# Construction Math for Dummies



## BlueRidgeGreen

I'm about to start cutting the driveway for this one in a couple weeks and have been going over the prints for a month or so trying to familiarize myself with all of the peculiar details.

As I was working my way through the framing, I ran into a math problem way to complicated for my puny brain.

I had a solution after one conference call with the architects, but I brought my two leads into my office for an afternoon and had them chew on it as an exercise.

One of them is a VMI grad and actually worked pretty deep into the equations, but was stymied by missing information on the prints.
The other has a degree in Classical Guitar....and just stood there looking dumber than me....which was not an easy task.


I'm wondering......without the use of the CAD files, how would you guys do this?

The ridge beams are skewed at irregular and differing angles from the exterior walls at each individual "pod".
Due to the non-perpendicular orientation, you end with sloped exterior wall heights.

How do you guys frame this thing?
How do you generate the stud lengths?
Ascertain the exact angle of slope for the walls (bevel cuts)?

I know I would have had to simply guerrilla that thing after I got the deck built with complete mathematical perfection.
Pythags....plumb sticks/bobs.....lasers.....some free jazz....and I'm not even sure what.
But I could get it done.
Seems like that would take an incredible amount of time.

I understand the values necessary to generate the answers using equations.....
Angle of the ridge beams.
Perpendicular distance from the ridge beam to certain key points (corners....etc.).
Distance from sub-floor to underside of ridge.
I just have no concept of what equations to use.

Forget about where the roof line meets the radiuses.....
I would be pulling my hair out.

Is there an easy(ier) way?
How would you do it?


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## hdavis

Odd angles like those studs I like to draw out on 3d graph paper so I can see what is going on. Draw the stud, then the roof plane intersection. You can use that diagram to set up the trig calculations without getting too lost. 

Or you can go old school and direct measure off your diagram what the xyz difference is. It's like doing rise and run, except with the added slope on the cut. Set your saw up directly based on those, or do the trig to convert to saw angles.

If you don't have graph paper, you can just draw the axis on a sheet of paper or on the subfloor. A large drawing is good.

You can also just dummy one small section of roof and stud up and direct measure with an angle finder.


You can also do it with a steel square....

Stud lengths are easy, because it's the same as normal once you convert the roof run and rise to the specified angle.


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## CENTERLINE MV

Man, how do you even begin to price that thing?

If it were my job, I’d put that thing into sketchup and have it on my site laptop.


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## hdavis

Obviously, dummying up and direct measuring is the fastest. Short of plugging into equations.


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## BlueRidgeGreen

hdavis said:


> Odd angles like those studs I like to draw out on 3d graph paper so I can see what is going on. Draw the stud, then the roof plane intersection. You can use that diagram to set up the trig calculations without getting too lost.
> 
> 
> 
> Or you can go old school and direct measure off your diagram what the xyz difference is. It's like doing rise and run, except with the added slope on the cut. Set your saw up directly based on those, or do the trig to convert to saw angles.
> 
> 
> 
> If you don't have graph paper, you can just draw the axis on a sheet of paper or on the subfloor. A large drawing is good.
> 
> 
> 
> You can also just dummy one small section of roof and stud up and direct measure with an angle finder.
> 
> 
> 
> 
> 
> You can also do it with a steel square....
> 
> 
> 
> Stud lengths are easy, because it's the same as normal once you convert the roof run and rise to the specified angle.



Drawing it on the floor is how I would have done it without the CAD files. 

Every ridge to wall angle is different. 

And the main issue is finding stud heights at any given point. 

I’m going to get a list of key points for the architect to generate off of CAD. 

I’m thinking I will need all of the corners...
And the points when the radius begins on each wall. 

Then I theoretically should be able to frame all the walls, and just frame the roof to the walls. 
If anything is off though....it could get messy. 
Never used CAD points before, but I think it should be fairly simple using them. 

Next issue...
Not having to field measure every rafter. 
Generating numbers based on layout. 

Then there’s the arched section between the ridges. 
That’s easy though. 
Make a pattern....go.....


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## Robie

CENTERLINE MV said:


> Man, how do you even begin to price that thing?
> 
> If it were my job, I’d put that thing into sketchup and have it on my site laptop.


I'm using an archaic version of TurboCad and there are many times I use it in the shop just to figure an angle or length of piece of wood to be cut. 
It would take me two forevers to try to do it without some "computerized" help. Geometry and the equations and I aren't the best of friends.


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## BlueRidgeGreen

CENTERLINE MV said:


> Man, how do you even begin to price that thing?
> 
> If it were my job, I’d put that thing into sketchup and have it on my site laptop.




