DESIGN OF Z PURLINS Purlin Designation P1
Created By: Madurai ES Consultancy Services Pvt Ltd. JOB No.: DATE :
Input Data: Purlin Geometry Span of the purlin Spacing of the purlin No. of Sag rods Slope of the Roof
= = = =
6.000 M 1.8 M 2 18 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 Self Weight of Purlin Extra for cleats, as % of Purlin weight Additional Dead Loads to Consider
= = = =
6 kg/sqm Automatically Calculated from Section properties 10 % 0 kg/sqm
Live Loads Live load on Roof
= Automatically Calculated from Slope = 59 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 2 k1 1 Maximum Horizontal Dimension of Building 33.528 m k3 1 Hence, Bldg Class B Height of Top 10.3632 m Based on the data on right, k2 is obtained from the tables k2 0.98 Ht of building at eaves level, h Width of the building, w Length of the Building, l Hence, h/w and l/w
= =
= = =
5 m 33.5 m 33.5 m 0.149 1.000
Based on the h/w and l/w, the values of Cpe is obtained from tables as noted below: Maximum Downward Cpe (include sign) -0.4 Maximum Upward Cpe (include sign) -0.7 Based on % of openings, Cpi is taken as +/-
Input Data: Purlin Section Being Checked Try
Z 200x60x2.3
0.5
Yield stress of material Flange Width, b Depth of section d Thickness t Length of Lip lip_l Inner Bending Radius
2400 60 200 2.3 20 3
Area Zxx Zyy Ixx Iyy
8.07 47.72 10.22 477.18 61.34
Purlin Weight
KG/CM2 mm mm mm mm mm cm2 cm3 cm3 cm4 cm4
Section Modulus about Major Axis Section Modulus about Minor Axis Moment of Inertia about Major Axis Moment of Inertia about Minor Axis
3.519 kg/sqm
Output Summary Section Properties OK?
OK OK
Stresses Ok? Critical Stress Factor
OK 0.73
Deflection Check OK?
OK
Hence, Overall:
OK
Based on Section 9 of BS:5950 Part 5 – 1998 Based on IS 801 Clause 5.2.2.1
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)
sultancy Services Pvt Ltd. 4786 22-03-2016
m Section properties
e entered as -ve of LL on roof) ad will be 0 effectively)
and not mandatory ay but all other checks are okay
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd Z Purlin Design Report
Prepared By Madurai ES Consultancy Services Pvt 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 :
Input Data: Purlin Geometry Span of the purlin Spacing of the purlin No. of Sag rods Slope of the Roof
= = = =
6.000 M 1.8 M 2 18 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) For Bending About Minor Axis, Number of spans= number of spans x (number of sagrods+1) Number of Spans about Minor Axis = Bending Moment Coefficient for Myy(BMCY) Cross Sectional Area of Purlin Purlin Weight = =
8.07 cm2 6.334 kg/m 3.519 kg/sqm
10 9 10
(Area in sqcm x 0.785 kg/sqcm/m) in kg/m (Weight in kg/m)/spacing
Design Calculations: Primary Load Cases DEAD LOAD Weight of Sheeting Self Weight of Purlin (calculated above) Extra load for weight Other Dead Loads
10 % of purlin weight
Total Dead Load =
6.000 3.519 0.352 0.000
kg/sqm kg/sqm kg/sqm kg/sqm
9.871 kg/sqm 0.099 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 Live load on Roof
=
59 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 = WIND LOAD Basic Wind Speed Vb k1
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39 m/s 1
59 kg/sqm 0.590 kN/sqm
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd k3
1
Terrain Category Maximum Horizontal Dimension of Building Hence, Building Class is Height of Top
2 33.528 m B 10.3632 m
Based on the above data, k2 is obtained from the tables k2 0.98 Design Wind Speed Vz=k1.k2.k3.Vb Design Wind Pressure pz=0.6Vz^2
38.22 m/s 876.461 N/sqm 0.876 kN/sqm
= Ht of building at eaves level, h Width of the building, w Length of the Building, l Hence, h/w and l/w
= = = = =
5 m 33.5 m 33.5 m 0.149 1.000
Based on the h/w and l/w, the values of Cpe is obtained from tables as noted below: Maximum Downward Cpe (including sign) -0.4 Maximum Upward Cpe (including sign) -0.7 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) Cpi to use (for upward, use -)
-0.7 -0.5
Hence, Cpe+Cpi =
-1.2
Design Wind Pressure pz Wind pressure for Purlin Design
0.876 kN/sqm -1.052 kN/sqm
WL2: Maximum Downward Wind Force – To be used in combination DL+LL+WL2 Maximum Downward Cpe (including sign) Cpi to use (for upward, use -) Hence, Cpe+Cpi =
