DESIGN OF Z PURLINS Created By: Madurai ES Consultancy Services Pvt Ltd.

Purlin Designation P1 JOB No.: 4786

DATE : 27-08-2025
Input Data: Purlin Geometry
Span of the purlin = 9.800 M
Spacing of the purlin = 1.4 M
No. of Sag rods = 4
Slope of the Roof = 5 deg.

Number of Spans = 4
(for 1 or 2 spans, Bending Moment Coefficient is 8, for 3 or more spans, it is 10)
(in case of Bending about minor axis, (No of spans)x(No of sagrods+1) is used.

Input Data: Loads

Dead Loads
Weight of Sheeting = 5 kg/sqm
Self Weight of Purlin = Automatically Calculated from Section properties
Extra for cleats, as % of Purlin weight = 10 %
Additional Dead Loads to Consider = 0 kg/sqm

Live Loads
Live load on Roof = Automatically Calculated from Slope
= 75 kg/sqm
Additional Live Loads to be considered = 0 kg/sqm
(For Design of Wall Girt (Cladding Runner), additional Live loads to be considered can be entered as -ve of LL on roof)
(Live load will be 0 effectively)
Wind Loads
Basic Wind Speed 39 m/s Terrain Category 1
k1 1 Maximum Horizontal Dimension of Building 176 m
k3 1 Hence, Bldg Class C
Height of Top 12.3 m
Based on the data on right, k2 is obtained from the tables
k2 0.85

Ht of building at eaves level, h = 12.3 m

Width of the building, w = 77 m
Length of the Building, l = 163 m

Hence, h/w = 0.160

and l/w = 2.117

Based on the h/w and l/w, the values of Cpe is obtained from tables as noted below:
Maximum Downward Cpe (include sign) 0
Maximum Upward Cpe (include sign) -0.943

Based on % of openings, Cpi is taken as +/- 0.5

Input Data: Purlin Section Being Checked

Try Z 220 X 55 X 1.75

Yield stress of material 3450 KG/CM2

Flange Width, b 63 mm
Depth of section d 300 mm
Thickness t 2 mm
Length of Lip lip_l 20 mm
Inner Bending Radius 1.8 mm

Area 9.16 cm2

Zxx 75.40 cm3 Section Modulus about Major Axis
Zyy 9.69 cm3 Section Modulus about Minor Axis
Ixx 1131.02 cm4 Moment of Inertia about Major Axis
Iyy 61.04 cm4 Moment of Inertia about Minor Axis

Purlin Weight 5.136 kg/sqm

Output Summary

Section Properties OK? NOT OK Based on Section 9 of BS:5950 Part 5 – 1998

OK Based on IS 801 Clause 5.2.2.1

Stresses Ok? OK
Critical Stress Factor 0.95

Deflection Check OK? OK

Hence, Overall: OK

Notes:
1. Section Properties Check based on Section 9 of B:5950 Part 5 is a guideline and not mandatory
Hence, Design is considered Safe even if above check only is not okay but all other checks are okay
2. Currently, this design only works if full width is effective. If full width is not effective,
this spreadsheet will report Failure in Stress Check
3. Not suitable currently for curved roofs.
4. Design is not suitable for varying spans of purlins (varying truss spacing)
 Z Purlin Design Report Created by Madurai ES Consultancy Services Pvt Ltd

Z Purlin Design Report Prepared By Madurai ES Consultancy Services Pvt Ltd.

Code Author: S. Arunkumar, Managing Director.

Code Version: R1 Code Year: 2011

Revision History R0: Basic Design with checks for Stresses and Deflection based on IS 800 only
R1: Added Section property checks and Allowable Stress Calculations based on IS 801

JOB No.: 4786 DATE : 8/27/25

Input Data: Purlin Geometry

Span of the purlin = 9.800 M
Spacing of the purlin = 1.4 M
No. of Sag rods = 4
Slope of the Roof = 5 deg.

