Design of Purlins Design data Yield strength of steel Slope of roof (to horizontal)
py = =
Span of purlin Spacing of purlins
2 275.0 N/mm 10.0 o or
l =
7.00 m
=
1.20 m
0.174 radians
Sectional properties of purlin. Member D = 203.2 B = 76.40 t
=
7.1
= RSC203x76x24 3 Z xx = 192.42 cm 3 Z yy = 27.7 cm
T = 11.20
Gross area of cross section Loads Dead load Roofing sheet & accessories load Dead weight of purlin Total
A =
30.4 cm
2
4 I xx = 1955.00 cm 4 cm = 152.0 Iyy
r.min =
22.4 mm PDL/PL
PDL-1 = PDL-2 = PDL =
0.10 kN/m 0.24 kN/m
PLL = PWL =
1.00 kN/m
Live load Wind load
0.34 kN/m
PDL*cos(x)/ PLL*cos(x)/ PWL PDL*sin(x)/ PLL*sin(x)
-1.32 kN/m
(-1.302x0.843x1.2-Refer Wind load calculations for roofs) Load case I a) Load combination 1.4DL+1.6LL W 1 = [1.4PDLcos(x)+ 1.6PLLcos(x)]
=
2.0
kN/m
W 1y = [1.4PDLsin(x)+1.6 PLLsin(x)]
=
0.4
kN/m
b) Load combination 1.4DL+1.4WL W 2 = [PDLcos(x)+ PWLcos(x)] W 2y = [1.4PDLsin(x)+1.4 PWLsin(x)]
= =
-1.3 -0.2
kN/m kN/m
c) Load combination 1.2DL+1.2LL+1.2WL W 3 = [1.2PDLcos(x)+1.2PLLcos(x)+1.2 PWLcos(x)] W 3y = [1.2PDLsin(x)+1.2 PLLsin(x)+1.2 PWLsin(x)]
= =
0.0 0.0
kN/m kN/m
x
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 = M xx
12.52 kN-m
2 = [P DLcos(x )+ P LLcos(x )]*leff /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 2 M yy = ([P DLsin(x )+ P LLsin(x )]*(l /2) )/10 Moment capacity check: Moment capacity of Mazor axis, Mcx Moment capacity of Minor axis, Mcy (Mc = 1.2 x py x Z) Local capacity of check, Mxx/Mcx+Myy/Mcy < 1 Mxx/Mcx+Myy/Mcy
= =
=
63.50 9.14
kN-m kN-m
0.25 Hence ok
Buckling capacity check: Slenderness ratio, Leff/r.min Equivalent Slenderness ratio, lLT
= 312.50 = uvw
buckling parameter, u Torsional index, x = D/T Ratio, w
= = =
The slenderness factor, v Equivalent Slenderness ratio, lLT
= 0.50 = 140.99
(v = 1/(1+0.05x(/x) )
Bending strength, pb
=
74.20
N/mm2
Buckling resisting moment, Mb = 1.2 x pb x Zx = The overall buckling check, mMx/Mb+mMyy/Mcy < 1
17.13
kN.m
mMx/Mb+mMyy/Mcy
=
0.90 18.14 1.00 2 0.25
)
(From table-16 of BS 5950-2000, part-1)
0.78 Hence ok
Shear check: Max. shear force, wL/2 Shear area, Avx
= 1.26 = 1442.72
kN mm2
Shear capacity, Pvx = 0.6 x py x Avx Shear area, Avy = 0.9 x Ao
= 238.05 = 1540.22
kN mm2
Shear capacity, Pvx = 0.6 x py x Avx
= 254.14
kN
Hence ok Check of deflection: Deflection, dx dx = (5 x wl4)/384EI Deflection, dy dy = (5 x wl4)/384EI Allowable deflection, d.allow (d.allow = L/250, as per SP-1275)
=
10.29
mm
=
1.46
mm
28.00
mm
=
Hence ok
(Ao = area of flanges)
Cladding Purlin Design data Yield strength of steel Span of purlin Spacing of purlins
py = l = =
2 275.0 N/mm 7.00 m 1.20 m
Sectional properties of purlin. Member D = 203.2 B = 76.40 t
=
7.1
T = 11.20
Gross area of cross section
= RSC203x76x24 3 Z xx = 192.42 cm 3 Z yy = 27.7 cm A =
