Purlin Design As Per Is 800 2007

Design of Purlins per IS:800, 2007 & SP38, 1987:

(IS:800,2007 clause - 8.9, 8.4, 8.2.1, 8.2.2, 5.6.1, 5.3.3, 3.8, 3.5.1, Table-2, Table-3, Table-4, Table-6) Data: General Arrangement, Material Properties & Section Properties: 2 Yield Stress for the Steel, fy = 250 N/mm

2 Elastic Modulus of Steel, Es = 200000 N/mm Partial Safety Factor for Materials, γ m0 (Table-5) = 1.10 Slope of Roof, θ = 5.71 degrees Effective Length of the Purlin, @ Z-axis, Lz = 6 m Effective Length of the Purlin, @ Y-axis, Ly = 3 m …...with due consideration of sag rods. Maximum c/c spacing of purlins, s = 1.5 m Purlin Section = ISMC 125 Section properties for ISMC 125 : (All ISMC Channels are Class-1 Plastic Sections) 2 Azz = rzz = 16.19 cm 5.07 cm 4 cm Izz = ryy = 416.4 1.92 cm

Iyy

Zzz

=

=

4 59.9 cm 3 66.6 cm

cyy

=

λzz = Lz/rzz =

1.94 cm

118.3 <=300 , Hence O.K.

…. (Cl.- 3.8) 3 Zyy = λyy= Ly/ryy = 13.1 cm 156.3 <=300 , Hence O.K. …. (Cl.- 3.8) Design Shear Strength for the Section, V d @ major axis z-z = 71.38 KN …. (cl. 8.4) Design Shear Strength for the Section, V d @ minor axis y-y = 138.17 KN …. (cl. 8.4) 2 Permissible Bending Stress for the section = fy / γmo = 227 N/mm …. (cl. 8.2.1.2) …. Rounded to preceding highest integer. Forces & Moments: Load case 1- Dead Load, DL 2 Weight of Sheeting = 0.08 KN/m 2 Other Loads (insulation, sag rods etc…) = 0.005 KN/m 2 Therefore Total Dead Load = 0.085 KN/m Udl on Purlin due to Dead Load, = 0.128 KN/m Self weight of Purlin, ISMC 125 = 0.127 KN/m Total Udl = 0.255 KN/m Load case 2- Live Load, LL 2 Total Live Load = 0.75 KN/m Udl on Purlin due to Live Load, = 1.125 KN/m Load case 3- Wind Load, WL C/S of Purlin 2 Maximum Upward Wind Pressure = 0.8 KN/m Udl on Purlin due to Upward Wind Pressure = 1.2 KN/m 2 Maximum Downward Wind Pressure = 0.5 KN/m Udl on Purlin due to Downward Wind Pressure = 0.75 KN/m Load Factors, γf for Load Combinations considered as per clauses- 3.5.1 & 5.3.3 & Table-4 : Limit State of Strength Limit State of Serviceability Combinations DL LL WL DL LL WL 1. DL+LL 1.5 1.5 --1.0 1.0 --2. DL+WL(Upwards) 0.9 --1.5 1.0 --1.0 3. DL+WL(Downwards) 1.5 --1.5 1.0 --1.0 4. DL+LL+WL(Dnwards) 1.2 1.2 0.6 0.8 0.8 0.8 Load combination 1- DL+LL Factored Udl on Purlin due to DL+LL = 2.069 KN/m …. Acting Vertically Downwards. Shear Force, @ local Z-axis (major), Vz = 6.18 KN Shear Force, @ local Y-axis (minor), Vy = 0.62 KN Bending Moment, @ local Z-axis (major), Mz = 9.27 KN.m Bending Moment, @ local Y-axis (minor), M y = 0.23 KN.m Checking the section ISMC 125 Check for Stressesf bc = (Mz / Zzz) + (My / Zyy) = ( (9.27 x 10^6) / (66.6 x 10^3) ) + ( (0.23 x 10^6) / (13.1 x 10^3) ) N/mm2 = 156.75 <= 227 N/sq.mm, O.K. Section Utilization Ratio = 0.69 Check for Deflection- (cl.5.6.1, Table-6) Deflection @ major axis, Z-Z: Actual Deflection, d = (5/384) x w x L 4 / (E x I) = 27.81 mm <= L/150 = 40mm , O.K. Deflection @ minor axis, Y-Y: Actual Deflection, d = (5/384) x w x L 4 / (E x I) = 0.64 mm <= L/150 = 20mm , O.K.

