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Purliin Design BS code
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Design of Purlins
Design data
Yield strength of steel py = 275.0 N/mm2
Slope of roof (to horizontal) = 10.0o
or 0.174 radians
Span of purlin l = 7.00 m
Spacing of purlins = 1.20 m
Sectional properties of purlin.
Member = RSC203x76x24
D = 203.2 B = 76.40 Z xx = 192.42 cm3
I xx = 1955.00 cm4
t = 7.1 T = 11.20 Z yy = 27.7 cm3
Iyy = 152.0 cm4
Gross area of cross section A = 30.4 cm2
r.min = 22.4 mm
Loads
Dead load
Roofing sheet & accessories load PDL-1 = 0.10 kN/m
Dead weight of purlin PDL-2 = 0.24 kN/m
Total PDL = 0.34 kN/m
Live load PLL = 1.00 kN/m
Wind load PWL = -1.32 kN/m
(-1.302x0.843x1.2-Refer Wind load calculations for roofs)
Load case I
a) Load combination 1.4DL+1.6LL
W1 = [1.4PDLcos(x)+ 1.6PLLcos(x)] = 2.0 kN/m
W1y = [1.4PDLsin(x)+1.6 PLLsin(x)] = 0.4 kN/m
b) Load combination 1.4DL+1.4WL
W2 = [PDLcos(x)+ PWLcos(x)] = -1.3 kN/m
W2y = [1.4PDLsin(x)+1.4 PWLsin(x)] = -0.2 kN/m
c) Load combination 1.2DL+1.2LL+1.2WL
W3 = [1.2PDLcos(x)+1.2PLLcos(x)+1.2 PWLcos(x)] = 0.0 kN/m
W3y = [1.2PDLsin(x)+1.2 PLLsin(x)+1.2 PWLsin(x)] = 0.0 kN/m
Case a) and Case b) are critical, case a) adopted for deisgn.
Load combination 1.4DL+1.6LL
Applied moment at mid span of purlin
M xx = 12.52 kN-m
M xx = [P DLcos(x )+ P LLcos(x )]*leff2/8
Effective length =1.0*L =leff l=leff = 7.00 m
Note: Sag rods are provided at mid span of every purlin. Hence, connection point of sag rod to purlin
will act as a support in y-y axis of purlin and the effective length in y-y axis will be 0.5 times the
spacing of truss.
M yy = 0.44 kN-m
M yy = ([P DLsin(x )+ P LLsin(x )]*(l /2)2)/10
Moment capacity check:
Moment capacity of Mazor axis, Mcx = 63.50 kN-m
Moment capacity of Minor axis, Mcy = 9.14 kN-m
(Mc = 1.2 x py x Z)
Local capacity of check, Mxx/Mcx+Myy/Mcy < 1
Mxx/Mcx+Myy/Mcy = 0.25
Hence ok
PDL*sin(x)/
PLL*sin(x)
x
PDL/PL
PDL*cos(x)/
PLL*cos(x)/
PWL
Buckling capacity check:
Slenderness ratio, Leff/r.min = 312.50
Equivalent Slenderness ratio, lLT = uvw
buckling parameter, u = 0.90
Torsional index, x = D/T = 18.14
Ratio, w = 1.00
The slenderness factor, v = 0.50 (v = 1/(1+0.05x(/x)2)0.25
)
Equivalent Slenderness ratio, lLT = 140.99
Bending strength, pb = 74.20 N/mm2
(From table-16 of BS 5950-2000, part-1)
Buckling resisting moment, Mb = 1.2 x pb x Zx = 17.13 kN.m
The overall buckling check, mMx/Mb+mMyy/Mcy < 1
mMx/Mb+mMyy/Mcy = 0.78
Hence ok
Shear check:
Max. shear force, wL/2 = 1.26 kN
Shear area, Avx = 1442.72 mm2
Shear capacity, Pvx = 0.6 x py x Avx = 238.05 kN
Shear area, Avy = 0.9 x Ao = 1540.22 mm2
(Ao = area of flanges)
Shear capacity, Pvx = 0.6 x py x Avx = 254.14 kN
Hence ok
Check of deflection:
Deflection, dx = 10.29 mm
dx = (5 x wl4)/384EI
Deflection, dy = 1.46 mm
dy = (5 x wl4)/384EI
Allowable deflection, d.allow = 28.00 mm
(d.allow = L/250, as per SP-1275) Hence ok
Cladding Purlin
Design data
Yield strength of steel py = 275.0 N/mm2
Span of purlin l = 7.00 m
Spacing of purlins = 1.20 m
Sectional properties of purlin.