2 30.4 cm
4 I xx = 1955.00 cm 4 cm = 152.0 Iyy
r.min =
Loads Dead load Roofing sheet & accessories load Dead weight of purlin Total Wind load
22.4 mm PDL
PDL-1 = PDL-2 = PDL = PWL =
0.14 kN/m 0.24 kN/m 0.38 kN/m 1.36 kN/m
PWL
(1.1x0.826x1.5-Refer Wind load calculations on walls)
Load combination 1.4WL Applied moment at mid span of purlin 2 M xx = P WL*leff /8 Effective length =1.0*L =leff Note:
M xx = l=leff =
11.66 kN-m 7.00 m
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 Equivalent Slenderness ratio, lLT
= 312.50 = uvw
buckling parameter, u Torsional index, x = D/T Ratio, w
= 0.90 = 18.14 = 1.00 = 0.50 = 140.99
The slenderness factor, v Equivalent Slenderness ratio, lLT Bending strength, pb Buckling resisting moment, Mb = pb x Zx The overall buckling check, mMx/Mb mMx/Mb+mMyy/Mcy Shear check: Max. shear force, wL/2 Shear area, Avx Shear capacity, Pvx = 0.6 x py x Avx Shear area, Avy = 0.9 x Ao Shear capacity, Pvx = 0.6 x py x Avx Check of deflection: Deflection, dx dx = (5 x wl4)/384EI Deflection, dy dy = (5 x wl4)/384EI Allowable deflection, d.allow (d.allow = L/250, as per SP-1275)
= = =
74.20 14.28
(v = 1/(1+0.05x(/x)2)0.25) N/mm2
(From table-16 of BS 5950-2000, part-1)
kN.m
0.82 Hence ok
=
1.31 kN 2 = 1442.72 mm = 238.05 kN 2 = 1540.22 mm = 254.14 kN Hence ok =
10.61
mm
=
2.35
mm
=
28.00 mm Hence ok
(Ao = area of flanges)
Design of Purlins Design data Yield strength of steel Slope of roof (to horizontal)
py = =
Span of purlin Spacing of purlins
2 275.0 N/mm 10.0 o or
l =
7.00 m
=
1.20 m
0.174 radians
Sectional properties of purlin. Member D = 203.2 B = 76.40 t
=
7.1
= RSC203x76x24 3 Z xx = 192.42 cm 3 Z yy = 27.7 cm
T = 11.20
Gross area of cross section
30.4 cm
A =
2
4 I xx = 1955.00 cm 4 cm = 152.0 Iyy
r.min =
22.4 mm PDL/PL
Loads Dead load Roofing sheet & accessories load Dead weight of purlin Total
PDL-1 = PDL-2 = PDL =
0.10 kN/m 0.24 kN/m
PLL = PWL =
1.00 kN/m
Live load Wind load
0.34 kN/m
PDL*cos(x)/ PLL*cos(x)/ PWL PDL*sin(x)/ PLL*sin(x)
0.84 kN/m
(0.833x0.843x1.20-Refer Wind load calculations for roofs) Load case I a) Load combination 1.4DL+1.6LL W 1 = [1.4PDLcos(x)+ 1.6PLLcos(x)]
=
2.0
kN/m
W 1y = [1.4PDLsin(x)+1.6 PLLsin(x)]
=
0.4
kN/m
b) Load combination 1.4DL+1.4WL W 2 = [PDLcos(x)+ PWLcos(x)] W 2y = [1.4PDLsin(x)+1.4 PWLsin(x)]
= =
1.6 0.3
kN/m kN/m
c) Load combination 1.2DL+1.2LL+1.2WL W 3 = [1.2PDLcos(x)+1.2PLLcos(x)+1.2 PWLcos(x)] W 3y = [1.2PDLsin(x)+1.2 PLLsin(x)+1.2 PWLsin(x)]
= =
2.6 0.5
kN/m kN/m
x
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
M xx = 2 = [P DLcos(x )+ P LLcos(x )+PWL cos(x)]*leff /8
15.80 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. M yy = 0.56 kN-m 2 M yy = ([P DLsin(x )+ P LLsin(x )+PWL sin(x)]*(l /2) )/10 Moment capacity check: Moment capacity of Mazor axis, Mcx Moment capacity of Minor axis, Mcy (Mc = 1.2 x py x Z) Local capacity of check, Mxx/Mcx+Myy/Mcy < 1 Mxx/Mcx+Myy/Mcy