Load combination 2- DL+WL (Upward Wind Pressure) Factored Udl on Purlin due to DL+WL = -1.572 KN/m …. Negative sign indicates Net Uplift. Shear Force, @ local Z-axis (major), Vz = 4.72 KN Shear Force, @ local Y-axis (minor), Vy = 0.07 KN Bending Moment, @ local Z-axis (major), Mz = 7.07 KN.m Bending Moment, @ local Y-axis (minor), M y = 0.03 KN.m Checking the section ISMC 125 Check for Stressesf bc = (Mz / Zzz) + (My / Zyy) = ( (7.07 x 10^6) / (66.6 x 10^3) ) + ( (0.03 x 10^6) / (13.1 x 10^3) ) N/mm2 = 108.45 <= 227 N/sq.mm, O.K. Section Utilization Ratio = 0.48 Check for Deflection- (cl.5.6.1, Table-6) Deflection @ major axis, Z-Z: Actual Deflection, d = (5/384) x w x L 4 / (E x I) = 19.18 mm <= L/150 = 40mm , O.K. Deflection @ minor axis, Y-Y: Actual Deflection, d = (5/384) x w x L 4 / (E x I) = 0.22 mm <= L/150 = 20mm , O.K. Load combination 3- DL+WL (Downward Wind Pressure) Factored Udl on Purlin due to DL+WL = 1.505 KN/m …. Acting Normal to Flange of the Purlin. Shear Force, @ local Z-axis (major), Vz = 4.51 KN Shear Force, @ local Y-axis (minor), Vy = 0.11 KN Bending Moment, @ local Z-axis (major), Mz = 6.77 KN.m Bending Moment, @ local Y-axis (minor), M y = 0.04 KN.m Checking the section ISMC 125 Check for Stressesf bc = (Mz / Zzz) + (My / Zyy) = ( (6.77 x 10^6) / (66.6 x 10^3) ) + ( (0.04 x 10^6) / (13.1 x 10^3) ) N/mm2 = 104.71 <= 227 N/sq.mm, O.K. Section Utilization Ratio = 0.46 Check for Deflection- (cl.5.6.1, Table-6) Deflection @ major axis, Z-Z: Actual Deflection, d = (5/384) x w x L 4 / (E x I) = 20.33 mm <= L/150 = 40mm , O.K. Deflection @ minor axis, Y-Y: 4 Actual Deflection, d = (5/384) x w x L / (E x I) = 0.22 mm <= L/150 = 20mm , O.K. Load combination 4- DL+LL+WL (Downward Wind Pressure) Factored Udl on Purlin due to DL+LL+WL = 2.097 KN/m …. Acting Normal to Flange of the Purlin. Shear Force, @ local Z-axis (major), Vz = 6.29 KN Shear Force, @ local Y-axis (minor), Vy = 0.49 KN Bending Moment, @ local Z-axis (major), Mz = 9.44 KN.m Bending Moment, @ local Y-axis (minor), M y = 0.19 KN.m Checking the section 0.62 Check for Stressesf bc = (Mz / Zzz) + (My / Zyy) = ( (9.44 x 10^6) / (66.6 x 10^3) ) + ( (0.19 x 10^6) / (13.1 x 10^3) ) N/mm2 = 156.25 <= 227 N/sq.mm, O.K. Section Utilization Ratio = 0.69 Check for Deflection- (cl.5.6.1, Table-6) Deflection @ major axis, Z-Z: Actual Deflection, d = (5/384) x w x L 4 / (E x I) = 34.41 mm <= L/150 = 40mm , O.K. Deflection @ minor axis, Y-Y: Actual Deflection, d = (5/384) x w x L 4 / (E x I) = 0.97 mm <= L/150 = 20mm , O.K. Conclusion: For the above Load Combinations, 1) Section is safe against Limit State of Strength. 2) Section is safe against Limit State of Serviceability (Deflection). 3) Section, has more than 54% Reserved Strength.