-0.4 0.5 0.1
Design Wind Pressure pz
0.876 kN/sqm
Wind pressure for Purlin Design
0.088 kN/sqm
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd Design Calculations: Primary Load Cases – Conversion of forces to Normal And Tangential Components Spacing of the purlin Slope of the Roof
= =
1.8 m 18 degrees
Total Dead Load
=
0.099 kN/sqm
DL Normal Component = DL x Spacing x cos(slope) = DL Tangential Component = DL x Spacing x sin(slope) =
0.169 kN/m 0.055 kN/m
Total Live Load
0.590 kN/sqm
=
LL Normal Component = LL x Spacing x cos(slope) = LL Tangential Component = LL x Spacing x sin(slope) = Total Wind Load in WL1
1.010 kN/m 0.328 kN/m
=
-1.052 kN/sqm
WL is normal to roof Hence, WL1 normal component = WL1 x Spacing = And, WL1 Tangential component = Total Wind Load in WL2
-1.893 kN/m 0 kN/m
=
0.088 kN/sqm
WL is normal to roof Hence, WL2 normal component = WL2 x Spacing = And, WL2 Tangential component =
0.158 kN/m 0 kN/m
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 1.179 -1.724 1.337 kN/m Tangential Load 0.383 0.055 0.383 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 1.179 -1.293 1.003 kN/m Tangential Load 0.383 0.041 0.287 kN/m Maximum Normal Component =
1.179 kN/m
Purlin Section Selected: Section Name Yield stress of material Flange Width, b Depth of section d Thickness t Length of Lip lip_l Internal Bending radius Total bending Radius, rad
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Z 200x60x2.3 2400 60 200 2.3 20 3 5.3
kg/sqcm mm mm mm mm mm mm
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd Flange Width w/o bend, w = b – 2 x rad
Purlin Weight
49.4 mm
Area
8.07 cm2
Zxx
47.72 cm3
Zyy
10.22 cm3
Ixx
477.18 cm4
Iyy
61.34 cm4
= =
6.334 kg/m 3.519 kg/sqm
(Area in sqcm x 0.785 kg/sqcm/m) in kg/m (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 100t = L/45 = Hence
200 mm 230 mm 133.333 mm
OK
Check No. 2 – Overall Width of Compression Flange<=35t Flange Width, b 60 mm 35t = 80.5 mm Hence
OK
Check No. 3 – Width of Lip >= b/5 Width of Lip B/5 = Hence
20 mm 12 mm OK
Check No. 4 – Total Width over both flanges >= L/60 Total Width over both flanges 117.7 mm L/60 = 100.000 mm Hence
OK
Check No. 5 – Zxx of Purlin >= WL/1400 for Simply Supported Purlin and >=WL/1800 for Continuous Purlin Zxx = 47.72 cm3 W is normal component of unfactored distributed dead load plus imposed load in kN L is span of purlin in mm W= 7.074 kN L= 6000 mm Number of Spans = 3 Hence, denominator = 1800 WL/denominator Hence
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23.580 OK
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd 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= w= Fy= w/t= 2.8 x t x ((w/t)^2-281200/Fy)^(1/6) 4.8t=
2.3 49.4 2400 21.4782608696 17.048 11.04
Lip l=
mm mm kg/sqcm mm mm
20 mm
Hence
OK
Lip is Edge stiffener only if w/t<60 Here, w/t =
21.4782608696
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 = 6.000 m Span for minor axis bending = Span of purlin / (no. of sagrods + 1) = 2 m Bending Moment Coefficient for Mxx(BMCX) Bending Moment Coefficient for Myy(BMCY) Note: Calculation for the above is at the top of the report DL+LL Normal Load Tangential Load
1.179 0.383
-1.724 0.055
DL+LL+WL2 1.337 kN/m 0.383 kN/m
Mxx Myy
4.244 0.153
6.207 0.022
4.812 KN-m 0.153 KN-m
88.947 14.988
130.077 2.148
Mxx/Zxx Myy/Zyy
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DL+WL1
10 10
100.849 N/sqmm 14.988 N/sqmm
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd Mxx/Zxx+Myy/Zyy
103.935
132.225
Max. Compression Stress = f
132.225 N/sqmm
= =
1435/sqrt(f) = w/t =
115.837 N/sqmm
132.225 N/sqmm 1322.249 kg/sqcm 39.463 21.4782608696
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) 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) Sxc = Compression Section Modulus of section about major axis = Zxx d = Depth of Section = Iyc = Moment of Inertia of the compression portion = Iyy/2 Hence, X =
200 47.72 20 30.6708864958
cm Cm^3 cm Cm^4
3111.639 (unitless)
Pi = E = Modulus of Elasticity, as per IS 801 is taken as Cb as per IS 801 can be taken conservatively assuming M1=0 (end span) Fy =
