C Purlin Design

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Modified By: Multibuild Consultants, Vapi

Purlin Designation

P1

JOB No.:

DATE :

Input Data: Purlin Geometry

Span of the purlin

=

5.500 M

Spacing of the purlin

=

1.15 M

No. of Sag rods

=

1 Slope of the Roof

=

10 deg.

Number of Spans

=

3 (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

=

6 kg/sqm

Self Weight of Purlin

=

Automatically Calculated from Section properties

Extra for cleats, as % of Purlin weight

=

10 %

Additional Dead Loads to Consider

=

4 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

44 m/s

Terrain Category

3 k1

1 Maximum Horizontal Dimension of Building

44 m

k3

1 Hence, Bldg Class

B

Height of Top

8.25 m

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

k2

0.88 Ht of building at eaves level, h

=

6.35 m

Width of the building, w

=

24 m

Length of the Building, l

=

44 m

Hence, h/w

=

0.265 and l/w

=

1.833 Based on the h/w and l/w, the values of Cpe is obtained from tables as noted below:

Maximum Downward Cpe (include sign)

-1.2

Maximum Upward Cpe (include sign)

-0.8

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

0.7

DESIGN OF PURLINS (COLD FORM SECTION)

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Modified By: Multibuild Consultants, Vapi

26.MBC.MWV.FGPM3

16-06-2017

Automatically Calculated from Section properties

(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)

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Input Data: Purlin Section Being Checked

Try

C 200x50x20x3.15

Yield stress of material

2400

Flange Width, b

50 mm

Depth of section d

200 mm

Thickness t

3.15 mm

Length of Lip lip_l

20 mm

Inner Bending Radius

4.73 mm

Area

9.86 Zxx

53.50 Section Modulus about Major Axis

Zyy

7.89 Section Modulus about Minor Axis

Ixx

535.00 Moment of Inertia about Major Axis

Iyy

29.20 Moment of Inertia about Minor Axis

Purlin Weight

7.740 kg/sqm

Output Summary

Section Properties OK?

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

0.999 Deflection Check OK?

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)

KG/CM

2

cm

2

cm

3

cm

3

cm

4

cm

4

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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,

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Z Purlin Design ReportCreated by Madurai ES Consultancy Services Pvt Ltd

Page 5

Cold Form Purlin Design Report Modified By: Multibuild Consultants, Vapi User: Arif

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.: 26.MBC.MWV.FGPM3 DATE : 16/6/17

Input Data: Purlin Geometry

Span of the purlin = 5.500M

Spacing of the purlin = 1.15M

No. of Sag rods = 1

Slope of the Roof = 10deg.

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 = 6

Bending Moment Coefficient for Myy(BMCY) 10

TRY PURLIN SIZE - C 200x50x20x3.15 (IS 811)

Cross Sectional Area of Purlin 9.86

Purlin Weight = 7.740 kg/m (Area in sqcm x 0.785 kg/sqcm/m) in kg/m

= 6.731 kg/sqm (Weight in kg/m)/spacing

Design Calculations: Primary Load Cases

DEAD LOAD

Weight of Sheeting 6.000kg/sqm

Self Weight of Purlin (calculated above) 6.731 kg/sqm

Extra load for weight 10 % of purlin weight 0.673 kg/sqm

Other Dead Loads 4.000kg/sqm

Total Dead Load 17.404 kg/sqm

= 0.174 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

Additional Live Loads to be considered = 0

(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 44m/s

k1 1

k3 1

Terrain Category 3

Maximum Horizontal Dimension of Building 44m

Hence, Building Class is B

Height of Top 8.25m

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

k2 0.88

Design Wind Speed Vz=k1.k2.k3.Vb 38.72 m/s

Design Wind Pressure pz=0.6Vz^2 899.543 N/sqm

= 0.900 kN/sqm

Ht of building at eaves level, h = 6.35m

cm2

KG/M2

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Page 6

Width of the building, w = 24m

Length of the Building, l = 44m

Hence, h/w = 0.265

and l/w = 1.833

Based on the h/w and l/w, the values of Cpe is obtained from tables as noted below:

Maximum Downward Cpe (including sign) -1.2

Maximum Upward Cpe (including sign) -0.8

Based on % of openings, Cpi is taken as +/- 0.7

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) -1.2

Cpi to use (for upward, use -) -0.7

Hence, Cpe+Cpi = -1.9

Design Wind Pressure pz 0.900 kN/sqm

Wind pressure for Purlin Design -1.709 kN/sqm

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

Maximum Downward Cpe (including sign) -0.8

Cpi to use (for upward, use -) 0.7

Hence, Cpe+Cpi = -0.1

Design Wind Pressure pz 0.900 kN/sqm

Wind pressure for Purlin Design -0.090 kN/sqm

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

Spacing of the purlin = 1.15 m

Slope of the Roof = 10 degrees

Total Dead Load = 0.174 kN/sqm

DL Normal Component = DL x Spacing x cos(slope) = 0.197 kN/m DL Tangential Component = DL x Spacing x sin(slope) = 0.035 kN/m

Total Live Load = 0.750 kN/sqm

LL Normal Component = LL x Spacing x cos(slope) = 0.849 kN/m LL Tangential Component = LL x Spacing x sin(slope) = 0.150 kN/m Total Wind Load in WL1 = -1.709 kN/sqm WL is normal to roof

Hence, WL1 normal component = WL1 x Spacing = -1.966 kN/m And, WL1 Tangential component = 0.000 kN/m Total Wind Load in WL2 = -0.090 kN/sqm WL is normal to roof

Hence, WL2 normal component = WL2 x Spacing = -0.103 kN/m And, WL2 Tangential component = 0.000 kN/m

Design Calculations:Summary of Loads in Load Combinations

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Page 7

DL+LL DL+WL1 DL+LL+WL2

Normal Load 1.046 -1.768 0.943 kN/m Tangential Load 0.185 0.035 0.185 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 1.046 -1.327 0.707 kN/m Tangential Load 0.185 0.026 0.138 kN/m Maximum Normal Component = 1.046 kN/m

Purlin Section Selected:

Section Name C 200x50x20x3.15

Yield stress of material 2400kg/sqcm

Flange Width, b 50mm

Depth of section d 200mm

Thickness t 3.15mm

Length of Lip lip_l 20mm

Internal Bending radius 4.73mm

Total bending Radius, rad 7.88 mm

Flange Width w/o bend, w = b – 2 x rad 34.24 mm

Area 9.86

Zxx 53.50

Zyy 7.89

Ixx 535.00

Iyy 29.20

Purlin Weight = 7.740 kg/m (Area in sqcm x 0.785 kg/sqcm/m) in kg/m

= 6.731 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 200 mm

100t = 315 mm

L/45 = 122.222 mm

Hence Ok

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

Flange Width, b 50 mm

35t = 110.25 mm

Hence Ok

Check No. 3 – Width of Lip >= b/5

Width of Lip 20 mm

B/5 = 10 mm

Hence OK

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

Total Width over both flanges 96.85 mm

L/60 = 91.667 mm

Hence OK

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

Zxx = 53.50

W is normal component of unfactored distributed dead load plus imposed load in kN L is span of purlin in mm W = 5.756 kN cm2 cm3 cm3 cm4 cm4 cm3

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Z Purlin Design ReportCreated by Madurai ES Consultancy Services Pvt Ltd Page 8 L = 5500 mm Number of Spans = 3 Hence, denominator = 1800 WL/denominator 17.587 Hence Ok

Result 1: Check for Section Properties Based on BS 5950 Part 5 Sec.9: 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= 3.15 mm w= 34.24 mm Fy= 2400 kg/sqcm w/t= 10.87 2.8 x t x ((w/t)^2-281200/Fy)^(1/6) 8.810 mm 4.8t= 15.12 mm Lip l= 20 mm Hence Ok

Lip is Edge stiffener only if w/t<60

Here, w/t = 10.8698412698

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

= 5.500 m

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

= 2.75 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 1.046 -1.768 0.943 kN/m Tangential Load 0.185 0.035 0.185 kN/m Mxx 3.166 5.349 2.853 KN-m Myy 0.140 0.026 0.140 KN-m Mxx/Zxx 59.171 99.989 53.322 N/sqmm Myy/Zyy 17.687 3.331 17.687 N/sqmm Mxx/Zxx+Myy/Zyy 76.858 103.320 71.009 N/sqmm Max. Compression Stress = 103.320 N/sqmm

f = 103.320 N/sqmm

= 1033.202 kg/sqcm

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https://www.youtube.com/watch?v=OBXsA1vuKR0 https://www.483scaffolddesign.com/design-calculations https://www.youtube.com/watch?v=OsIsmRdoJ8I