Member = RSC203x76x24
D = 203.2 B = 76.40 Z xx = 192.42 cm3
I xx = 1955.00 cm4
t = 7.1 T = 11.20 Z yy = 27.7 cm3
Iyy = 152.0 cm4
Gross area of cross section A = 30.4 cm2
r.min = 22.4 mm
Loads
Dead load
Roofing sheet & accessories load PDL-1 = 0.14 kN/m
Dead weight of purlin PDL-2 = 0.24 kN/m
Total PDL = 0.38 kN/m
Wind load PWL = 1.36 kN/m
(1.1x0.826x1.5-Refer Wind load calculations on walls)
Load combination 1.4WL
Applied moment at mid span of purlin
M xx = P WL*leff2/8 M xx = 11.66 kN-m
Effective length =1.0*L =leff l=leff = 7.00 m
Note: Sag rods are provided at mid span of every purlin. Hence, connection point of sag rod to purlin
will act as a support in y-y axis of purlin and the effective length in y-y axis will be 0.5 times the
spacing of truss. Calculations in this direction are negelected,hence Dead load is very small)
Moment capacity check:
Moment capacity of Mazor axis, Mcx = 63.50 kN-m
Moment capacity of Minor axis, Mcy = 9.14 kN-m
(Mc = 1.2 x py x Z)
Local capacity of check, Mxx/Mcx < 1
Mxx/Mcx = 0.18
Hence ok
Buckling capacity check:
Slenderness ratio, Leff/r.min = 312.50
Equivalent Slenderness ratio, lLT = uvw
buckling parameter, u = 0.90
Torsional index, x = D/T = 18.14
Ratio, w = 1.00
The slenderness factor, v = 0.50 (v = 1/(1+0.05x(/x)2)0.25
)
Equivalent Slenderness ratio, lLT = 140.99
Bending strength, pb = 74.20 N/mm2
(From table-16 of BS 5950-2000, part-1)
Buckling resisting moment, Mb = pb x Zx = 14.28 kN.m
The overall buckling check, mMx/Mb
mMx/Mb+mMyy/Mcy = 0.82
Hence ok
Shear check:
Max. shear force, wL/2 = 1.31 kN
Shear area, Avx = 1442.72 mm2
Shear capacity, Pvx = 0.6 x py x Avx = 238.05 kN
Shear area, Avy = 0.9 x Ao = 1540.22 mm2
(Ao = area of flanges)
Shear capacity, Pvx = 0.6 x py x Avx = 254.14 kN
Hence ok
Check of deflection:
Deflection, dx = 10.61 mm
dx = (5 x wl4)/384EI
Deflection, dy = 2.35 mm
dy = (5 x wl4)/384EI
Allowable deflection, d.allow = 28.00 mm
(d.allow = L/250, as per SP-1275) Hence ok
PDL
PWL
Design of Purlins
Design data
Yield strength of steel py = 275.0 N/mm2
Slope of roof (to horizontal) = 10.0o
or 0.174 radians
Span of purlin l = 7.00 m
Spacing of purlins = 1.20 m
Sectional properties of purlin.
Member = RSC203x76x24
D = 203.2 B = 76.40 Z xx = 192.42 cm3
I xx = 1955.00 cm4
t = 7.1 T = 11.20 Z yy = 27.7 cm3
Iyy = 152.0 cm4
Gross area of cross section A = 30.4 cm2
r.min = 22.4 mm
Loads
Dead load
Roofing sheet & accessories load PDL-1 = 0.10 kN/m
Dead weight of purlin PDL-2 = 0.24 kN/m
Total PDL = 0.34 kN/m
Live load PLL = 1.00 kN/m
Wind load PWL = 0.84 kN/m
(0.833x0.843x1.20-Refer Wind load calculations for roofs)
Load case I
a) Load combination 1.4DL+1.6LL
W1 = [1.4PDLcos(x)+ 1.6PLLcos(x)] = 2.0 kN/m
W1y = [1.4PDLsin(x)+1.6 PLLsin(x)] = 0.4 kN/m
b) Load combination 1.4DL+1.4WL
W2 = [PDLcos(x)+ PWLcos(x)] = 1.6 kN/m
W2y = [1.4PDLsin(x)+1.4 PWLsin(x)] = 0.3 kN/m
c) Load combination 1.2DL+1.2LL+1.2WL
W3 = [1.2PDLcos(x)+1.2PLLcos(x)+1.2 PWLcos(x)] = 2.6 kN/m
W3y = [1.2PDLsin(x)+1.2 PLLsin(x)+1.2 PWLsin(x)] = 0.5 kN/m
Case a) and Case b) are critical, case c) adopted for deisgn.
c) Load combination 1.2DL+1.2LL+1.2WL
Applied moment at mid span of purlin
M xx = 15.80 kN-m
M xx = [P DLcos(x )+ P LLcos(x )+PWL cos(x)]*leff2/8
Effective length =1.0*L =leff l=leff = 7.00 m
Note: Sag rods are provided at mid span of every purlin. Hence, connection point of sag rod to purlin
will act as a support in y-y axis of purlin and the effective length in y-y axis will be 0.5 times the
spacing of truss.