3.1415926536 2074000 kgf/sqcm 1.75 2400 kg/sqcm
Hence Y =
14925.720 (unitless)
Hence, 0.18 Y = And, 0.9 Y =
2686.630 13433.148
Comparing X with 0.18Y and 0.9Y, the applicable case is
2
Hence, Fb = = =
0.667Fy-Fy.X/(2.7Y) 1414.6889296355 kg/sqcm 141.469 N/sqmm
=
1440 kg/sqcm 144 N/sqmm
=
141.469 N/sqmm
Basic Allowable Design Stress = 0.6Fy
Hence, allowable stress is calculated as lower of the two DL+LL
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DL+WL1
DL+LL+WL2
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd Mxx/Zxx+Myy/Zyy Allowed
103.935 141.469
132.225 188.154
Safety Ratio
0.735
0.703
Max. Safety Ratio
0.735
115.837 N/sqmm, calculated above 188.154 0.616 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) Case 2: If h/t is more than 4590/sqrt(Fy), Fv=5850000 / (h/t)^2 Both are subject to maximum 0.4Fy h t Hence, h/t =
195.400 mm 2.300 84.957
4590/sqrt(Fy) =
Actual Shear
1 to maximum of 0.4Fy = 735.223 kgf/sqcm '=wl/2
Here, w = SQRT(Wn^2+Wt^2)
DL+LL
0.75(DL+WL1) 0.75(DL+LL+WL2) -1.293 1.003 kN/m 0.041 0.287 kN/m
Normal Load Tangential Load
1.179 0.383
w= Hence, Shear= Shear Stress fv=V/dt
1.240 3.719 8.275
1.294 3.881 8.636
1.043 kN/m 3.129 kN 6.962
Stress Ratio
0.113
0.117
0.095
Max. Shear Stress Ratio in Web
Hence
0.117
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 84.957 Hence, Fbw =
5065.388 kg/sqcm 506.539 N/sqmm Basic Allowable Design Stress calculated earlier = 0.6Fy 144 N/sqmm
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735.223 810.518 960
(Clear Depth between flanges = Depth – 2 x thickness)
93.693
Hence, Case is : Hence, Fv =
1275 x sqrt(Fy)/(h/t) = 5850000/(h/t)^2 = 0.4Fy =
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd Hence, governing value for Fbw =
144 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 88.947 130.077 100.849 N/sqmm Fbw 144 191.52 191.52 Safety Ratio 0.618 Max. Safety Ratio 0.679 In summary, Bending stresses in Web is:
0.679
0.527 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 506.539 735.223
673.697 977.847
DL+LL+WL2 673.697 977.847
Actual stresses already calculated are fbw 88.947 fv= 8.275
130.077 8.636
100.849 6.962
Hence, Fbw = And Fv =
DL+WL1
fbw/Fbw fv/Fv
0.176 0.011
0.193 0.009
0.150 0.007
SQRT of sum of squar
0.176
0.193
0.150
Maximum Combined Stress Ratio in Web is
0.193
In summary, Combined stresses in Web is:
Result 3: Check for Stresses: Overall Safety Ratio
OK
OK 0.735
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 = Hence, formula to use =
3 (3/384) (wl^4/EI)
w is normal component of unfactored distributed load in kN/m, max. of all load combinations = 1.724 kN/m L = Span of the Purlin
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6.000 m
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd E = Modulus of Elasticity, as per IS 801 is taken as =
2074000 kg/sqcm 207400 N/sqmm
I = Ixx
477.18 Cm^4
Hence, Theoretical Deflection =
17.64 mm
Allowable Deflection as IS codes is Span/180:
33.33 mm
Hence
OK
As per MBMA, allowed deflection from Live load component must be within Span/240 Span
6.000 m 6000 mm
or Span/240 =
25.00 mm
Normal Component of Live Load Hence, deflection from Live Load =
1.01 kN/m 10.3331229651
Hence
OK
Result 4: Check for Deflection:
OK
Results Summary Section Properties OK?
OK OK
Stresses Ok? Critical Stress Factor
OK 0.73
Deflection Check OK?
OK
Hence, Overall:
OK
Based on Section 9 of BS:5950 Part 5 – 1998 Based on IS 801 Clause 5.2.2.1
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)
Page 15
Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
onsultancy Services Pvt Ltd. r, Managing Director.
S 800 only ns based on IS 801 3/22/16
m/m) in kg/m
), subject to minimum of 40 kg/sqm
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
omponents
allowed
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
m/m) in kg/m
– 1998
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
hickness)
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
multiple spans
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Z Purlin Design Created Report by Madurai ES Consultancy Services Pvt Ltd
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