 YCP 1025 YCP 1030 YCP 1216 YCP 1220 YCP 1225 YCP 1230 YCP 1516 YCP 1520 YCP 1525 YCP 1530 YCP 1716 YCP 1720 YCP 1725 YCP 1730 YCP 2016 YCP 2020 YCP 2025 YCP 2030 YCP 2216 YCP 2220 YCP 2225 YCP 2230 YCP 2520 YCP 2525 YCP 2530 YCP 3020 YCP 3025 YCP 3030 YCP 3520 YCP 3525 YCP 3530

Area

Ix

Iy

Zx

Zy

kg/m

D

t

357 442 546 648 397 492 609 723 486 604 749 891 538 668 829 987 582 724 899 1071 646 804 999 1191 854 1061 1266 1054 1311 1566 1274 1586 1896

0.595 0.730 0.892 1.045 0.990 1.218 1.491 1.753 1.808 2.230 2.741 3.235 2.588 3.197 3.936 4.652 3.654 4.517 5.568 6.589 4.988 6.174 7.621 9.031 7.907 9.767 11.580 14.250 17.640 20.970 23.970 29.720 35.390

0.132 0.160 0.193 0.223 0.142 0.172 0.208 0.240 0.281 0.344 0.417 0.486 0.351 0.430 0.523 0.610 0.368 0.450 0.547 0.639 0.498 0.611 0.745 0.872 0.630 0.769 0.900 1.250 1.533 1.804 2.451 3.018 3.566

11.85 14.60 17.92 21.11 15.79 19.48 23.95 28.27 23.88 29.54 36.43 43.13 29.85 36.96 45.64 54.09 36.29 44.95 55.54 65.89 44.66 55.37 68.51 81.36 63.77 78.93 93.78 95.64 118.60 141.20 137.70 171.10 204.00

4.05 4.95 6.01 7.01 4.15 5.07 6.16 7.19 6.25 7.67 9.36 10.97 7.10 8.72 10.66 12.51 7.21 8.85 10.82 12.70 8.89 10.93 13.40 15.76 11.04 13.54 15.92 18.03 22.20 26.23 28.30 34.96 41.43

3.05 3.72 4.60 5.29 3.20 3.94 4.89 5.90 4.01 4.92 6.01 7.35 4.27 5.26 6.67 8.08 4.70 5.74 7.13 8.79 5.28 6.55 8.16 9.80 6.69 8.34 10.20 8.63 10.84 12.10 9.92 12.37 15.07

102 102 102 102 127 127 127 127 153 153 153 153 175 175 175 175 203 203 203 203 225 225 225 225 250 250 250 300 300 300 350 350 350

1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 2.0 2.5 3.0 2.0 2.5 3.0 2.0 2.5 3.0

Z PURLIN DESIGN CALCULATION SIMPLE SPAN Member Properties Purlin Size Purlin span, L Purlin spacing, Pitch angle Thickness, t Depth, D

= = = = = =

YZP 2020 6 1.2 5 2 203

m m degree mm mm

Design strength, p y

=

450

N/mm

Yield strength, Ys

=

450

N/mm3

Elastic modulus, Zx-x

=

44.2

x 103 mm3

Elastic modulus, Zy-y Ix-x

=

9.79

x 10 mm

=

4.912

x 106 mm4

Support condition Coefficient for bending Coefficient for deflection

= = =

1 0.125 0.01302

Load Data Dead load, DL

=

0.3

kN/m2

Live Load, LL

=

0.25

kN/m2

Load Combination 1.4DL+1.6LL

=

0.82

kN/m2

= =

0.82 0.98

x kN/m

Design ultimate load, W

5.74 kg/m

2

3

3

(1 = simply support, 2 = double span, 3 = continuos)

1.2

Bending Stress Calculation Max. Bending Moment, Mx

= =

(Wx L²) x 4.41

0.125 x cos kNm

5 °

Max. Bending Moment, My

= =

(Wx L²) x 0.39

0.125 x sin kNm

5 °

Bending stress (x-x)