M yy = 0.56 kN-m
M yy = ([P DLsin(x )+ P LLsin(x )+PWL sin(x)]*(l /2)2)/10
Moment capacity check:
Moment capacity of Mazor axis, Mcx = 63.50 kN-m
Moment capacity of Minor axis, Mcy = 9.14 kN-m
(Mc = 1.2 x py x Z)
Local capacity of check, Mxx/Mcx+Myy/Mcy < 1
Mxx/Mcx+Myy/Mcy = 0.31
Hence ok
PDL*sin(x)/
PLL*sin(x)
x
PDL/PL
PDL*cos(x)/
PLL*cos(x)/
PWL
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Buckling capacity check:
Slenderness ratio, Leff/r.min = 312.50
Equivalent Slenderness ratio, lLT = uvw
buckling parameter, u = 0.90
Torsional index, x = D/T = 18.14
Ratio, w = 1.00
The slenderness factor, v = 0.50 (v = 1/(1+0.05x(/x)2)0.25
)
Equivalent Slenderness ratio, lLT = 140.99
Bending strength, pb = 94.90 N/mm2
(From table-16 of BS 5950-2000, part-1)
Buckling resisting moment, Mb = 1.2 x pb x Zx = 21.91 kN.m
The overall buckling check, mMx/Mb+mMyy/Mcy < 1
mMx/Mb+mMyy/Mcy = 0.8
Hence ok
Shear check:
Max. shear force, wL/2 = 1.26 kN
Shear area, Avx = 1442.72 mm2
Shear capacity, Pvx = 0.6 x py x Avx = 238.05 kN
Shear area, Avy = 0.9 x Ao = 1540.22 mm2
(Ao = area of flanges)
Shear capacity, Pvx = 0.6 x py x Avx = 254.14 kN
Hence ok
Check of deflection:
Deflection, dx = 10.29 mm
dx = (5 x wl4)/384EI
Deflection, dy = 1.46 mm
dy = (5 x wl4)/384EI
Allowable deflection, d.allow = 28.00 mm
(d.allow = L/250, as per SP-1275) Hence ok
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Cladding Purlin
Design data
Yield strength of steel py = 275.0 N/mm2
Span of purlin l = 7.00 m
Spacing of purlins = 1.20 m
Sectional properties of purlin.
Member = RSC203x76x24
D = 203.2 B = 76.40 Z xx = 192.42 cm3
I xx = 1955.00 cm4
t = 7.1 T = 11.20 Z yy = 27.7 cm3
Iyy = 152.0 cm4
Gross area of cross section A = 30.4 cm2
r.min = 22.4 mm
Loads
Dead load
Roofing sheet & accessories load PDL-1 = 0.14 kN/m
Dead weight of purlin PDL-2 = 0.24 kN/m
Total PDL = 0.38 kN/m
Wind load PWL = 1.36 kN/m
(1.1x0.826x1.5-Refer Wind load calculations on walls)
Load combination 1.4WL
Applied moment at mid span of purlin
M xx = P WL*leff2/8 M xx = 11.66 kN-m
Effective length =1.0*L =leff l=leff = 7.00 m
Note: Sag rods are provided at mid span of every purlin. Hence, connection point of sag rod to purlin
will act as a support in y-y axis of purlin and the effective length in y-y axis will be 0.5 times the
spacing of truss. Calculations in this direction are negelected,hence Dead load is very small)
Moment capacity check:
Moment capacity of Mazor axis, Mcx = 63.50 kN-m
Moment capacity of Minor axis, Mcy = 9.14 kN-m
(Mc = 1.2 x py x Z)
Local capacity of check, Mxx/Mcx < 1
Mxx/Mcx = 0.18
Hence ok
Buckling capacity check:
Slenderness ratio, Leff/r.min = 312.50
Equivalent Slenderness ratio, lLT = uvw
buckling parameter, u = 0.90
Torsional index, x = D/T = 18.14
Ratio, w = 1.00
The slenderness factor, v = 0.50 (v = 1/(1+0.05x(/x)2)0.25
)
Equivalent Slenderness ratio, lLT = 140.99
Bending strength, pb = 74.20 N/mm2
(From table-16 of BS 5950-2000, part-1)
Buckling resisting moment, Mb = pb x Zx = 14.28 kN.m
The overall buckling check, mMx/Mb
mMx/Mb+mMyy/Mcy = 0.82
Hence ok
Shear check:
Max. shear force, wL/2 = 1.31 kN
Shear area, Avx = 1442.72 mm2
Shear capacity, Pvx = 0.6 x py x Avx = 238.05 kN
Shear area, Avy = 0.9 x Ao = 1540.22 mm2
(Ao = area of flanges)
Shear capacity, Pvx = 0.6 x py x Avx = 254.14 kN
Hence ok
Check of deflection:
Deflection, dx = 10.61 mm
dx = (5 x wl4)/384EI
Deflection, dy = 2.35 mm
dy = (5 x wl4)/384EI
Allowable deflection, d.allow = 28.00 mm
(d.allow = L/250, as per SP-1275) Hence ok
PDL
PWL
8 of 5