Cost Plus 15. 

That’s how. 



I just threw a pretty heavy square foot number on the framing. 

I think
My estimate is around $325 per square ft. for the whole thing. 

Estimate...key word. 


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## BlueRidgeGreen

Robie said:


> I'm using an archaic version of TurboCad and there are many times I use it in the shop just to figure an angle or length of piece of wood to be cut.
> 
> It would take me two forevers to try to do it without some "computerized" help. Geometry and the equations and I aren't the best of friends.




Problem is....
Computers and I ain’t the best of friends either. 

I’m just going to have the architects do their jobs and generate everything I need. 

I’m thinking that I’ll need to check everything first somehow......just to be sure they didn’t screw up a value.
Like plotting to underside of double plate...or top. 
That kind of thing. 

It’s gonna be a ride no matter what. 


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## Robie

BlueRidgeGreen said:


> Problem is....
> Computers and I ain’t the best of friends either.
> 
> I’m just going to have the architects do their jobs and generate everything I need.
> 
> I’m thinking that I’ll need to check everything first somehow......just to be sure they didn’t screw up a value.
> Like plotting to underside of double plate...or top.
> That kind of thing.
> 
> It’s gonna be a ride no matter what.
> 
> 
> Sent from my iPhone using Tapatalk


I'd hire Warren....:thumbsup:


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## BlueRidgeGreen

Robie said:


> I'd hire Warren....:thumbsup:




No offense to Warren....
But me and my boys got this. 

I’m doing it because it’s interesting. 
I blew off a few much easier customs to take it. 
Certainly not going to let someone else have the fun. 


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## hdavis

If you have the CAD files, you dump it into your CAD program and you just pull all the numbers off of that.

Honestly, the stud lengths are the easiest part. Figure the roof run at the wall angle, then it's like cutting any run and rise wall intersection.


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## CENTERLINE MV

BlueRidgeGreen said:


> Cost Plus 15.
> 
> That’s how.
> 
> 
> 
> I just threw a pretty heavy square foot number on the framing.
> 
> I think
> My estimate is around $325 per square ft. for the whole thing.
> 
> Estimate...key word.
> 
> 
> Sent from my iPhone using Tapatalk


DAMN!  I’d have a hard time building a simple cape out here for $325 finished. That place would be double or triple that figure out here.


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## BlueRidgeGreen

CENTERLINE MV said:


> DAMN!  I’d have a hard time building a simple cape out here for $325 finished. That place would be double or triple that figure out here.




Yeah...
I hear that.
Different market here. 
Simple cape “could” be built for 150 here. 
Not by me. 
But it’s done. 

I should get close to my number. 

We are going to do almost everything in house. 
Time is not a factor. 


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## BlueRidgeGreen

hdavis said:


> If you have the CAD files, you dump it into your CAD program and you just pull all the numbers off of that.
> 
> 
> 
> Honestly, the stud lengths are the easiest part. Figure the roof run at the wall angle, then it's like cutting any run and rise wall intersection.




Yeah....
And that’s where we ended up in the office. 
Those equations. 
But without knowing the ridge to wall angle, or even the exact ridge placement,...the numbers would be useless. 

(When I say “we”....I mean Chad. )


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## BlueRidgeGreen

CENTERLINE MV said:


> DAMN!  I’d have a hard time building a simple cape out here for $325 finished. That place would be double or triple that figure out here.




Ha!!!!

Just checked. 

You’re on the Vineyard. 

I’ve did a couple kitchens up there for my Manhattan clients back in the old days. 

$$$$$$$$$$$$$$$$$$$$$$$$$

You are no longer allowed to comment on pricing in the real world. 


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## CENTERLINE MV

BlueRidgeGreen said:


> Ha!!!!
> 
> Just checked.
> 
> You’re on the Vineyard.
> 
> I’ve did a couple kitchens up there for my Manhattan clients back in the old days.
> 
> $$$$$$$$$$$$$$$$$$$$$$$$$
> 
> You are no longer allowed to comment on pricing in the real world.
> 
> 
> Sent from my iPhone using Tapatalk


Ya, stupid money out here. They have it but hate spending it. I’m just about to begin building a porch with a balcony above on a $7 million house and they can’t figure out why my price is so high...


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## 91782

That **** hurts my pretty little head.


