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How Do You Prescriptively Size A Hip Rafter on Hip Style Roof?

wwhitney said:
For a simple hip of length L, if it needed to be designed as a beam, the tributary area is 1/2*L^2.
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Wrong.

The tributary area is not uniform on a hip or valley. Running calculations, as is necessary, requires that the distributed load be reflective of the tributary area acting on the member. The load may start at 70lbs (i.e. 2' jacks each side; length / 2 * 2 sides = 2'/2*2*35psf=70lbs), but at the end could be 280lbs (i.e. 8' jacks each side; 8'/2*2*35=280lbs). The load is not equally distributed across the member. This can also put one end of the member at risk for shear failure.
 
classicT said:
Wrong.

The tributary area is not uniform on a hip or valley. Running calculations, as is necessary, requires that the distributed load be reflective of the tributary area acting on the member. The load may start at 70lbs (i.e. 2' jacks each side; length / 2 * 2 sides = 2'/2*2*35psf=70lbs), but at the end could be 280lbs (i.e. 8' jacks each side; 8'/2*2*35=280lbs). The load is not equally distributed across the member. This can also put one end of the member at risk for shear failure.
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Agree. This is why I am bringing this up again.
 
classicT said:
Wrong.
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Ah, yes, working with horizontally projected distances and lengths, 1/2 * L^2 is the tributary area not when L is the hip length, but when L is the common rafter length. If M is the hip length, M = sqrt(2) * L, and so the tributary area would be 1/4 * M^2.

classicT said:
The tributary area is not uniform on a hip or valley.
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Agreed, and I take no issue with your subsequent comments, but as the topic of the thread is IRC prescriptive design for a hip rafter, per R802.4.4 such design considerations are only required when the roof slope is below 3:12.

Cheers, Wayne
 
wwhitney said:
Ah, yes, working with horizontally projected distances and lengths, 1/2 * L^2 is the tributary area not when L is the hip length, but when L is the common rafter length. If M is the hip length, M = sqrt(2) * L, and so the tributary area would be 1/4 * M^2.


Agreed, and I take no issue with your subsequent comments, but as the topic of the thread is IRC prescriptive design for a hip rafter, per R802.4.4 such design considerations are only required when the roof slope is below 3:12.

Cheers, Wayne
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This is prescriptive for connection support but has nothing to do with loading as previously stated. The section is misleading if you read it the way you do.
 
jar546 said:
You are forgetting about the second sentence that discusses the assembly.
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I believe you are referring to "The assembly shall be designed and constructed in accordance with the provisions of this chapter and Figures R606.11(1), R606.11(2) and R606.11(3) or in accordance with AWC NDS." So it suffices to comply with the rest of R802, i.e. R802.2 imposes no sizing requirements on its own.

Cheers, Wayne
 
wwhitney said:
Ah, yes, working with horizontally projected distances and lengths, 1/2 * L^2 is the tributary area not when L is the hip length, but when L is the common rafter length. If M is the hip length, M = sqrt(2) * L, and so the tributary area would be 1/4 * M^2.


Agreed, and I take no issue with your subsequent comments, but as the topic of the thread is IRC prescriptive design for a hip rafter, per R802.4.4 such design considerations are only required when the roof slope is below 3:12.

Cheers, Wayne
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The rafter span tables are for uniformly loaded rafters.

By your own agreement, the load is not uniform. We are not discussing rafters, nor is the load uniform, therefore the span tables do not apply.

R802.4.1 Rafter Size​

Rafters shall be sized based on the rafter spans in Tables R802.4.1(1) through R802.4.1(8). Rafter spans shall be measured along the horizontal projection of the rafter. For other grades and species and for other loading conditions, refer to the AWC STJR.
 
classicT said:
The rafter span tables are for uniformly loaded rafters.
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Agreed that the rafter span tables do not apply to hips. Moreover, the rafter span tables refer to rafter spacing, and the hip is a singular member, not a repetitive one.

So the IRC covers hip rafter sizing in R802.4.3. It amends that in R802.4.4 by specifying that in certain conditions you also have to design the hip rafter as a beam. Comply with R802.4.3 and R802.4.4, and you have prescriptively sized the hip rafter.

Look, I'm not arguing that the IRC provisions are good, or in accordance with what you'd get if you engineered the structure. I'm just commenting on what the IRC says--if those provisions are bad, then they need amending.

Cheers, Wayne
 
jar546 said:
This is prescriptive for connection support but has nothing to do with loading as previously stated. The section is misleading if you read it the way you do.
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Are you referring to R802.4.4? It precisely covers the hip rafter, and when you have to design it as a beam for its loading. It's not about connection details.

Cheers, Wayne
 
Ultimately, R301.7 rules it all.
Show me compliance with R301.7 when there is not a table for hip beams that is prescriptive other than by reference to the WFCM.

To assume that R802.4.3 covers spans of hip beams with a pitch greater than 3/12 would not be a wise choice and there would be a lot of structural issues.
 
