Project Location
(Insert logo here) Subject Revision
Calc Date Checked Date Approved
Roof C-purlin and sagrod design
in accordance with NSCP 2015 2nd printing
1 | Section properties
Depth of purlin h 125.00 mm
Width of purlin bf 50.00 mm 125
Length of purlin lip hl 12.00 mm
Thickness of purlin t 1.50 mm
Ai xi Ai*xi dxi² Ai*dxi² Iybar
web 187.5 0.75 140.63 200.81 37652.07 35.16
flange top 70.5 25.00 1762.50 101.59 7162.14 12977.88
flange bot 70.5 25.00 1762.50 101.59 7162.14 12977.88
lip top 18 49.25 886.50 1178.50 21212.91 3.38
lip bot 18 49.25 886.50 1178.50 21212.91 3.38
TOTALS 364.5 5438.63
Ai*yi dyi² Ai*dyi² Ixbar Ix (1/3)*b*t³
web 11719 0.00 0.00 244140.63 244140.63 140.63
flange top 8759.63 3813.06 268820.91 13.22 268834.13 52.88
flange bot 52.875 3813.06 268820.91 13.22 268834.13 52.88
lip top 2142 3192.25 57460.50 216.00 57676.50 13.50
lip bot 108 3192.25 57460.50 216.00 57676.50 13.50
TOTALS 22781 897161.88 273.38
Cross-section area A 364.50
Linear weight ω 0.03
x-coordinate of the section centroid xbar 14.92
y-coordinate of the section centroid ybar 62.50
Moment of inertia about x-axis Ix 897,161.88
Elastic modulus about x-axis Sx 14,354.59
Radius of gyration about x-axis rx 49.61
Plastic modulus about x-axis Zx 16,600.13
Moment of inertia about y-axis Iy 120,399.84
Elastic modulus about y-axis Sy 3,432.23
Radius of gyration about y-axis ry 18.17
Location of plastic neutral axis from left end xp 30.63
Plastic modulus about y-axis Zy 8,023.73
2 | Roof framing layout
Distance between rafters/trusses L 3.00
Length of overhang Lc 1.20
Spacing of purlins s 0.60
Location of sagrods (1 = no sagrod, 2 = sagrods @ midpoints, 3 = sagrods @ third points)
sagrods 1.00
Roof angle θ 8.00
3 | Material properties
Yield strength Fy 248.00
Ultimate strength Fu 400.00
Modulus of elasticity E 200,000.00
4 | Loads
Load decomposition to purlins
px (kPa) py (kPa) ωx (kN/m)
Roof weight 0.05 kPa 0.0070 0.0495 0.0042
Ceiling 0.05 kPa 0.0069 0.0490 0.0041
MEPF 0.30 kPa 0.0413 0.2942 0.0248
Purlin self-weight 0.0039
Dead load 0.0370
Live load 0.50 kPa 0.0696 0.4951 0.0418
Roof live load 0.75 kPa 0.1044 0.7427 0.0626
Wind load - 1.87 kPa 0.0000
5 | Purlin design strengths
Major axis bending
Case 1 : Yielding
Nominal moment capacity Mn 4.12
Case 2 : Lateral-torsional buckling
Moment of inertia of one flange about y-axis If 15,625.00
Warping constant Cw 122,070,313
Distance between flange centroids ho 123.50
Torsional constant modification factor c 1.94
Radius of gyration of section effective in lateral torsional buckling about y-axis
rts 16.34
Torsional constant J 273.38
Critical length for compactness Lp 908.38
Critical length for slenderness Lr 1,863.23
Effective length about the x-axis Lb 3,000.00
Moment gradient factor Cb 1.14
Critical bending stress Fcr 88.96
Nominal moment capacity Mn 1.28
Ultimate moment capacity about major axis φMnx 1.15
Minor axis bending
Case 1: Yielding
Nominal moment capacity Mn 1.36
Case 2: Flange local buckling
Critical slenderness ratio for compactness λp 10.79