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## hdavis

BlueRidgeGreen said:


> Yeah....
> And that’s where we ended up in the office.
> Those equations.
> But without knowing the ridge to wall angle, or even the exact ridge placement,...the numbers would be useless.
> 
> (When I say “we”....I mean Chad. )
> 
> 
> Sent from my iPhone using Tapatalk


I've pulled those off the scale drawing before. Better to have actual measurements, especially in this case.


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## BlueRidgeGreen

hdavis said:


> I've pulled those off the scale drawing before. Better to have actual measurements, especially in this case.




I could just set those values myself and roll on. 

Angle of ridge to wall. 
Exact placement. 

But only if I did the calcs. 

That’s what I’d do if it were pre-CAD. 


Using their CAD figures for anything binds me to them fully. 


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## ScipioAfricanus

I think the most important thing is to see if you can a hold of the 
Architect and beat the holy **** out of him.

That is where I would start anyway.

Andy.


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## Robie

Have you and the customer "signed" yet?


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## griz

Robie said:


> Have you and the customer "signed" yet?


why are they deaf????????....:whistling:laughing:


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## Calidecks

You can find all your stud lengths on your rake walls with a Construction Master calculator. Repetitively. 


Mike.
_______________


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## BlueRidgeGreen

Californiadecks said:


> You can find all your stud lengths on your rake walls with a Construction Master calculator. Repetitively.
> 
> 
> Mike.
> _______________




By all means Micheal. 


Show me how a Construction Master generates those numbers 


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## Calidecks

.....


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## Calidecks

https://www.manualslib.com/manual/220247/Calculated-Industries-4065.html?page=21


Mike.
_______________


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## Calidecks

Mike.
_______________


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## Calidecks

Break big jobs into smaller tasks as to not get too overwhelmed. 


Mike.
_______________


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## Calidecks

Simply put, rise, run and diagonal. run being 16"

Put the pitch in the calculator first, 4/12 5/12 or whatever.

16 inch run, then hit rise. It will tell you how much it rises in 16" 

Then hit diagonal and it will give you the length of the stud at the top plate. 

You'll need to write each stud length on paper.

Making a cut list. 

You'll need to add each rise to your original stud height, for example. Your first stud may be 92-1/4"

Keep adding the rise to your starting point. My starting point example was 92-1/4"

repetitively


Mike.
_______________


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## BlueRidgeGreen

Californiadecks said:


> Simply put, rise, run and diagonal. run being 16"
> 
> Put the pitch in the calculator first, 4/12 5/12 or whatever.
> 
> 16 inch run, then hit rise. It will tell you how much it rises in 16"
> 
> Then hit diagonal and it will give you the length of the stud at the top plate.
> 
> You'll need to write each stud length on paper.
> 
> Making a cut list.
> 
> You'll need to add each rise to your original stud height, for example. Your first stud may be 92-1/4"
> 
> Keep adding the rise to your starting point. My starting point example was 92-1/4"
> 
> repetitively
> 
> 
> Mike.
> _______________




The only problem with that Mike, is that the walls do not behave like rake walls. 

Their pitch isn’t tied to roof pitch and variable. 

Although...by just looking at the prints quickly, it seems that some are identical, in that they match each other.....but again, not the roof pitch. (I think....I’m out at the farm and the prints are in the office.)

Question....
Can I enter a specific value for pitch...say 11.26 degrees into the CMaster and generate the stud heights?

That....would be a huge time saver. 


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## Jay hole

BlueRidgeGreen said:


> The only problem with that Mike, is that the walls do not behave like rake walls.
> 
> Their pitch isn’t tied to roof pitch and variable.
> 
> Although...by just looking at the prints quickly, it seems that some are identical, in that they match each other.....but again, not the roof pitch. (I think....I’m out at the farm and the prints are in the office.)
> 
> Question....
> Can I enter a specific value for pitch...say 11.26 degrees into the CMaster and generate the stud heights?
> 
> That....would be a huge time saver.
> 
> 
> Sent from my iPhone using Tapatalk




You can enter 11.26 as a pitch and as long as it’s consistent than the CM will spit out stud lengths.


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## Robie

Is this the build you were going to record with your drone?

Can we get videos of you guys scratching your heads?

Sorry...couldn't resist.


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## BlueRidgeGreen

Robie said:


> Is this the build you were going to record with your drone?
> 
> Can we get videos of you guys scratching your heads?
> 
> Sorry...couldn't resist.




I do all my head scratching ...pre-game. 

Then.....when the drone flies....

I’m like Jordan....game 7....nothin but net. 




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## Texas Wax

Lots 'o fun! Top down the only way I know how to do it.... the rake walls pitch needs to be figured from the theoretical rise at each rafter minus the differences of rise from ridge. And each rafter rise needs to be figured from the run in plan using roof pitch. To figure the runs in plan gonna have some trig to do.