= =

Mx/Zx 99.80

N/mm2

= =

My/Zy 39.40

N/mm2

=

1     D  Ys  2    py 1.13  0.0019  t  280      

=

398.48

N/mm2

= =

398.48 2.86

/ (My/Zy) + (Mx/Zx)

Bending stress (y-y)

Allowable bending stress

Factor of safety

BS 5950 : 5 CL 5.2.2.2

OK

Deflection Check Deflection, D

=

for serviceability dead load

=

6.03

mm

for serviceability live load

=

5.03

mm

Allowable deflection

= =

L/150 40.00

mm

= =

40.00 3.62

Factor of safety

No. 1 2 3 4

0.01302

WL4/EIx

x

/

11.06 OK

Table of Coefficient Support Condition Bending simply-supported 0.12500 double span 0.12500 continuos span 0.08330 cantilever 0.50000

Deflection 0.01302 0.00540 0.00607 0.12500

Bolt Shear Capacity No of bolts Diameter of bolts Bolt Grade Shear Area, As

= = = =

2 12 4.6 84.3

nos mm

Shear Strength, ps =

160

N/mm

Shear Capacity per bolts = Shear Capacity of Purlin Cleat Bolts =

13.49 26.98

N/mm

kN kN

2 2

Section Identification YZP 1016 YZP 1020 YZP 1025 YZP 1030 YZP 1216 YZP 1220 YZP 1225 YZP 1230 YZP 1516 YZP 1520 YZP 1525 YZP 1530 YZP 1716 YZP 1720 YZP 1725 YZP 1730 YZP 2016 YZP 2020 YZP 2025 YZP 2030 YZP 2216 YZP 2220 YZP 2225 YZP 2230 YZP 2520 YZP 2525 YZP 2530 YZP 3020 YZP 3025 YZP 3030 YZP 3520 YZP 3525 YZP 3530

Area

Ix

Iy

Zx

Zy

kg/m

D

t

366 454 561 666 406 504 624 741 483 600 744 885 538 668 829 987 582 724 899 1071 637 792 984 1173 850 1056 1260 1056 1314 1569 1290 1606 1920

0.805 0.985 1.199 1.402 1.198 1.471 1.797 2.108 2.066 2.544 3.120 3.673 2.931 3.615 4.443 5.242 3.977 4.912 6.046 7.144 5.257 6.500 8.012 9.480 8.294 10.240 12.120 15.370 19.010 22.570 26.850 33.270 39.580

0.087 0.105 0.127 0.148 0.102 0.124 0.150 0.173 0.169 0.206 0.250 0.292 0.221 0.271 0.330 0.385 0.241 0.295 0.359 0.420 0.300 0.368 0.448 0.525 0.403 0.492 0.577 0.845 1.037 1.221 1.730 2.131 2.521

12.00 14.79 18.16 21.40 16.00 19.74 24.28 28.66 23.17 28.64 35.32 41.80 29.31 36.29 44.80 53.10 35.68 44.20 54.61 64.77 42.92 53.21 65.81 78.13 62.10 76.86 91.31 94.65 117.40 139.70 138.80 172.40 205.50

5.08 6.22 7.56 8.82 5.07 6.20 7.54 8.80 6.88 8.44 10.31 12.07 7.98 9.80 11.98 14.05 7.97 9.79 11.96 14.03 9.20 11.31 13.85 16.28 11.88 14.55 17.11 19.93 24.53 28.98 33.04 40.81 48.38

3.05 3.72 4.60 5.29 3.20 3.94 4.89 5.90 4.01 4.92 6.01 7.35 4.27 5.26 6.67 8.08 4.70 5.74 7.13 8.79 5.28 6.55 8.16 9.80 6.69 8.34 10.20 8.71 10.84 12.10 9.92 12.37 15.07

102 102 102 102 127 127 127 127 153 153 153 153 175 175 175 175 203 203 203 203 225 225 225 225 250 250 250 300 300 300 350 350 350

1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 1.6 2.0 2.5 3.0 2.0 2.5 3.0 2.0 2.5 3.0 2.0 2.5 3.0