Number of Spans = 3

Bending Moment Coefficients: Use 8 for Single/Two spans, 10 for 3 or more spans
Bending Moment Coefficient for Mxx(BMCX) 10
For Bending About Minor Axis, Number of spans= number of spans x (number of sagrods+1)
Number of Spans about Minor Axis = 15
Bending Moment Coefficient for Myy(BMCY) 10

Cross Sectional Area of Purlin 9.16 cm2

Purlin Weight = 7.191 kg/m (Area in sqcm x 0.785 kg/sqcm/m) in kg/m
= 5.136 kg/sqm (Weight in kg/m)/spacing

Design Calculations: Primary Load Cases

DEAD LOAD

Weight of Sheeting 5.000 kg/sqm

Self Weight of Purlin (calculated above) 5.136 kg/sqm
Extra load for weight 10 % of purlin weight 0.514 kg/sqm
Other Dead Loads 0.000 kg/sqm

Total Dead Load 10.650 kg/sqm

= 0.106 kN/sqm

LIVE LOAD

Live Load on Roof = 75 kg/sqm if slope is less than 10 degrees. If Slope is more than 10 degrees, LL = 75 – 2x(slope-10), subject to minimum of 40 kg/sqm
Live load on Roof = 75 KG/M2
Additional Live Loads to be considered = 0 KG/M2
(For Design of Wall Girt (Cladding Runner), additional Live loads to be considered can be entered as -ve of LL on roof)

Total Live Load 75 kg/sqm

= 0.750 kN/sqm
WIND LOAD

Basic Wind Speed Vb 39 m/s

k1 1
k3 1

Terrain Category 1
Maximum Horizontal Dimension of Building 176 m
Hence, Building Class is C
Height of Top 12.3 m

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 Z Purlin Design Report Created by Madurai ES Consultancy Services Pvt Ltd

Based on the above data, k2 is obtained from the tables

k2 0.85

Design Wind Speed Vz=k1.k2.k3.Vb 33.15 m/s

Design Wind Pressure pz=0.6Vz^2 659.353 N/sqm
= 0.659 kN/sqm

Ht of building at eaves level, h = 12.3 m

Width of the building, w = 77 m
Length of the Building, l = 163 m

Hence, h/w = 0.160

and l/w = 2.117

Based on the h/w and l/w, the values of Cpe is obtained from tables as noted below:
Maximum Downward Cpe (including sign) 0
Maximum Upward Cpe (including sign) -0.943

Based on % of openings, Cpi is taken as +/- 0.5

Wind Load is included in two load combinations – DL+WL and DL+LL+WL

Since, Dead Load and Live Load are downward, DL+WL will be critical for the maximum upward wind force
Similarly, DL+LL+WL will be critical for the maximum downward wind force

WL1: Maximum Upward Wind Force – To be used in combination DL+WL1

Maximum Upward Cpe (including sign) -0.943

Cpi to use (for upward, use -) -0.5

Hence, Cpe+Cpi = -1.443

Design Wind Pressure pz 0.659 kN/sqm

Wind pressure for Purlin Design -0.951 kN/sqm

WL2: Maximum Downward Wind Force – To be used in combination DL+LL+WL2

Maximum Downward Cpe (including sign) 0

Cpi to use (for upward, use -) 0.5

Hence, Cpe+Cpi = 0.5

Design Wind Pressure pz 0.659 kN/sqm

Wind pressure for Purlin Design 0.330 kN/sqm

Design Calculations: Primary Load Cases – Conversion of forces to Normal And Tangential Components

Spacing of the purlin = 1.4 m

Slope of the Roof = 5 degrees

Total Dead Load = 0.106 kN/sqm

DL Normal Component = DL x Spacing x cos(slope) = 0.149 kN/m

DL Tangential Component = DL x Spacing x sin(slope) = 0.013 kN/m

Total Live Load = 0.750 kN/sqm

LL Normal Component = LL x Spacing x cos(slope) = 1.046 kN/m

LL Tangential Component = LL x Spacing x sin(slope) = 0.092 kN/m

Total Wind Load in WL1 = -0.951 kN/sqm

WL is normal to roof
Hence, WL1 normal component = WL1 x Spacing = -1.332 kN/m
And, WL1 Tangential component = 0 kN/m