You get the rake pitch it's easy to calculate the stud lengths. You also get the common rafter difference length on that rake wall, for 16" (in pic) o.c. by figuring the two lengths and subtracting.


:laughing: The beginnings kinda look like this??? Yup tell me to go get 'D Sure as hell would love to see another way :thumbsup:


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## Robie

Like I said....Hire Warren.


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## Texas Wax

Robie said:


> Like I said....Hire Warren.


It's just some basic trig and Pythagorean math. Maybe some mental gymnastics easy peasy. :laughing:

Kind of believe it might be easier, especially for adjustments on the fly on site to do the math vs cadding it out. :whistling I'd probably triple check the math in Cad, just to be safe.


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## Fouthgeneration

It looks like an Alabama trailer After the Tornado.....:thumbsup:

How do you keep the flat top of the roof from leaking?

The roof section doesn't appear to be thick enough for the roof rafter depths needed on the longer spans.....IMHO

The ratio of exterior wall to square footage is sub-moronic in my opinion.

How do keep inside corners dry and tight under roof that only over hangs an inch or two?

Love to see the HVAC plan....:laughing:It needs 2x + Heat and cooling vs a "normal" wall to floor ratio home....

The good news the Tax assessor might end giving the HO a yearly grant till they move

How can the designer claim all the fees for the design when the plans aren't finished?

If you bring this thing to life Dr. Frankenstein, are you partially responsible or fully responsible for any Civil torts or code violations?

Can't the building meeting the intent if not the actual verbiage of energy building codes, maybe at low elevations in Hawaii?

Would any bank loan enough money for a mortgage that approaches a fraction of its construction cost?:no:

Can you afford the HO walking away with out paying for all the work you have done, if they suddenly develop commonsense? 

Successes have a thousand Fathers, failures always are illegitimate children of no-one.


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## Robie

Oh geez Edith.....


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## Fouthgeneration

T-Wax @#34 Looks like you're 95% there, But, the roof center(ridge) is aways from the line you drew... and the Roof is "rolled" over the ridge area ~ 2 feet, to add to the cost of the roof framing on every one...

One could "balloon" frame the studs temporarily, using a sloped ledger board to set the lower end of the rafters on, then cutting the studs to fit under the roof deck, having erected a temp ridge a the 'Missing' ridge height, chase the rafter down a jackline to intersect the off grid wall line.

Hopefully all the roofs spring from a constant wall height at the low point? 8-9' aff?

You could frame this in big tin shed, and haul out the rooms on medium sized trailer.

Good luck, keep posting as the wheel turns please:thumbsup:


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## Robie

Fouthgeneration said:


> T-Wax @#34 Looks like you're 95% there, But, the roof center(ridge) is aways from the line you drew... and the Roof is "rolled" over the ridge area ~ 2 feet, to add to the cost of the roof framing on every one...
> 
> One could "balloon" frame the studs temporarily, using a sloped ledger board to set the lower end of the rafters on, then cutting the studs to fit under the roof deck, having erected a temp ridge a the 'Missing' ridge height, chase the rafter down a jackline to intersect the off grid wall line.
> 
> Hopefully all the roofs spring from a constant wall height at the low point? 8-9' aff?
> 
> You could frame this in big tin shed, and haul out the rooms on medium sized trailer.
> 
> Good luck, keep posting as the wheel turns please:thumbsup:


That's what I would do.....:laughing:


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## BlueRidgeGreen

tgeb said:


> You didn't have to carve out bottom plates for the radius walls?
> 
> 
> 
> Looks very good, a whole lot of detail work in that one. :thumbsup:
> 
> 
> 
> I'm feeling sorry for the sheet rock guys. The clean up guy mostly, there's gonna be a lot of scraps.....




Nah....
I decided to simplify them. 
Decided........I had too. 

So much waste. 
My dumpster went from 25% to 85% in a couple weeks with sheathing. 
I’m bleeding money on wasted Ice and Water now. 
It’s a horror show. 

Ceilings now. 
And crazy interior stuff. 
More gray hairs....

Thanks 


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## Tinstaafl

I give up. WTF is this edifice intended for?


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## BlueRidgeGreen

Tinstaafl said:


> I give up. WTF is this edifice intended for?




It’s a residence Tins....

We are all builders. 
As such, the wildly impractical nature of it offends our sensibilities in a deeply intuitive way. 

Not so for the architects and the clients. 

They choose art over logic. 
Form over function. 