Critical slenderness ratio for slenderness λr 28.40
Slenderness ratio λ 32.33
Nominal moment capacity Mn 1.71
Ultimate moment capacity about minor axis φMny 1.23
6 | Purlin strength checks
Between rafters/trusses
Load combinations (LRFD) ωux (kN/m) ωuy (kN/m) Mux (kN-m)
(203-1) 1.4D 0.05 0.37 0.41
(203-2) 1.2D + 1.6L + 0.5Lr 0.14 1.01 1.14
(203-3) 1.2D + 1.6Lr + 0.5L 0.17 1.18 1.32
1.2D + 1.6Lr + 0.5W 0.14 0.09 0.10
(203-4) 1.2D + 1.0W + 0.5L + 0.5Lr 0.10 - 1.19 - 1.33
(203-5) 1.2D + 0.5L 0.07 0.46 0.52
(203-6) 0.9D + 1.0W 0.03 - 1.64 - 1.84
At overhangs
Load combinations (LRFD) ωux (kN/m) ωuy (kN/m) Mux (kN-m)
(203-1) 1.4D 0.05 0.37 0.27
(203-2) 1.2D + 1.6L + 0.5Lr 0.14 1.01 0.73
(203-3a) 1.2D + 1.6Lr + 0.5L 0.17 1.18 0.85
(203-3b) 1.2D + 1.6Lr + 0.5W 0.14 0.09 0.07
(203-4) 1.2D + 1.0W + 0.5L + 0.5Lr 0.10 - 1.19 - 0.85
(203-5) 1.2D + 0.5L 0.07 0.46 0.33
(203-6) 0.9D + 1.0W 0.03 - 1.64 - 1.18
7 | Purlin serviceability checks
Between rafters/trusses
Allowable deflection δall = L/ 360
Load combinations (ASD) ωsx (kN/m) ωsy (kN/m) δx (mm)
(203-8) D 0.04 0.26 1.62
(203-9) D+L 0.08 0.56 3.45
(203-10) D + Lr 0.10 0.71 4.36
(203-11) D + 0.75L + 0.75Lr 0.12 0.82 5.05
(203-12) D + 0.6W 0.04 - 0.86 1.62
(203-13) 0.75(D + 0.75(L + Lr + 0.6W) 0.09 - 0.02 3.79
(203-14) 0.75(0.6D + 0.6W) 0.02 - 0.72 0.73
(203-15) 0.6D 0.02 0.16 0.97
(203-16) D + L + Lr 0.14 1.01 6.19
(203-17) 0.75(D + L + 0.6W) 0.06 - 0.42 2.59
At overhangs
Allowable deflection δall = L/ 360
Load combinations (ASD) ωsx (kN/m) ωsy (kN/m) δx (mm)
(203-8) D 0.04 0.26 0.40
(203-9) D+L 0.08 0.56 0.85
(203-10) D + Lr 0.10 0.71 1.07
(203-11) D + 0.75L + 0.75Lr 0.12 0.82 1.24
(203-12) D + 0.6W 0.04 - 0.86 0.40
(203-13) 0.75(D + 0.75(L + Lr + 0.6W) 0.09 - 0.02 0.93
(203-14) 0.75(0.6D + 0.6W) 0.02 - 0.72 0.18
(203-15) 0.6D 0.02 0.16 0.24
(203-16) D + L + Lr 0.14 1.01 1.52
(203-17) 0.75(D + L + 0.6W) 0.06 - 0.42 0.64
8 | Sagrod design
Load combinations (LRFD) ωux (kN/m) Tu (kN)
(203-1) 1.4D 0.05 -
(203-2) 1.2D + 1.6L + 0.5Lr 0.14 -
(203-3) 1.2D + 1.6Lr + 0.5L 0.17 -
1.2D + 1.6Lr + 0.5W 0.14 -
(203-4) 1.2D + 1.0W + 0.5L + 0.5Lr 0.10 -
(203-5) 1.2D + 0.5L 0.07 -
(203-6) 0.9D + 1.0W 0.03 -
Axial force in sagrod Tu -
Minimum diameter of sagrod db -
Location
Revision
Approved Date
1.5
12
x
y
50
Iy yi
37687.23 62.50
20140.01 124.25
20140.01 0.75
21216.29 119.00
21216.29 6.00
120399.84
mm²
kN/m
mm
mm
mm⁴
mm³
mm
mm³
mm⁴
mm³
mm
mm
mm³
m
m
m
deg
MPa
MPa
MPa
to purlins
ωy (kN/m)
0.0297 kN/m
0.0294 kN/m
0.1765 kN/m
0.0278 kN/m
0.2634 kN/m
0.2971 kN/m
0.4456 kN/m
-1.8740 kN/m
kN-m
mm⁴
mm⁶
mm
mm
mm⁴
mm
mm
mm
MPa
kN-m
kN-m
kN-m
kN-m
kN-m
Muy (kN-m) UR
0.06 0.41
0.16 1.12
0.19 1.30
0.16 0.22
0.11 1.25
0.07 0.51
0.04 1.63
FAIL
Muy (kN-m) UR
0.04 0.26
0.10 0.72
0.12 0.83
0.10 0.14
0.07 0.80
0.05 0.33
0.02 1.05
FAIL
8.33 mm
δy (mm) UR
1.55 0.27
3.29 0.57
4.17 0.72
4.82 0.84
- 5.06 0.64
- 0.10 0.45
- 4.26 0.52
0.93 0.16
5.91 1.03
- 2.49 0.43
FAIL
3.33 mm
δy (mm) UR
0.38 0.17
0.81 0.35
1.02 0.44
1.19 0.51
- 1.24 0.39
- 0.02 0.28
- 1.05 0.32
0.23 0.10
1.45 0.63
- 0.61 0.26
PASS
kN
mm