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Page 10

w/t = 10.8698412698

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

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) 275 cm Sxc = Compression Section Modulus of section about major axis = Zxx 53.50 Cm^3

d = Depth of Section = 20 cm

Iyc = Moment of Inertia of the compression portion = Iyy/2 14.6 Cm^4

Hence, X = 13855.950 (Unitless)

Pi = 3.1415926536

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

Fy = 2400 kg/sqcm

Hence Y = 14925.720 (Unitless)

Hence, 0.18 Y = 2686.630

And, 0.9 Y = 13433.148

Comparing X with 0.18Y and 0.9Y, the applicable case is 3

Hence, Fb = 0.3 Fy . Y / X

= 775.588710987 kg/sqcm

= 77.559 N/sqmm

Basic Allowable Design Stress = 0.6Fy 1440 kg/sqcm

= 144 N/sqmm

Hence, allowable stress is calculated as lower of the two = 77.559 N/sqmm DL+LL DL+WL1 DL+LL+WL2

Mxx/Zxx+Myy/Zyy 76.858 103.320 71.009 N/sqmm, calculated above

Allowed 77.559 103.386 103.386

Safety Ratio 0.991 0.999 0.687

Max. Safety Ratio 0.999 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) = 1015.773 Case 2: If h/t is more than 4590/sqrt(Fy), Fv=5850000 / (h/t)^2 5850000/(h/t)^2 = 1547.098

Both are subject to maximum 0.4Fy 0.4Fy = 960

h 193.700 mm (Clear Depth between flanges = Depth – 2 x thickness)

t 3.150

Hence, h/t = 61.492 4590/sqrt(Fy) = 93.693 Hence, Case is : 1

Hence, Fv = 1275 x sqrt(Fy)/(h/t), subject to maximum of 0.4Fy = 960.000 kgf/sqcm

Calculate X=L2_S xc/(dIyc) and Y = Pi2_EC

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Page 11

= 96.000 kgf/sqmm

Actual Shear '=wl/2 Here, w = SQRT(Wn^2+Wt^2) DL+LL 0.75(DL+WL1) 0.75(DL+LL+WL2) Normal Load 1.046 -1.327 0.707 kN/m Tangential Load 0.185 0.026 0.138 kN/m w= 1.063 1.327 0.721 kN/m Hence, Shear= 2.922 3.649 1.982 kN Shear Stress fv=V/dt 4.789 5.980 3.249 Stress Ratio 0.050 0.062 0.034

Max. Shear Stress Ratio in Web 0.062

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 61.492

Hence, Fbw = 9668.699 kg/sqcm 966.870 N/sqmm Basic Allowable Design Stress calculated earlier = 0.6Fy

144 N/sqmm Hence, governing value for Fbw = 144.000 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 59.171 99.989 53.322 N/sqmm

Fbw 144.00 191.952 191.952

Safety Ratio 0.411 0.521 0.278

Max. Safety Ratio 0.521

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 = 966.870 1289.160 1289.160 And Fv = 1015.773 1354.364 1354.364 Actual stresses already calculated are

fbw 59.171 99.989 53.322

fv= 4.789 5.980 3.249

fbw/Fbw 0.061 0.078 0.041

fv/Fv 0.005 0.004 0.002

SQRT of sum of squar 0.061 0.078 0.041 Maximum Combined Stress Ratio in Web is 0.078 In summary, Combined stresses in Web is: Ok

Result 3: Check for Stresses: Ok

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Page 12

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 = 3

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

= 1.768 kN/m

L = Span of the Purlin 5.500 m

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

= 207400 N/sqmm

I = Ixx 535.00 Cm^4

Hence, Theoretical Deflection = 11.39 mm Allowable Deflection as IS codes is Span/180: 30.56 mm

Hence Ok

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

Span 5.500 m

or 5500 mm

Span/240 = 22.92 mm

Normal Component of Live Load 0.85 kN/m Hence, deflection from Live Load = 5.47 mm

Hence Ok

Result 4: Check for Deflection: OK

Results Summary

Section Properties OK? 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 0.999

Deflection Check OK? 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.