Design of Purlins :
Design data :
Spacing of purlins = 1.09 m
Max. Span of Purlin = 5.0 m
Angle of sloped roof = 18.747 degrees
Depth of Channel Purlin = 100 mm (Assumed)
Weight of Purlin = 0.090 kN/m
Grade of Steel (fy) = 250 N/mm2
Step 1 : Load calculations :
i. Dead Load :
Self weight of Sheeting = 0.069 kN/m2 (As per IS:875, (Part-I))
Self weight of fiixtures and fastings (assu = 0.100 kN/m 2
item 38 of table 1)
Self weight of purlin = 0.083 kN/m 2
Total dead load = 0.069 + 0.1 + 0.083
= 0.252 kN/m2
ii. Imposed Load :
Imposed Load = 0.75 - ( 0.02 x 8.747 )
= 0.576 kN/m 2
iii. Wind Load :
Wind pressure co-efficient = 1.300 (As per wind load calulation sheet)
Wind pressure = 1.176 kN/m2
Wind Load = 1.300 x 1.176
= 1.529 kN/m2
Step 2 : Bending Moment calculation :
DL+IL
Y
X
18.747 WL
i. Calculation of Loads :
a. Load nomal to the Purlin in kN/m
i. DL + IL = (0.252+0.576)*(COS(18.747*PI()/180))*1.09
= 0.855 kN/m
ii. DL + WL = ((0.252*(COS(18.747*PI()/180)))-(1.529))*1.09
= -1.407 kN/m
b. Load tangential to the Purlin in kN/m
i. DL + IL = (0.252+0.576)*(SIN(18.747*PI()/180))*1.09
= 0.290 kN/m
ii. DL + WL = ((0.252*(SIN(18.747*PI()/180)))*1.09
= 0.088 kN/m
Summary of loads :
Load nomal to Load Tangential to
Load case
the Purlin in kN/m the Pulin in kN/m
DL + IL 0.855 0.290
DL + WL 1.407 0.088
ii. Calculation of Bending Moments :
a. Moment normal to thePurlin :
i. DL + IL = (0.855 * 5 ^2)/10
= 2.137 kN-m
ii. DL + WL = (1.407 * 5 ^2)/10
= 3.516 kN-m
b. Moment tangential to the Purlin :
Note: Sag rod is provided at centre,hence half span is considered.
i. DL + IL = (0.291 * 2.5 ^2)/10
= 0.181 kN-m
ii. DL + WL = (0.089 * 2.5 ^2)/10
= 0.055 kN-m
Summary of Bending Moments :
Moment normal Moment tangential
Load case
to Purlin in kN-m to Purlin in kN-m
DL + IL 2.137 0.181
DL + WL 3.516 0.055
Allowable Bending Stress = 0.66* fy = 165.000 N/mm2 (For DL+IL case)
Allowable Bending Stress = 0.66*1.33 * fy = 219.450 N/mm2 (For DL+WL case)
iii. Calculation of Shear Forces :
a.Shear Force nomal to thePurlin :
i. DL + IL = (0.855 * 5 * 0.6)
= 2.564 kN
ii. DL + WL = (1.407 * 5 * 0.6)
= 4.220 kN
b. Shear Force tangential to the Purlin :
i. DL + IL = (0.291 * 2.5*0.6)
= 0.435 kN
ii. DL + WL = (0.089 * 5*0.6)
= 0.265 kN
Summary of Shear Forces :
Shear Force normal Shear Force tangential
Load case
to Purlin in kN to Purlin in kN
DL + IL 2.564 0.435
DL + WL 4.220 0.265
Step 3 : Selection of section :
Allowable Bending Stress = 0.66*250
(cl. 6.2.1 of IS 800-1984) = 165.000 N/mm2
Max. B.M. = 3.516 kN-m
Section Modulus Required = (3.517 * 10^6) / 165
= 21310.646 mm3
Provide ISMC100
Weight of the section = 0.090 kN/m
Area of the section = 1170 mm2
Width of channel = 50.000 mm
Thickness of flange = 7.500 mm
Thickness of web = 4.700 mm
Depth of section = 100.000 mm