Total Wind Load in WL2 = 0.330 kN/sqm

WL is normal to roof
Hence, WL2 normal component = WL2 x Spacing = 0.462 kN/m
And, WL2 Tangential component = 0 kN/m

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 Z Purlin Design Report Created by Madurai ES Consultancy Services Pvt Ltd

Design Calculations:Summary of Loads in Load Combinations

From above calculations, the components of load in the various load combinations are tabulated
DL+LL DL+WL1 DL+LL+WL2
Normal Load 1.195 -1.183 1.656 kN/m
Tangential Load 0.105 0.013 0.105 kN/m

For Strength Design, 0.75 factor is applicable for combinations with Wind Load since 33.33% extra stress is allowed
Hence, the components of load in the various load combinations for Strength design are
DL+LL 0.75(DL+WL1) 0.75(DL+LL+WL2)
Normal Load 1.195 -0.888 1.242 kN/m
Tangential Load 0.105 0.010 0.078 kN/m

Maximum Normal Component = 1.242 kN/m

Purlin Section Selected:

Section Name Z 220 X 55 X 1.75

Yield stress of material 3450 kg/sqcm

Flange Width, b 63 mm
Depth of section d 300 mm
Thickness t 2 mm
Length of Lip lip_l 20 mm
Internal Bending radius 1.8 mm
Total bending Radius, rad 3.8 mm

Flange Width w/o bend, w = b – 2 x rad 55.4 mm

Area 9.16 cm2

Zxx 75.40 cm3
Zyy 9.69 cm3
Ixx 1131.02 cm4
Iyy 61.04 cm4

Purlin Weight = 7.191 kg/m (Area in sqcm x 0.785 kg/sqcm/m) in kg/m

= 5.136 kg/sqm (Weight in kg/m)/spacing

Design Calculations: Checking Basic Section Properties based on Section 9 of BS:5950 Part 5 – 1998

Check No. 1 – Overall Depth <= 100t & >=L/45

Overall Depth 300 mm
100t = 200 mm
L/45 = 217.778 mm

Hence NOT OK

Check No. 2 – Overall Width of Compression Flange<=35t

Flange Width, b 63 mm
35t = 70 mm

Hence OK

Check No. 3 – Width of Lip >= b/5

Width of Lip 20 mm
B/5 = 12.6 mm

Hence OK

Check No. 4 – Total Width over both flanges >= L/60

Total Width over both flanges 124 mm
L/60 = 163.333 mm

Hence NOT OK

Check No. 5 – Zxx of Purlin >= WL/1400 for Simply Supported Purlin and >=WL/1800 for Continuous Purlin
Zxx = 75.40 cm3

W is normal component of unfactored distributed dead load plus imposed load in kN

L is span of purlin in mm
W= 11.706 kN
L= 9800 mm
Number of Spans = 3

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 Z Purlin Design Report Created by Madurai ES Consultancy Services Pvt Ltd

Hence, denominator = 1800

WL/denominator 63.735

Hence OK

Result 1: Check for Section Properties Based on BS 5950 Part 5 Sec.9: NOT OK

Design Calculations: Checking Basic Section Properties based on IS 801 for Lip of Purlin

Minimum Depth of Lip shall be 2.8 x t x ((w/t)^2-281200/Fy)^(1/6) and not less than 4.8t

t= 2 mm
w= 55.4 mm
Fy= 3450 kg/sqcm
w/t= 27.7
2.8 x t x ((w/t)^2-281200/Fy)^(1/6) 16.630 mm
4.8t= 9.6 mm

Lip l= 20 mm

Hence OK

Lip is Edge stiffener only if w/t<60

Here, w/t = 27.7

Hence OK

Result 2: Check for Section Properties Based on IS 801 Clause 5.2.2.1: OK

Design Calculations: Stress Checks

Check for w/t, lim = 1435/sqrt(f)

As per clause 5.2.1.1 of IS 801,

f is the actual stress in compression element computed based on effective width

Compression stress based on full width = Max (Mxx/Zxx+Myy/Zyy) for all three unfactored combinations

Span for major axis bending = Span of purlin

= 9.800 m
Span for minor axis bending = Span of purlin / (no. of sagrods + 1)
= 1.96 m

