Rafter stresses in hip roof construction

[JEmH]

This question has bothered me for some time, and it seems to be coming up more often, so I guess it's time to delurk.
In almost any residential construction code or publication, (I'm thinking of the IRC, specifically) there are rafter span tables. These list the maximum horizontal span for a roof rafter given species, grade, dead and live/snow loading, and spacing. There are few caveats on their use: The whole system must sit on joists with sheathing, ties, or something that resists horizontal reaction at the lower rafter ends. Tops of rafters must be fastened to each other or a 1" ridge board, hips and valleys must have a 2" board as deep as the cut ends of the rafters, and the free ends of hip and valley beams must somehow transfer load down to a wall or something. Pretty simple.
Yet, I am troubled. I note that with few exceptions, the spans seem to be calculated by treating the rafter as a simply supported continuously laterally braced beam using typical NDS Fb values with appropriate C's for duration, repetitive use, etc. This seems fine except that I'm not seeing the rafter as a simple span. Two rafters and a ceiling joist are acting like a truss, so there is also axial force in the rafter. Am I to assume that neglecting this is an expediency that the codes permit based on experience? If so, I can buy that.
But here's where I'm really troubled: it appear to me that hip and valley beams will have to resist the end reactions of all the rafters framed into it, which again might be combined bending and compression. Yet I can find close to no code requirements to "design" these beams, even for a complicated roof, where the load paths might be nonobvious and circuitous. (Every other roof nowadays.) Or am I missing something?
Here's why I ask. Apparently, the P in PE stands for paranoid. I think that residential plans that wouldn't stand up to engineering analysis are being reviewed and approved by code enforcement officials. (At least here is Pennsylvania, where, I should point out, a statewide building code is fairly new.)
Anyone have any insight or observations, or should I just slink back into my world of concrete?

 

[JAE]

Rafter framing, in actuality, has all sorts of complex load paths running through it. I do believe you are fairly on-target with the idea that the simplified analysis is just trying to allow some expediency in design...and also allow for long-term experience.

The idea that a ceiling joist and a rafter somehow form a truss, and thus add compressive load into the rafter would only be accurate if there was some mechanism to develop the horizontal shear through the "truss" - without any diagonals, the two would tend to act more independently with no truss action.

Hip and valley beams taking compressive loads from intersecting rafters - the fact that the rafters are at 45 degrees (or whatever) to the supporting ridge/valley beam does cause axial force to flow into the supporting beam. But this is usually taken out by the roof sheathing in my opinion. some axial perhaps is produced...but it may be that the amount of axial is negligible with regard to the stresses induced by the flexure....just a thought.

As a side story to this, I once had an engineer on my staff have a new house built. He would leave work every day to go inspect the progress. During the carpentry framing, he would spot all sorts of things that "just didn't work" in terms of good engineering design and proper load path. He would write all sorts of notes on the framing, instructing the contractor to do this and that, or he would call. Once, he even brought some tools and added a few struts and braces where he thought there should be some, climbing all over the roof framing to do so. It was his new house and dangit...it had to be right. Needless to say, it probably drove the framer nuts.

 

[SacreBleu]

Wood framing is really strange. There is some humor here. What you and JAE are saying is essentially true. But, since we do not design wood framing with FEA like a aircraft structure, we oversimplify things, and I suppose that is fine. Like JAE says, the plywood can take up loads, and there are plenty of "redundant" load paths in the finished structure.
Now, after we calculate the forces with seemingly (+-)50% accuracy, we apply all sorts of finely-tuned coefficients to the calculate the allowable stresses of the members, to the extent that would make any PHD scientist proud.
And if you think that's a little strange, the IBC has us checking seismic loads to probably 4 decimal significant digits.

 

[whyun]

Oversimplification is absolutely necessary in wood design as there are lack of homogeneity in the makeup, many different species that are most commonly visually graded, no ways of determining any splits or checks inside the member, direction of cut and many other issues.