Ohhhh let me count the ways!
(I stopped counting a long time ago....)

Give me a minute. 
I’ll post the drawings of the useless custom fabricated steel “sunshades” (they block about .0000372% of the sun) that I argued with the architects about being essentially purely aesthetic. 
And...I’ll post just one of the interior details that seem to rely on magic fairy dust to accomplish....and will cost a fortune...and have no meaningful purpose whatsoever. 
(Tip o the iceberg my friend....
Endless supply...)

All that said...
It’s growing on me. 
In a “stuck in a foxhole with it” kind of way. 

It is beautiful in its own way. 
It is a stunning departure from the million dollar chitboxes being built all over this fine country that offend me as a craftsman and a lover of architecture. 

If you gave me a $1.5 mil budget ....
I would build something very different. 
Very ...interesting and unique...but different than this. 
But...it ain’t my 1.5. 
The cash gets wired to my accounts....
It beats the hell out of building aforementioned chitboxes ...
And I very....very much enjoy the challenge. 


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## BlueRidgeGreen

That’s a 3-9/8-0 pocket door under a fixed glass transom. 

You got some extra fairy dust I can use?

(To say nothing of the wall in section to the left. 
Pocket door....recessed medicine cabs....wall hung vanity.....curved LED light cove on top. 
2x4 Wall.....
Lots of dust....lots. )

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## BlueRidgeGreen

Sunshades....
5”-1” tapered projection on an 8-0/8-0 fixed panel window and 8-0/8-0 sliders. 

“It’s not just merely aesthetic.”

Sure bro...
Whatever helps you sleep at night. 

(I held a piece of CDX up in one of the openings to show the client how much sun it “shaded”...
I laughed...and laughed...)


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## BlueRidgeGreen

I could do this all night long. 

For days in fact. 

The struggle is real. 

#hangthearchitectsbytheiranklestillsomebloodrushestotheirbrains

(I actually still like them both, and the client is a great guy. 
Spent the better part of last weekend with them all, drinking, eating, arguing about curved concealed LED light cove details and trying to explain why their ceiling framing will be another $25k....

Good times. )


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## Tinstaafl

Color me gobsmacked. I could maybe see it as some sort of extravagantly perverted funhouse, but even that is a stretch.

They wouldn't perchance be planning on building something up my way, would they? :whistling:


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## Fouthgeneration

thank GOd they don't want brick.....


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## hdavis

The ceiling framing isn't completed? What's going on there?


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## hdavis

I won't mock the design choices, I'm not the INE that has to "get it". 

Great build so far.:thumbsup:


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## BlueRidgeGreen

Fouthgeneration said:


> thank GOd they don't want brick.....




.....




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## BlueRidgeGreen

hdavis said:


> The ceiling framing isn't completed? What's going on there?




Has to mimic the curvature of the roof line. 

Worked through every possible method in my mind. 

Like everything on this house....no easy way to do it. 

Underside of rafters have to be framed down equal to the lowest protrusion in any given pod. 
Bottom of ridge beams (except for the big pod where the flitch plate is the low point). 
Then the arches have to be inserted between the ridge.....just like the roof 




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## BlueRidgeGreen

hdavis said:


> I won't mock the design choices, I'm not the INE that has to "get it".
> 
> 
> 
> Great build so far.:thumbsup:




Thanks H.....


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## Dirtywhiteboy

It looks very unique! Looks like a ton of work to achieve that. Looks like there a lot of metal to go on yet.


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## hdavis

BlueRidgeGreen said:


> Has to mimic the curvature of the roof line.


That's just unfortunate.


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## BlueRidgeGreen

hdavis said:


> That's just unfortunate.




I know....
But during the recent meeting, I actually came down on the side of doing it. 

Why spend all this money, go through all the trouble to bring this design to life, only to bail on the dramatic ceiling and leave it in flat sections with wrapped LVL’s. 

Seems like such a waste to me. 

We came this far.....might as well honor the concept. 




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## hdavis

I agree, it isn't complete without it .

I can only imagine this is going to involve a lot more plywood....


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## BlueRidgeGreen

hdavis said:


> I agree, it isn't complete without it .
> 
> 
> 
> I can only imagine this is going to involve a lot more plywood....




Nope. 

None. 

Just a bunch of framing. 


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## Dirtywhiteboy

Man that's a he!! of a house,, I hope you came out good on the $$$ end. I can see a ton of thinking and work there. Is working for this architect something you'd like to do more of?


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## Calidecks

Is that a frank Lloyd Wright concept? Lol


Mike.
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