Bending Moment Coefficient for Mxx(BMCX) 10

Bending Moment Coefficient for Myy(BMCY) 10
Note: Calculation for the above is at the top of the report

DL+LL DL+WL1 DL+LL+WL2

Normal Load 1.195 -1.183 1.656 kN/m
Tangential Load 0.105 0.013 0.105 kN/m

Mxx 11.472 11.366 15.905 KN-m

Myy 0.040 0.005 0.040 KN-m

Mxx/Zxx 152.150 150.744 210.938 N/sqmm

Myy/Zyy 4.144 0.515 4.144 N/sqmm

Mxx/Zxx+Myy/Zyy 156.294 151.260 215.082 N/sqmm

Max. Compression Stress = 215.082 N/sqmm

f = 215.082 N/sqmm
= 2150.821 kg/sqcm

1435/sqrt(f) = 30.942
w/t = 27.7

Hence OK Design is restricted to Fully Effective Section

Maximum Compressive Stress based on Lateral Buckling of Flange, as per Clause 6.3 of IS 801

Calculate X=L2Sxc/(dIyc)

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 Z Purlin Design Report Created by Madurai ES Consultancy Services Pvt Ltd

and Y = Pi2ECb/Fy

Fb, the Allowable Compressive Stress based on Lateral Buckling of Flange is calculated as
X<0.18Y implies, Fb = 0.6 Fy - CASE (i)
X>0.18Y but X<0.9Y implies, Fb= 0.667 Fy – Fy . X / (2.7 Y) - CASE (ii)
X>0.9Y implies Fb = 0.3 Fy . Y / X - CASE (iii)

L = Unbraced Length of member = Span / (Number of sagrods+1) 196 cm

Sxc = Compression Section Modulus of section about major axis = Zxx 75.40 Cm^3
d = Depth of Section = 30 cm
Iyc = Moment of Inertia of the compression portion = Iyy/2 30.519266666667 Cm^4

Hence, X = 3163.699 (unitless)

Pi = 3.1415926535898
E = Modulus of Elasticity, as per IS 801 is taken as 2074000 kgf/sqcm
Cb as per IS 801 can be taken conservatively assuming M1=0 (end span) 1.75
Fy = 3450 kg/sqcm

Hence Y = 10383.110 (unitless)

Hence, 0.18 Y = 1868.960

And, 0.9 Y = 9344.799

Comparing X with 0.18Y and 0.9Y, the applicable case is 2

Hence, Fb = 0.667Fy-Fy.X/(2.7Y)
= 1910.6654163439 kg/sqcm
= 191.067 N/sqmm

Basic Allowable Design Stress = 0.6Fy 2070 kg/sqcm

= 207 N/sqmm

Hence, allowable stress is calculated as lower of the two = 191.067 N/sqmm

DL+LL DL+WL1 DL+LL+WL2

Mxx/Zxx+Myy/Zyy 156.294 151.260 215.082 N/sqmm, calculated above
Allowed 191.067 254.119 254.119

Safety Ratio 0.818 0.595 0.846

Max. Safety Ratio 0.846 OK

Shear Stress in Web

As per clause 6.4.1 of IS 801,allowed maximum average shear stress Fv in kgf/sqcm is calculated as

Case 1: If h/t is less than 4590/sqrt(Fy), Fv=1275 x sqrt(Fy) / (h/t) 1275 x sqrt(Fy)/(h/t) = 506.009
Case 2: If h/t is more than 4590/sqrt(Fy), Fv=5850000 / (h/t)^2 5850000/(h/t)^2 = 267.075
Both are subject to maximum 0.4Fy 0.4Fy = 1380

h 296.000 mm (Clear Depth between flanges = Depth – 2 x thickness)

t 2.000
Hence, h/t = 148.000

4590/sqrt(Fy) = 78.145

Hence, Case is : 2

Hence, Fv = 5850000/(h/t)^2
= 267.075 kgf/sqcm

Actual Shear '=wl/2 Here, w = SQRT(Wn^2+Wt^2)

