DESIGN OF PURLINS Sheet Content: Preliminary Data Sheet 1 of 28

PRELIMINARY DATA

Roof Data

Roof Angle 10.22

Roof Span 15 m

Spacing of Purlins 0.9 m

Length of Purlins 6 m

Material Type Weight Reference

Roofing GA 24 pre-

painted rib type roofing

1.3 psf Weight of

materials from:

www.pole-

barn.info

Insulation Fiberboard 1.5 psf

Conversion of Roofing and Insulation Weight to metric:

Roofing:

Insulation:

Trial Section: LC 175 x 50 x 20 x 2

mass in kg/m=4.68kg/m Sx = 30x103 mm3 Sy =5.5x103 mm3 (ASEP STEEL HANDBOOK)

DESIGN OF PURLINS Sheet Content:Loadings Sheet 2 of 28

LOADINGS

DESIGN OF PURLINS Sheet Content: Loadings Sheet 3 of 28

Dead Loads

Roofing (N/m) Weight of roofing x purlin spacing 71.85 x .9 =64.67 N/m

Insulation(N/m) Weight of insulation x purlin

spacing 62.67 x .9 =56.40 N/m

Total 121.07 N/m

Self Weight(N/m) Mass of purlin x gravity constant 4.68x 9.81=45.91 N/m

Live Loads

ROOF SLOPE: rise/run; 2.705/15

18.03%

Reference

Table 205-3

NSCP

Flat or rise less than 4 units vertical in 12 units horizontal

(33.3% slope). Arch and dome with rise less than one-eight of

span.

Tributary Area

95 m²

Uniform load (kPa)

0.6

Roof Live Load (N/m) Live load pressure x purlin spacing 540 N/m

DESIGN OF PURLINS Sheet Content: Wind Load Cases Sheet 4 of 28

WIND LOAD CASES

NORMAL TO RIDGE

(+GCpi)

(-GCpi)

38.06

DESIGN OF PURLINS Sheet Content: Wind Load Cases Sheet 5 of 28

WIND LOAD CASES

PARALLEL TO RIDGE

(+GCpi)

(-GCpi)

CRITICAL WIND PRESSURES

(+GCpi) (-Gcpi)

Wind Normal to the Ridge:

Windward: -863.932 -458.665

Leeward: -498.214 -92.947

Wind Parallel to the Ridge: -1063.824 -658.558

DESIGN OF PURLINS Sheet Content: Normal and Tangential Loads of Different Load Combinations Sheet 6 of 28

NORMAL AND TANGENTIAL LOADS OF DIFFERENT LOAD COMBINATIONS

D+W CASE 1:NORMAL TO RIDGE WINDWARD (+GCpi)

WINDLOAD=(863.93 N/m2)(.9 m)=777.54 N/m

NORMAL COMPONENT

TANGENTIAL COMPONENT

AT TOP AT CENTROID

DESIGN OF PURLINS Sheet Content: Normal and Tangential Loads of Different Load Combinations Sheet 7 of 28

D+W CASE 2: NORMAL TO RIDGE WINDWARD (-GCpi)

WINDLOAD=(458.67 N/m2)(.9 m)=412.80 N/m

NORMAL COMPONENT

TANGENTIAL COMPONENT

AT TOP AT CENTROID

DESIGN OF PURLINS Sheet Content: Normal and Tangential Loads of Different Load Combinations Sheet 8 of 28

D+W CASE 3:NORMAL TO RIDGE LEEWARD (-GCpi)

WINDLOAD=(498.21 N/m2)(.9 m)=448.39 N/m

NORMAL COMPONENT

TANGENTIAL COMPONENT

AT TOP AT CENTROID

DESIGN OF PURLINS Sheet Content: Normal and Tangential Loads of Different Load Combinations Sheet 9 of 28

D+W CASE 4:NORMAL TO RIDGE LEEWARD (-GCpi)

WINDLOAD=(92.95 N/m2)(.9 m)=83.66 N/m

NORMAL COMPONENT

TANGENTIAL COMPONENT

AT TOP AT CENTROID

DESIGN OF PURLINS Sheet Content: Normal and Tangential Loads of Different Load Combinations Sheet 10 of 28

D+W CASE 5:PARALLEL TO RIDGE (+GCpi)

WINDLOAD=(1063.83N/m2)(.9 m)=957.45 N/m

NORMAL COMPONENT

TANGENTIAL COMPONENT

AT TOP AT CENTROID

DESIGN OF PURLINS Sheet Content: Normal and Tangential Loads of Different Load Combinations Sheet 11 of 28

D+W CASE 6:PARALLEL TO RIDGE (-GCpi)

WINDLOAD=(658.56/m2)(.9 m)=592.70 N/m

NORMAL COMPONENT

TANGENTIAL COMPONENT

AT TOP AT CENTROID

DESIGN OF PURLINS Sheet Content: Normal and Tangential Loads of Different Load Combinations Sheet 12 of 28

