Example Calculations for Purlins [Ver 1.1 1098]

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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 Roof slope

16 ft. Sidewall height

25 ft. Purlin span

Determine support area for purlin

5 ft. Tributary length supported by purlin 125 sq. ft. 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 Negative internal pressure coefficient

VIII-C-3 15 October 1998

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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

20 16 12

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

16 14 12

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 12 12 12

Arch or dome with rise 3/8 of span or greater

< 200 sq. ft.

20 psf Live load to purlins

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Trial section: 8 X 2.5 Z 16 G

Compute member loads for current trial section

5 ft. Purlin spacing

2.796 lb/ft. Purlin weight 0.559 psf Purlin dead load

0.92 psf Panel weight

107.396 lb/ft. 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 Applied Load (lb/ft.) Section Capacity (lb/ft.) Laps Reference Continuously braced Positive down 109 0 33 11 33 0 page III-K-44 Negative (up) 109 Through-fastened Positive (down) 109 0 33 11 33 0 page III-K-44 Negative (up) ** Laterally braced Positive (down) 89 0 33 11 33 0 page III-N-109 Negative (up) 89

** 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 Load Direction Applied Load (lb/ft.) Section Capacity (lb/ft.) Laps Reference Laterally braced Positive (down) 108 0 33 11 33 0 page III-N-84 Negative (up) 108 VIII-C-6 15 October 1998

RECOMPUTE LOADS FOR CURRENT TRIAL SECTIONS Use exact section weights.

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Through-fastened: Trial section: 8 X 2.5 Z 16 G (no change from initial trial) 107.68 lb/ft. Uniform purlin positive load -67.041 lb/ft. Uniform purlin negative load

Laterally braced: New trial section: 8 X 3.5 Z 16 G 3.197 lb/ft. Purlin weight 0.639 psf Purlin dead load

VIII-C-7 15 October 1998

CHECK CAPACITIES AGAINST APPLIED LOADS Successful sections are indicated by Bold Italics. Section & Condition Load Direction Applied Load (lb/ft.) Section Capacity (lb/ft.) Laps Reference 8 X 2.5 Z 16 G Continuously braced Positive (down) 109 0 33 11 33 0 page III-K-44 Negative (up) 109 8 X 2.5 Z 16 G Through-fastened Positive down) 109 0 33 11 33 0 page III-K-44 Negative (up) 8 X 3.5 Z 16 G Laterally braced Positive (down) 108 0 33 11 33 0 page III-N-84 Negative (up) 108

All sections pass.

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

Condition

Laps Number of Braces per Bay Weight for 12 Rows (lb) Reference 8 X 2.5 Z 16 G Continuously braced 0 33 11 33 0 0 3852 page III-K-44 8 X 2.5 Z 16 G Through-fastened 0 33 11 33 0 0 3852 page III-K-44 8 X 3.5 Z 16 G

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braced