Example Calculations for Purlins [Ver 1.1 1098]

Example Calculations for Purlins [ver 1.1 1098]

  Example Calculations for Purlins   REQUIREMENTS Select Z-section member size for Dead + Live and Dead + Wind load combinations for metal building purlins. Select sections for each of the following lateral stability conditions: both flanges continuously braced through-fastened (See pages I-B-1 to I-B-3 for a definition of through-fastened condition.) both flanges laterally braced at intervals specified in four span Laterally Braced Capacities tables in Part III. Deflection and web crippling will not be considered in this example.   DESIGN INFORMATION For this example, purlins are designed as continuous over all interior supports with pinned supports at the endwalls. Because web crippling is ignored in this example, forces from supports must be transferred directly to the web of the purlin sections by way of a clip that bolts to the purlin web.   DETERMINE UNIFORM WIND LOAD 2 16 25

ft. ft.

Roof slope Sidewall height Purlin span

5 125

ft. sq. ft.

Tributary length supported by purlin Support area for purlin

Determine support area for purlin

Determine external pressure coefficients GCp Reference BOCA, Figure 1609.8.1(2), page 175, using area 1. Positive values are toward the surface. BOCA has no provisions for positive wind pressure to purlins for buildings with roof slopes of less than 30 degrees. -1.2 Negative external pressure coefficient   Determine internal pressure coefficients GCpi Reference BOCA, Table 1609.7(6), page 173. .25 VIII-C-3   Figure VIII-C-1: PRESSURE COEFFICIENTS

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Negative internal pressure coefficient 15 October 1998

Example Calculations for Purlins [ver 1.1 1098]

Compute resulting uniform wind load 1 -19.357

psf

Uniform pressure

VIII-C-4

15 October 1998

  DETERMINE UNIFORM LIVE LOAD Reference BOCA, Table 1607.3, page 161, MINIMUM ROOF LIVE LOADS.   Roof slope

Tributary loaded area in square feet for any structural member 0 to 200 201 to 600 Over 600

     

 

 

Flat or rise less than 4 inches per foot (1:3) Arch or dome with rise less than 1/8 of span

 

16

 

 

Rise 4 inches per foot (1:3) to less than 12 inches per foot (1:1)

 

 

 

< 200

14

   

  12

 

  20

sq. ft. psf

12

    Live load to purlins

  SELECT A TRIAL SECTION AND COMPUTE TOTAL APPLIED LOADS

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12

 

12

 

12

 

16

Arch or dome with rise of 1/8 of span or less than 3/8 of span Rise 12 inches per foot(1:1) and greater Arch or dome with rise 3/8 of span or greater

 

20

Example Calculations for Purlins [ver 1.1 1098]

Trial section: 8 X 2.5 Z 16 G Compute member loads for current trial section 5 2.796 0.559

ft. lb/ft. psf

Purlin spacing Purlin weight Purlin dead load

0.92 107.396

psf lb/ft.

Panel weight Uniform purlin positive load

-67.041

lb/ft.

Uniform purlin negative load

VIII-C-5

15 October 1998

  CHECK CAPACITIES AGAINST APPLIED LOADS Successful sections are indicated by Bold Italics. Condition

 

Load Direction

 

Continuously braced

 

Section Capacity (lb/ft.)

 

 

Throughfastened

 

 

 

Laterally braced

 

page III-K-44

109

 

 

 

 

 

page III-K-44

0 33 11 33 0

 

**

 

 

0 33 11 33 0

109

 

Positive (down) Negative (up)

Reference

109

 

Positive (down) Negative (up)

 

Laps

 

Positive down Negative (up)

   

Applied Load (lb/ft.)

89

0 33 11 33 0

89

 

  page III-N-109

 

** Apply .7 reduction factor for through-fastened. The trial section has a capacity greater than the applied load in the continuously braced and through-fastened conditions. Therefore, the section passes for these conditions. The section capacity is less than the applied for the laterally braced condition. Additional trials are necessary to find an adequate section for this condition.   Laterally braced: It is necessary to find a section that will carry 107.396 ignoring differences in dead load of the section. Options are: 8 X 2.5 Z 14 G @ 374 lb 8 X 3.0 Z 15 G @ 379 lb 8 X 3.5 Z 16 G @ 367 lb Trial section: 8 X 3.5 Z 16 G Condition Laterally braced

 

Load Direction Positive (down) Negative (up)

Applied Load (lb/ft.)

Section Laps Capacity (lb/ft.) 108 0 33 11 33 0 108

 

VIII-C-6

Reference page III-N-84

  15 October 1998

  RECOMPUTE LOADS FOR CURRENT TRIAL SECTIONS Use exact section weights.   Continuously braced: Trial section: 8 X 2.5 Z 16 G (no change from initial trial)

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Example Calculations for Purlins [ver 1.1 1098]

107.396 -67.041

lb/ft. lb/ft.

Uniform purlin positive load Uniform purlin negative load

  Through-fastened: Trial section: 8 X 2.5 Z 16 G (no change from initial trial) lb/ft. lb/ft.

107.68 -67.041

Uniform purlin positive load Uniform purlin negative load

  Laterally braced: New trial section: 8 X 3.5 Z 16 G 3.197 0.639

lb/ft. psf

Purlin weight Purlin dead load

107.797

lb/ft.

Uniform purlin positive load

-66.741

lb/ft.

Uniform purlin negative load

VIII-C-7

15 October 1998

  CHECK CAPACITIES AGAINST APPLIED LOADS Successful sections are indicated by Bold Italics. Section & Condition

  8 X 2.5 Z 16 G Continuously braced

Load Direction

   

 

 

 

   

   

   

   

   

 

   

    0 33 11 33 0 page III-K-44

   

Positive (down) Negative (up)

   

 

109

   

Reference

0 33 11 33 0 page III-K-44

109

   

   

Laps

109

Positive down) Negative (up)

  8 X 3.5 Z 16 G Laterally braced

Section Capacity (lb/ft.)

Positive (down) Negative (up)

  8 X 2.5 Z 16 G Throughfastened

Applied Load (lb/ft.)

 

 

   

    0 33 11 33 0 page III-N-84

108

 

108

 

All sections pass.   SUMMARY OF SECTIONS AND WEIGHTS For definition of laps, see pages I-C-1 and I-C-2. Section & Condition

  8 X 2.5 Z 16 G Continuously braced

  8 X 2.5 Z 16 G Throughfastened

  8 X 3.5 Z 16 G Laterally

Laps

   

Number of Braces per Bay

    0 33 11 33 0

   

    0

    0 33 11 33 0

   

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page III-K-44

3852

0

    page III-K-44

3852

    3

Reference

   

   

    0 33 11 33 0

Weight for 12 Rows (lb)

    4404

page III-N-84

Example Calculations for Purlins [ver 1.1 1098]

braced VIII-C-8

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15 October 1998