# A Wood Purlin Design Question

Chances are good if you have to ask a structural design question, then you are in over your head.

“Can you 2 by 4 flat on an 8 foot span Truss”

A few years ago, one of my neighbors bought a pole building kit from someone other than Hansen Pole Buildings. It was for a garage and sidewall columns and single roof trusses were placed every eight feet. Now I am relatively certain this building’s roof purlins were supposed to be 2×8 on edge between trusses – however for some obscure reason, they got installed flat wise! I am unsure as to how they were even able to get roofing installed without falling through.

This is just one of many reasons why post frame buildings should be designed by a Registered Professional Engineer.

When it comes to designing whether a roof purlin can achieve a given span, it takes a lot of calculations – both for live or snow loads, as well as wind loads. In high wind areas, wind will fail purlins (or their connections) rather than snow! I have condensed calculations down to just bending and deflection and will use minimum snow loads in this example:

ROOF PURLIN DESIGN – Main Building (Balanced snow load)

Assumptions:

Roof slope = 4:12 (18.435° roof angle)
Trusses spaced 8-ft. o.c.
Purlin span = 8-ft.
Purlin spacing = 24 in.
Purlin size 2″ x 4″ #2 Southern Pine
Roof steel dead load = 0.63 psf steel American Building Components catalogue

Bending Stresses

Fb: allowable bending pressure
Fb‘ = Fb * CD * CM * Ct * CL * CF * Cfu * Ci * Cr
CD = 1.15 NDS 2.3.2
CM: wet service factor
CM = 1 because purlins are protected from moisture by roof
Ct: temperature factor
Ct = 1 NDS 2.3.3
CL: beam stability factor
CL = 1 NDS 4.4.1
CF: size factor
CF = 1 NDS Supplement table 4B
Cfu: flat use factor
Cfu = 1.1 NDS Supplement table 4B
Ci: incising factor
Ci = 1 NDS 4.3.8
Cr: repetitive member factor
Cr = 1.15 NDS 4.3.9
Fb = 1100 psi NDS Supplement Table 4B
Fb‘ = 1100 psi * 1.15 * 1 * 1 * 1 * 1 * 1.1 * 1 * 1.15
Fb‘ = 1600 psi

fb = (purlin_dead_load + S) * spacing / 12 * cos(θ) / 12 * (sf * 12 – 3)2 / 8 * 6 / b / d2 * cos(θ)
S = 21.217 psf using the appropriate load calculated above
fb = 21.217 psf * 24″ / 12 in./ft. * cos(18.435) / 12 in./ft. * (8′ * 12 in./ft.)2 / 8 * 6 / 3.5″ / 1.5″2 * cos(18.435)
fb = 2961.59 psi > 1600 psi; stressed to 185.1%

Deflection

Δallow: allowable deflection
Δallow = l / 180 IBC table 1604.3
l = 96″
Δallow = 96″ / 180
Δallow = 0.533″
Δmax: maximum deflection
Δmax = S * spacing * cos(θ * π / 180) * (sf * 12)4 / 185 / E / I from http://www.awc.org/pdf/DA6-BeamFormulas.pdf p.18
E: Modulus of Elasticity
E = 1400000 psi NDS Supplement
I: moment of inertia
I = b * d3 / 12
I = 3.5″ * 1.5″3 / 12
I = 0.984375 in.4
Δmax = 21.217 psf / 144 psi/psf * 24″ * cos(18.435° * 3.14159 / 180) * (8′ * 12 in./ft.)4 / 185 / 1400000 psi / 0.984375 in.4
Δmax = 1.118″ > 0.533″; 209.68% overstressed in deflection

These calculations are based upon purlins every 24 inches on center. If you were to reduce spacing to say 11 inches on center then flatwise 2×4 #2 Southern Pine with a 20 psf roof snow load would be adequate.

If you were able to somehow acquire 2850f Machine Stress Rated 2×4 with a E value of 2300000 psi (very high grade material used by some truss manufacturers) spacing could be 18 inches on center.

Again – remember these equations are just for checking for bending due to a minimal snow load, wind conditions may dictate. Please consult with a Registered Professional Engineer for actual designs.

## 4 thoughts on “A Wood Purlin Design Question”

1. Woah thats way to far of distancing between trusses u can have posts that span 8ft oc. In doing that you’d have to use box beams or use LBL beams and and do a layout of 4′ oc. For your rafters and then id use 16 foot lumber and stagger your roof perlings. As well as roof perling a 2×6×16

1. Actually trusses could be placed 10, 12, or more feet on center. We are currently providing a municipal building with a pair of trusses (and columns) every 24′.

2. I’m looking to Know if I can use 2×4 Doug Fir in a vertical configuration on an 8ft span as purlins and gerts on a small pole building with 8″ walls’ Tks Jim in Madras,Or

1. It would depend upon grade of material, design wind speed and exposure, roof snow load and roofing and siding materials. Ultimately these should be determiend by the engineer who seals your building plans.