Wayne, you're dug in on your interpretation. Don't fault you, as I am dug in the same way.

That said, if you feel confident with the methodology you describe, I hope the best. I see an inevitable failure of any roof designed in such a way.
 
classicT said:
That said, if you feel confident with the methodology you describe, I hope the best. I see an inevitable failure of any roof designed in such a way.
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Oh, if I were to build a hip roof from scratch, I'd go with the WFCM or an engineered design. As it certainly sounds like the prescriptive allowances in IRC R802 are too lax.

But so far the only plausible code citation that has come up in this thread, for roofs at least 3:12 slope, is R301.7, which I am currently thinking about.

Cheers, Wayne
 
wwhitney said:
Caveat: I have not look at an engineering analysis of how the forces resolve in a hip roof--it is fairly complicated.
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Some interesting discussion here on the complexities involved: https://www.eng-tips.com/viewthread.cfm?qid=392097

Seems like a hip rafter need not always act like a beam. A quote at the end of the above thread seems applicable: "I always dislike the case where in reality it is probably OK, but proving this is just not worth the effort."

Cheers, Wayne
 
jar546 said:
Do tell.
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R60= 20" of fiberglass...So even if you built with 2x12 rafters and ceiling joist in a raised heel rafter configuration, you are hard pressed to get 20" with proper ventilation in place...

1691070882973.png

And then of course you need to figure out how to deal with roof thrust....
 
steveray said:
R60= 20" of fiberglass...So even if you built with 2x12 rafters and ceiling joist in a raised heel rafter configuration, you are hard pressed to get 20" with proper ventilation in place..
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There is more than one material & method for insulation compliance, but I get it. When you are use to doing things one way and one way only, change is hard.
 
steveray said:
R60= 20" of fiberglass...So even if you built with 2x12 rafters and ceiling joist in a raised heel rafter configuration, you are hard pressed to get 20" with proper ventilation in place...

View attachment 11074

And then of course you need to figure out how to deal with roof thrust....
Click to expand...

I see that Table N1102.1.3 requires R-60 given all of CT is Climate Zone 5A, but...

2022 CT Res. Code - N1102.2.2 (R402.2.2) Ceilings Without Attics​

Where Section N1102.1.3 requires insulation R-values greater than R-30 in the interstitial space above a ceiling and below the structural roof deck, and the design of the roof/ceiling assembly does not allow sufficient space for the required insulation, the minimum required insulation R-value for such roof/ceiling assemblies shall be R-30. Insulation shall extend over the top of the wall plate to the outer edge of such plate and shall not be compressed. This reduction of insulation from the requirements of Section N1102.1.3 shall be limited to 500 square feet (46 m2) or 20 percent of the total insulated ceiling area, whichever is less. This reduction shall not apply to the Total UA alternative in Section N1102.1.5.

The noted section does not entirely resolve the issue, particularly given the sentence I put in green text, but the 500sf/20% would definitely help
 
classicT said:
The noted section does not entirely resolve the issue, particularly given the sentence I put in green text, but the 500sf/20% would definitely help
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You quoted the section on Ceilings Without Attics. The preceding section "N1102.2.1 (R402.2.1) Ceilings With Attics" does not have that 500sf/20% limit.

As I read it, you basically put R-60 over the entire ceiling where it fits, and where it gets squished at the eaves, that's fine.

Cheers, Wayne
 
wwhitney said:
You quoted the section on Ceilings Without Attics. The preceding section "N1102.2.1 (R402.2.1) Ceilings With Attics" does not have that 500sf/20% limit.

As I read it, you basically put R-60 over the entire ceiling where it fits, and where it gets squished at the eaves, that's fine.

Cheers, Wayne
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I don't agree Wayne.

Given that Steveray was discussing insulation not fitting within the rafter cavity, I figured he was speaking directly to either no-attic or conditioned attic spaces.

The section you are referring to would apply to stick-frame construction with an attic. But in that case, the insulation can typically overflow the cavity (extend above the ceiling joists). Where I disagree with you is in that the requirement is R-49 over 100% including at wall top plates. It does not say anything about it being ok to "squish" the insulation at the eaves.

For those interested, posting the section wwhitney is referring to.

2022 CT Res. Code - N1102.2.1 (R402.2.1) Ceilings With Attics​

Where Section N1102.1.3 requires R-49 insulation in the ceiling or attic, installing R-38 insulation over 100 percent of the ceiling or attic area requiring insulation shall satisfy the requirement for R-49 insulation wherever the full height of uncompressed R-38 insulation extends over the wall top plate at the eaves. Where Section N1102.1.2 requires R-60 insulation in the ceiling or attic, installing R-49 over 100 percent of the ceiling or attic area requiring insulation shall satisfy the requirement for R-60 insulation wherever the full height of uncompressed R-49 insulation extends over the wall top plate at the eaves. This reduction shall not apply to the insulation and fenestration criteria in Section N1102.1.2 and the Total UA alternative in Section N1102.1.5.
 
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