DL+LL 0.75(DL+WL1) 0.75(DL+LL+WL2)

Normal Load 1.195 -0.888 1.242 kN/m
Tangential Load 0.105 0.010 0.078 kN/m

w= 1.199 0.888 1.245 kN/m

Hence, Shear= 5.876 4.350 6.098 kN
Shear Stress fv=V/dt 9.925 7.347 10.301

Stress Ratio 0.372 0.275 0.386

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 Z Purlin Design Report Created by Madurai ES Consultancy Services Pvt Ltd

Max. Shear Stress Ratio in Web 0.386

Hence OK

Bending Stress in Web

As per clause 6.4.2of IS 801 for the design check of allowable stress in combined shear and bending
Fbw = 36560000/(h/t)^2
Here, h/t already calculated above as 148.000

Hence, Fbw = 1669.102 kg/sqcm

166.910 N/sqmm
Basic Allowable Design Stress calculated earlier = 0.6Fy
207 N/sqmm

Hence, governing value for Fbw = 166.91015339664 N/sqmm

Already calculated fbw = Mxx/Zxx since Zyy at web is very high (x=t/2, Z=I/x)
DL+LL DL+WL1 DL+LL+WL2
Mxx/Zxx 152.150 150.744 210.938 N/sqmm
Fbw 166.91015339664 221.99050401753 221.99050401753

Safety Ratio 0.912 0.679 0.950

Max. Safety Ratio 0.950
In summary, Bending stresses in Web is: OK

Combined Shear and Bending Stresses in Web

As per clause 6.4.3 of IS 801 for the design check of allowable stress in combined shear and bending
SQRT((fbw/Fbw)^2+(fv/Fv)^2) must be less than 1

In this clause, Fbw is not restricted by 0.6Fy and Fv is not restricted by 0.4Fy

DL+LL DL+WL1 DL+LL+WL2

Hence, Fbw = 166.910 221.991 221.991
And Fv = 267.075 355.209 355.209

Actual stresses already calculated are

fbw 152.150 150.744 210.938
fv= 9.925 7.347 10.301

fbw/Fbw 0.912 0.679 0.950

fv/Fv 0.037 0.021 0.029

SQRT of sum of squares 0.912 0.679 0.951

Maximum Combined Stress Ratio in Web is 0.951

In summary, Combined stresses in Web is: OK

Result 3: Check for Stresses: OK

Overall Safety Ratio 0.951

Design Calculations: Deflection Check

Theoretical Deflection is calculated as (5/384) (wl^4/EI) for Simply Supported beam and (3/384) (wl^4/EI) for multiple spans

Here, number of spans = 4

Hence, formula to use = (3/384) (wl^4/EI)

w is normal component of unfactored distributed load in kN/m, max. of all load combinations
= 1.656 kN/m

L = Span of the Purlin 9.800 m

E = Modulus of Elasticity, as per IS 801 is taken as 2074000 kg/sqcm

= 207400 N/sqmm

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 Z Purlin Design Report Created by Madurai ES Consultancy Services Pvt Ltd

I = Ixx 1131.02 Cm^4

Hence, Theoretical Deflection = 50.87 mm

Allowable Deflection as IS codes is Span/180: 54.44 mm

Hence OK

As per MBMA, allowed deflection from Live load component must be within Span/240

Span 9.800 m
or 9800 mm

Span/240 = 40.83 mm

Normal Component of Live Load 1.05 kN/m

Hence, deflection from Live Load = 32.132871570887

Hence OK

Result 4: Check for Deflection: OK

Results Summary

Section Properties OK? NOT OK Based on Section 9 of BS:5950 Part 5 – 1998

OK Based on IS 801 Clause 5.2.2.1

Stresses Ok? OK
Critical Stress Factor 0.95

Deflection Check OK? OK

Hence, Overall: OK

Notes:
1. Section Properties Check based on Section 9 of B:5950 Part 5 is a guideline and not mandatory
2. Currently, this design only works if full width is effective. If full width is not effective,
this spreadsheet will report Failure in Stress Check
3. Not suitable currently for curved roofs.
4. Design is not suitable for varying spans of purlins (varying truss spacing)

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