Going back to the original question by JEmH, if the roof framing system is NOT designed as a truss, you can not have just the ridge plate, two sloping roof rafters and a horizontal ceiling joists on bearing walls. You actually need a ridge beam. Only exception to this would be when you have say two bearing corridor walls near the ridge, you can allow for the roof rafters to cantilever towards the ridge.

Dead and live loads are always acting downwards so you may design a typical simply supported sloping roof joist by taking the tributary dead and live load on the "projected length" of the joist. Alternately you may breakdown this uniform gravity load into components normal and parallel to the slope, use the force normal to the joist on the "actual length" of the joist combined with the axial load which is the component parallel to the joist.

This can be explained so much easier graphically...

 

[SacreBleu]

It is best shown in Breyer's Design of Wood Structures book. I don't know if the IRC Code Book addresses all this because we never use Prescriptive Design Methods. What about collar ties to create the "A" - frame sort of truss effect?

I live in the Southwest US, and stick framing is not used anymore. I recently did a remodel on a very old custom house, and it was very interesting to see how its stick framing was very cleverly configured to make the complex roof work. It took quite a while to "re-calculate" the entire roof. However, we did find a couple of overloads, but of course, wood design having a FS of about 4, the house was fine for all these years.

 

[whyun]

SacreBleu, yes I do see it in Breyer's Fourth Edition page 2.16... Thank you.

I'm in California here and wood structures have a very good track record even through many earthquakes. Safety factors and the redundancy of nailed connections contribute to the tremendous amount of energy wood structures can absorb.

 

[JAE]

whyun,
So in CA - do many houses simply fall down in seismic events, or do they generally stay up OK? I seem to remember most reports of failure having to do with masonry walled buildings and precast. Do most residential houses do fine?

 

[SacreBleu]

whyun,
Do many houses suffer some sort of damage, however slight? I recall hearing that the Northridge quake caused extensive damage. Are there many lawsuits claiming poor design/construction following a major earthquake?

 

[whyun]

It is evident that single family homes with plywood diaphragm and shearwalls generally perform very well in earthquakes. In a large seismic event, there may be damages in areas where inadequate holdowns were provided.

As a wood structure becomes more complex, damages incurred were proportional: One story wood framed home versus two story, 3 to 4 townhouse unit structures, larger wood framed apartments, etc.

Discontinuous shear wall such as a first floor level carport with only pipe columns below the second floor shear walls is a classic example of a weak story on one side. One apartment collapse (name which escapes me...) during the Northridge Earthquake was similar to this situation.

There are wood framed buildings with perimeter shear walls (til-up concrete, masonry, etc) commonly used in warehouses or megastores. Problems with this type of building had been related to connection of the heavy wall to the light roof diaphragm.

In general, one or two story homes performed very adequately compared with other "heavier" and what appears to be "stronger" buildings.

As for lawsuits, I really don't have the facts but... based on what I've observed, newer homes designed to higher seismic force level generally performed well so designers and builders were not much affected by lawsuits. Problem buildings may have been older structures where original builders and designers are no longer in business (no one to sue). There must have been many lawsuits related to "other" building types.

 

[SacreBleu]

whyun-
Thanks for the info.

 

[JEmH]

Thanks to everyone for the insight.

SacreBleu-
You comment that in SW US stick framing isn't used anymore. I'm curious as to what dominates construction there (any anywhere else, if anyone else is reading).

 

[SacreBleu]

JEmH-
I meant light-metal plate connected trusses (prefab), especially for roof construction.

 

[whyun]

Gang-Nail system was quite common in the 80s into maybe mid 90s. I hardly see these anymore out here... Did a web search and plated truss system seems to be still used in Canada and the UK. Try "Gang-Nail" in google.

Here's a site you might be interested in:

http://www.tpinst.org

 

[SacreBleu]

Further, we call the roof trusses as "2x4" trusses, and the floor trusses as "4x2" trusses, referring to the orientation and usual size of the top and bottom chords.
Girder trusses may be multi-ply and may have (in the case of roof) 2x6, 2x8 etc. bottom chords, in order to be able to support secondary girders framing into them.
Thge metal plates are those punched ("pronged"?) plates that replaced the nails that were used previously.