D+L WINDLOAD=(658.56/m2)(.9 m)=592.70 N/m

NORMAL COMPONENT

TANGENTIAL COMPONENT

AT TOP AT CENTROID

DESIGN OF PURLINS Sheet Content: PURLINS WITHOUT SAGROD Sheet 13 of 28

CASE 1: NO SAGROD

LOAD COMBINATION D+W

CASE 1

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 2

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITHOUT SAGROD Sheet 14 of 28

CASE 3

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 4

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 5

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 6

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITHOUT SAGROD Sheet 15 of 28

D+L COMBINATION

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITHOUT SAGROD Sheet 16 of 28

LOAD COMBINATION ACTUAL STRESS (MPa) ALLOWABLE STRESS

(Mpa)

D+W

CASE 1

PASS

CASE 2

PASS

CASE 3

PASS

CASE 4

CASE 5

PASS

CASE 6

PASS

D+L

FAIL

DESIGN OF PURLINS Sheet Content: PURLINS WITH SAGROD AT MIDPOINTS Sheet 17 of 28

CASE 2 : PURLINS WITH SAGROD AT MIDPOINTS

LOAD COMBINATION D+W

CASE 1

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 2

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITH SAGROD AT MIDPOINTS Sheet 18 of 28

CASE 3

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 4

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 5

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 6

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITH SAGROD AT MIDPOINTS Sheet 19 of 28

D+L LOAD COMBINATION

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITH SAGROD AT MIDPOINTS Sheet 20 of 28

LOAD COMBINATION ACTUAL STRESS (MPa) ALLOWABLE STRESS

(Mpa)

D+W

CASE 1

PASS

CASE 2

PASS

CASE 3

PASS

CASE 4

CASE 5

PASS

CASE 6

PASS

D+L

PASS

DESIGN OF PURLINS Sheet Content: PURLINS WITH SAGROD AT THIRD POINTS Sheet 21 of 28

PURLINS WITH SAGROD AT THIRD POINTS

LOAD COMBINATION D+W

If

The maximum moment is at third point, Otherwise, the moment is at midspan

Therefore, the maximum moment is at third points

CASE 1

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 2

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITH SAGROD AT THIRD POINTS Sheet 22 of 28

CASE 3

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 4

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 5

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

CASE 6

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITH SAGROD AT THIRD POINTS Sheet 23 of 28

LOAD COMBINATION D+L

MAXIMUM MOMENT

NORMAL COMPONENT

TANGENTIAL COMPONENT

At Top

At Centroid

DESIGN OF PURLINS Sheet Content: PURLINS WITH SAGROD AT THIRD POINTS Sheet 24 of 28

LOAD COMBINATION ACTUAL STRESS (MPa) ALLOWABLE STRESS

(Mpa)

D+W

CASE 1

PASS

CASE 2

PASS

CASE 3

PASS

CASE 4

PASS

CASE 5

PASS

CASE 6

PASS

D+L

PASS

Based on the calculations presented it is recommended to use LC 175 x 50 x 20 x 2 section of purlin with sagrods at third points.

SAGRODS AT MIDSPAN

LOAD COMBINATIONS

D+W

(Tangential forces at top of the purlin)

(Reaction of sag rod)

(Total Reaction of sagrod)

(Cross sectional area of sagrod)

(Diameter of sagrod)

D+L

(Tangential forces at top of the purlin)

(Reaction of sag rod)

(Total Reaction of sagrod)

(Cross sectional area of sagrod)

(Diameter of sagrod)

DESIGN OF PURLINS Sheet Content: CONCLUSION AND DESIGN OF SAGROD Sheet 25 of 28

CONCLUSION

DESIGN OF SAG ROD

SAGRODS AT THIRD POINTS

LOAD COMBINATIONS

D+W

(Tangential forces at top of the purlin)

(Reaction of sag rod)

(Total Reaction of sagrod)

(Cross sectional area of sagrod)

(Diameter of sagrod)

D+L

(Tangential forces at top of the purlin)

(Reaction of sag rod)

(Total Reaction of sagrod)

(Cross sectional area of sagrod)

(Diameter of sagrod)

DESIGN OF PURLINS Sheet Content: DESIGN OF SAGROD Sheet 26 of 28

DESIGN OF PURLINS Sheet Content: DESIGN OF TIEROD Sheet 27 of 28

DESIGN OF TIE ROD

TIE ROD FOR SAGROD AT MIDSPAN

FORCE TRIANGLE ANALYSIS COMPUTATION

RTOTAL

10.22

P

DESIGN OF PURLINS Sheet Content: DESIGN OF TIEROD Sheet 28 of 28

TIE ROD FOR SAGROD AT THIRD POINTS

FORCE TRIANGLE ANALYSIS COMPUTATION

RTOTAL

10.22

P