M.I.about X-X Axis (Ixx) = 1867000 mm4
M.I.about Y-Y Axis (Iyy) = 259000.000 mm4
Sectiom Modulus (Zxx) = 37300.000 mm3
Sectiom Modulus (Zyy) = 7500.000 mm3
Centroid of Channel (Cyy) = 15.300 mm
Step 4 : Stresses calculation :
a. Bending Stresses :
i. DL + IL
a. In X- Direction (For Loads Normal to the Roof) :
Bending Compressive Stress = ((2.137*10^6)/1867000)*(100/2)
= 57.220 N/mm2
Bending Tensile Stress = ((2.137*10^6)/1867000)*(100/2)
= 57.220 N/mm2
b. In Y- Direction (For Loads Tangrntial to the Roof ) :
Bending Compressive Stress = ((0.182*10^6)/(259000))*(15.3)
= 10.709 N/mm2
Bending Tensile Stress = ((0.182*10^6)/1867000)*(50-15.3)
= 24.288 N/mm2
Summary of Bending Stresses :
For Normal Loads For Tangential Loads
σbcxx σbtxx σbcyy σbtyy
N/mm 2
N/mm 2
N/mm 2
N/mm2
57.220 57.220 10.709 24.288
ii. DL + WL
a. In X- Direction (For Loads Normal to the Roof) :
Bending Compressive Stress = ((3.517*10^6)/1867000)*(100/2)
= 94.169 N/mm2
Bending Tensile Stress = ((3.517*10^6)/1867000)*(100/2)
= 94.169 N/mm2
b. In Y- Direction (For Loads Tangrntial to the Roof ) :
Bending Compressive Stress = ((0.056*10^6)/(259000))*(15.3)
= 3.259 N/mm2
Bending Tensile Stress = ((0.056*10^6)/1867000)*(50-15.3)
= 1.025 N/mm2
Summary of Bending Stresses :
For Normal Loads For Tangential Loads
σbcxx σbtxx σbcyy σbtyy
N/mm 2
N/mm 2
N/mm 2
N/mm2
94.169 94.169 3.259 1.025
b. Shear Stresses:
Note :Web is critical in shear.
Depth of web = 100 - (2 * 7.5)
= 85.000 mm
Thickness of web = 4.700 mm
i. DL + IL :
Shear Stress for normal loads = (2.564*10^3) / (4.7*85)
= 6.418 N/mm2
Shear Stress for Tangential loads = (0.436*10^3)/(85*4.7)
= 1.089 N/mm2
Summary of Shear Stresses :
Vertical Loads Horizantal Loads
τxx τyy
N/mm2 N/mm2
6.418 1.089
Allowable Shear stress = 0.4*250 (cl. 6.4.2 of IS 800-1984)
= 100 N/mm2
Combination of stresses = τxx + τyy
Total Shear = 6.418 + 1.09
= 7.507 N/mm2
7.507 <= 100 Safe
ii. DL + WL
Shear Stress for normal loads = (4.22 * 10^3) / (4.7*85)
= 10.562 N/mm2
Shear Stress for Tangential loads = (0.265 * 10^3) / 399.5
= 0.663 N/mm2
Summary of Shear Stresses :
Vertical Loads Horizantal Loads
τxx τyy
N/mm2 N/mm2
10.562 0.663
Combination of stresses = τxx + τyy
Actual Total Shear = 10.562 + 0.663
= 11.225 N/mm2
Allowable Shear stress = 0.4 * 1.33 * fy = 133 N/mm2
11.225 <= 133 Safe
Step 5 : Check for Bending Stresses due to Normal and Tangential loads :
a. Bending Stress :
i. DL + IL
DL+IL
Y
2 = C+ C
C+T = 1
X 4 = T+ C
3 =T+T
Combined Stress at different Points :
At point 1 = 57.220 - 24.288
= 32.932 N/mm2
At point 2 = 57.220 + 10.709
= 67.929 N/mm2
At point 3 = - 57.220 - 24.288
= -81.508 N/mm2
At point 4 = - 57.220 + 10.709
= -46.511 N/mm2
Summary of Bending Stresses :
Point 1 Point 2 Point 3 Point 4
32.932 67.929 -81.508 -46.511