= =
=
63.50 9.14
kN-m kN-m
0.31 Hence ok
6 of 5
Buckling capacity check: Slenderness ratio, Leff/r.min Equivalent Slenderness ratio, lLT
= 312.50 = uvw
buckling parameter, u Torsional index, x = D/T Ratio, w
= = =
The slenderness factor, v Equivalent Slenderness ratio, lLT
= 0.50 = 140.99
(v = 1/(1+0.05x(/x) )
Bending strength, pb
=
94.90
N/mm2
Buckling resisting moment, Mb = 1.2 x pb x Zx = The overall buckling check, mMx/Mb+mMyy/Mcy < 1
21.91
kN.m
mMx/Mb+mMyy/Mcy
0.90 18.14 1.00
=
2 0.25
)
(From table-16 of BS 5950-2000, part-1)
0.8 Hence ok
Shear check: Max. shear force, wL/2 Shear area, Avx
= 1.26 = 1442.72
kN mm2
Shear capacity, Pvx = 0.6 x py x Avx Shear area, Avy = 0.9 x Ao
= 238.05 = 1540.22
kN mm2
Shear capacity, Pvx = 0.6 x py x Avx
= 254.14
kN
Hence ok Check of deflection: Deflection, dx dx = (5 x wl4)/384EI Deflection, dy dy = (5 x wl4)/384EI Allowable deflection, d.allow (d.allow = L/250, as per SP-1275)
=
10.29
mm
=
1.46
mm
28.00
mm
=
Hence ok
7 of 5
(Ao = area of flanges)
Cladding Purlin Design data Yield strength of steel Span of purlin Spacing of purlins
py = l = =
2 275.0 N/mm 7.00 m 1.20 m
Sectional properties of purlin. Member D = 203.2 B = 76.40 t
=
7.1
T = 11.20
Gross area of cross section
= RSC203x76x24 3 Z xx = 192.42 cm 3 Z yy = 27.7 cm 2 30.4 cm
A =
4 I xx = 1955.00 cm 4 cm = 152.0 Iyy
r.min =
Loads Dead load Roofing sheet & accessories load Dead weight of purlin Total Wind load
22.4 mm PDL
PDL-1 = PDL-2 = PDL =
0.14 kN/m 0.24 kN/m 0.38 kN/m 1.36 kN/m
PWL =
PWL
(1.1x0.826x1.5-Refer Wind load calculations on walls)
Load combination 1.4WL Applied moment at mid span of purlin 2 M xx = P WL*leff /8 Effective length =1.0*L =leff Note:
M xx =
11.66 kN-m
l=leff =
7.00 m
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 Equivalent Slenderness ratio, lLT
= 312.50 = uvw
buckling parameter, u Torsional index, x = D/T Ratio, w
= 0.90 = 18.14 = 1.00 = 0.50 = 140.99
The slenderness factor, v Equivalent Slenderness ratio, lLT Bending strength, pb Buckling resisting moment, Mb = pb x Zx The overall buckling check, mMx/Mb mMx/Mb+mMyy/Mcy Shear check: Max. shear force, wL/2 Shear area, Avx Shear capacity, Pvx = 0.6 x py x Avx Shear area, Avy = 0.9 x Ao Shear capacity, Pvx = 0.6 x py x Avx Check of deflection: Deflection, dx dx = (5 x wl4)/384EI Deflection, dy dy = (5 x wl4)/384EI Allowable deflection, d.allow (d.allow = L/250, as per SP-1275)
= = =
74.20 14.28
(v = 1/(1+0.05x(/x)2)0.25) N/mm2
(From table-16 of BS 5950-2000, part-1)
kN.m
0.82 Hence ok
=
1.31 kN 2 = 1442.72 mm = 238.05 kN 2 = 1540.22 mm = 254.14 kN Hence ok =
10.61
mm
=
2.35
mm
=
28.00 mm Hence ok
8 of 5
(Ao = area of flanges)
