Roof Diaphragm for Solar Array

[jt0716]

In order to determine the load a roof can handle, I typically analyze one of the rafters, and convert the uniform roof load to a distributed load on each rafter. Long story short, I check up to deflection criteria. My question is, how do I account for roof sheathing as a diaphragm which in turn reduces deflection to one rafter and transfers load to adjacent rafters. Is there a code reference?

 

[a2mfk]

"how do I account for roof sheathing as a diaphragm"

Maybe it is me that is confused, but I think you are referring to load sharing between adjacent rafters. Diaphragm traditionally refers to the horizontal structure of the roof decking that carries lateral loads, nothing to do with gravity loads.

I would think metal and wood decking is too flexible to redistribute the load once it deflects, unlike perhaps a concrete or steel frame and floor system.

Others may have another take on it... I personally would only do tributary area in a wood decking system and not push the envelope, the load goes into the nearest member.

 

[jt0716]

Thanks, and yes I think load sharing is the better term. I have been using the tributary area for loading, but it was recently suggested to me that I should account for the sheathing which would aloow for greater spans/loading. I just wanted to be sure I wasnt missing something.

 

[a2mfk]

I don't think you get load sharing out of the sheathing, its way too flexible. However, if you cross brace to both trusses on either side, you may be able to justify this. I have done this several times with steel joists and steel angle cross bracing, but this is a much stiffer assembly then wood...

 

[MiketheEngineer]

Are you thinking about "Repetitive bending stress??" as allowed by NDS??

Under the correct conditions - you can increase wood load capacity up to 15% for this...

 

[jt0716]

That is correct, the repetitive member factor can be multiplied by the bending stress Fb in some conditions, but how does that factor relate to modulus of elasticity, E in a deflection calc?

 

[MiketheEngineer]

If I remember correctly - it doesn't

 

[cetiger]

For designing wood members, the repetitive member factor is only applied to the bending stress (Fb), as Mike mentioned, and not to the modulus of Elasticity (E). Check Table 4.3.1 of the NDSWC for applicable adjustment factors. When calculating deflections for solid wood sawn members, see section 3.5 of the NDSWC for assistance. I assume you are analyzing/designing solid 2X wood rafters, otherwise it can be a little difficult "by hand" calculating deflections of pre-fabbed wood trusses where the moment of inertia (I) varies along the length of the truss.
In respect to load distribution, it can be assumed that any gravity/lateral loads (as applicable) are distributed to the roof sheathing/plywood as a uniform load, then transferred as a linear load distributed along each rafter/truss top chord which in turn bear on load-bearing walls or beams, etc. Typically plywood has a span-rating, often stamped on one face of the sheet. If someone has suggested using a higher span-rating, it would suggest to me that they are trying to eliminate some of the roof/floor rafters by spacing them further apart. Keep in mind, depending on the new spacing and new load distribution, you may find a bigger rafter is needed for the additional span loads now applied. Higher span-rated plywood AND bigger rafter sizes could cost more than your original layout. If the project budget is tight, the recently suggested route may not be the correct route in all cases.

 

[jt0716]

Well, it is an existing dwelling, with 2x6 rafters 16"oc, 14' span. They would like to mount the system every 4 feet. Since the array basically becomes a new roof structure, all loads that would typically bear on the rafters at 16" on center, now would fall on a 2x6 48" on center. According to my calcs, the 2x6 just cant handle it.

 

[a2mfk]

ce- I think what the OP meant was can you use load sharing based on relative stiffness and deflection of a single rafter, by load distribution to the adjacent rafters. As the member deflects due to individual loading, does the roof decking transfer some of the load to the adjacent rafters.

You may be able to do this in a concrete floor with "T" beams or closely spaced composite steel beams with a very rigid floor, but not in wood sheathing IMO (not to an appreciable amount that I would consider). I have done this with X bracing between steel joists to redistribute point loads to adjacent joists...

An easier way to redistribute loads from a solar array to wood roof rafters is how you design your rack structure above. Place posts on as many rafters as possible in a manner that will spread the load out...

 

[jt0716]

a2- precisely, my original design submittal was to fasten to each rafter at 16"oc, but the contractor basically went ahead and did "past practice" and attached every 48" and would like us to certify.

 

[IRstuff]

Sheathing is pretty typically added when residential roofs are re-done, particularly with ceramic tile. Seems to me that one could beef up the sheathing and mount between two rafters, which would then share the load between themselves.

Have the panels already been procured? There are PV systems that are direct replacements for roofing tiles:

http://www.tollbrothers.com/communities/9506/preserve_solar.pdf

http://inhabitat.com/solar-panel-roof-tiles/

https://secure.mawebcenters.com/websites/atlantisenergy/sunslates2.html

TTFN

FAQ731-376

 

[cetiger]

a2 - Gotcha! Makes sense after reading jt's recent post explaining the layout.

jt- I agree with a2. Some load-distribution may be present but due to the lack of rigidity of the plywood, I would think it would be very minimal, not to mention quite time consuming to calculate even if you have all the variables.
Sure if the contractor (I'm assuming your client) wants to pay additional for a more rigourous analysis...knock yourself out and bill away. Otherwise, I would let him know it's understressed AND for additional services you can provide a reinforcing detail.

Lesson to contractor... "You're not an engineer. Just b/c it worked on the last project across town, doesn't mean it will work on the next one. Consult with the engineer FIRST!"

 

[jt0716]

IR- Panels have actually already been fastened to the roof...and therein lies my dilemma.

 

[IRstuff]

Too bad. How thick is the sheathing?

TTFN

FAQ731-376

 

[jt0716]

On a one story cape? i can only assume negligible...3/4 inch tops? maybe 1/2" tongue and groove?

 

[a2mfk]

If its not a vaulted ceiling and there is attic spacing, sistering 2x to match the existing members, either full length or in the middle section where bending stress is the worse... Are the support racks steel so you will have to have them in-field weld to add supports (which is what everyone is trying to avoid)?

If you post a sketch of a typical cross section including your rafters maybe we can come up with some type of easy solution...

 

[jt0716]

Sorry, correction, its actually a 1 1/2 story cape (attic space converted to loft) and shed dormer on rear. Contractor tells me adding rafters is nearly impossible (calcs show that a sistered 2x6 would work at 48" spacing) The solution IMO is to remove the system, and reattach as designed.

 

[cetiger]

How overstressed are the current rafters? IBC Chapter 34, Section 3403.2 allows up to a 5% overstress when adding to existing structures. Also if using ASD to analyze, try using LRFD, you'll probably see a little more capacity.

 

[IRstuff]

3/4" sheathing is pretty standard for roofing tile that weigh in at about 5-7 lb/ft^2. Certainly, for that type of loading, the load is shared amongst the rafters.

TTFN

FAQ731-376