Allowable Bending Stress = 0.66* fy = 165 N/mm2
All are less than alowable. Hence Safe
ii. DL + WL
Y
2 =T+C
DL+WL
T+T= 1
X
4 =C+C
3 = C+T DL+WL
18.747
Allowable Bending Stress = 1.33* 0.66* fy = 219.45 N/mm2
Combined Stress at different Points :
At point 1 = -94.169 - 3.259
= - 90.909 N/mm2
At point 2 = -94.169 + 3.259
= - 97.428 N/mm2
At point 3 = 3.259 -94.169
= - 97.428 N/mm2
At point 4 = 94.169 + 3.259
= 97.428 N/mm2
Summary of Bending Stresses :
Point 1 Point 2 Point 3 Point 4
- 90.909 - 97.428 - 97.428 97.428
Allowable Bending Stress = 0.66 *1.33* fy = 219.45 N/mm2
All are less than alowable. Hence Safe
Step 6 : Check for Deflection :
Case : DL + IL, Normal to slope
DL+LL = 0.855 kN/m
Span (L) = 5.0 m
Maximum Deflection in the Purlin (δ) = 5 * w * l4
384 * E * Ixx
Maximum Deflection (δ) = 18.627 mm
Permissible Deflection (δ) = L /180 ( As per IS:800-2007, Cl.5.6.1 )
Permissible Deflection (δ) = 27.778 mm
18.627 <= 27.778 , Hence Provided Section is Safe
Step 7: Design of Sag Rod
Span of Purlins = 5.000 m
No. of Purlins = 5.0
Total load on Sag Rod = 5.0 x 0.435 x 5.00 x 5.00
8.0
= 6.798 kN
Required net area of Sag Rod = 6.798 x 10.0 ^3
150
= 45.322 mm2
Use ISRO 10 mm dia. Sag Rods.
Provided area of Sag rod = 78.540 mm2
Designati Weight Sectional Depth of Width of Thicknes Thicknes Moment of Inertia Raddi of Gyration
on per Area (a) Section flange s of s of Web
Meter (h) (b) Flange (tw)
(w) (tf)
kg cm2 mm mm mm mm
Ixx cm4 Iyy cm4 rxx cm
ISMB 100 8.9 11.4 100 50 7 4.2 257.5 40.8 4
ISMB 125 13 16.6 125 75 7.6 4.4 449 1.62 5.2
ISMB 150 14.9 19 150 80 7.6 4.8 726.4 1.66 6.18
ISMB 175 19.3 24.62 175 90 8.6 5.5 1272 1.86 7.19
ISMB 200 25.4 32.33 200 100 10.8 5.7 2235.4 2.15 8.32
ISMB 225 31.2 39.72 225 110 11.8 6.5 3441.8 2.34 9.31
ISMB 250 37.3 47.55 250 125 12.5 6.9 5131.6 2.65 10.39
ISMB 300 44.2 56.26 300 140 12.4 7.5 8603.6 2.84 12.37
ISMB 350 52.4 66.71 350 140 14.2 8.1 13630.3 2.84 14.29
ISMB 400 61.6 78.46 400 140 16 8.9 20458.4 2.82 16.15
ISMB 450 72.4 92.27 450 150 17.4 9.4 30390.8 3.01 18.15
ISMB 500 86.9 110.74 500 180 17.2 10.2 45218.3 3.52 20.21
ISMB 550 103.7 132.11 550 190 19.3 11.2 64893.6 1833.8 22.16
ISMB 600 122.6 156.21 600 210 20.8 12 91813 2651 24.24
ISMC 75 6.8 8.67 75 40 7.3 4.4 76 12.6 2.96
ISMC100 9.2 11.7 100 50 7.5 4.7 186.7 25.9 4
ISMC125 12.7 16.19 125 65 8.1 5 416.4 59.9 5.07
ISMC150 16.4 20.88 150 75 9 5.4 779.4 102.3 6.11
Raddi of Gyration Modulli of Section
ryy cm Zxx cm3 Zyy cm3
1.05 36.6 5
1.62 71.8 11.7
1.66 96.9 13.1
1.86 145.4 18.9
2.15 223.5 30
2.34 305.9 39.7
2.65 410.5 53.5
2.84 573.6 64.8
2.84 778.9 76.8
2.82 1022.9 88.9
3.01 1350.7 111.2
3.52 1808.7 152.2
3.73 2359.8 193
4.12 3060.4 252.5
1.21 20.3 4.7 1.31
1.49 37.3 7.5 1.53
1.92 66.6 13.1 1.94
2.21 103.9 19.4 2.22
