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Building Homes or Extensions/New hipped roof over existing patio slab

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Question
I am in the process of talking with carpenters about adding a new hipped roof to the back of my house.  This is a 2 story house which, in the back where an existing 10 X 16 slab is located, goes up 90 degrees to the second story roof line.  There are no windows above the area to be constructed.  I have 16 in. eaves on all sides and will want the new roof to match.  The area (under roof) I wish to cover will be 24 X 12 not including the eaves.  I would like the eaves to extend behond the patio and will have either 3 or 4 footings incorporated in the new slab pour.  The existing pitch for my roof appears to be somewhere between a 5/12 and 8/12 as there are different pitches.  This hipped roof will, for all practical purposes, will look like it was built along with the existing house.  I'm looking at an 8 foot flat finished ceiling.  How do I figure how much slab I'm going to need to support this roof as far as area?  I need to know how far out from the house the slab will need to extend.  I've been told I will need to go out at least 15 feet from the house for a 24 foot lenght with a 3 foot ridge and add on a foot for each additional ridge line.  Is this correct.  Accordingly, if I chose a 20 foot roof, without eaves, I would need to go out 13 feet with a 3 foot ridge and an additional foot out for each foot added to the ridge.  Also, I'll be paying to have the roof finished separately from the carpenter and would like to know how I can calculate how many squares I'll need.  My geometry isn't too good these days but I'm willing to learn.  Any help you can provide will be greatly and sincerely appreciated.

Thanks.

Answer
The eave overhang has no bearing on slab size or anything else.  The overhang should match existing, you want to make sure you can close the eave back to the house line without interfering with window and door tops.

A normal hip roof works on a 45° angle in relation to the building corner.  A 45° triangle will have two sides identical in length.  If you want the addition to come away from the existing building 12 feet, then you will need the same 12 feet on the other side of the corner.  You have 2 corners, so the hips would touch at their tops at 24 feet.  If you want some ridge between the hip tops so it doesn't look like a pyramid, then you will need to be longer than 24.

At 8 in 12, with a 12' run, the rafters will be about 14'-6".  With overhang and losses, you will be slightly over 400 Square feet (four squares, in roofer talk).

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Dan Griffin

Expertise

I can answer almost all questions related to the total construction process. My expertise is in commercial construction, though I can field most any residential question. I have hands on experience in concrete, heavy equipment, masonry, all phases of carpentry, interior finishes, and I am fairly strong in mechanical and electrical.

Experience

I have over 20 years experience as a commercial carpenter and commercial construction superintendent. I have another 20 years experience in facility management for a major school district.

Organizations
My favorite hobby for he past 12 years has been singing bass in a The OkChorale men's barbershop chorus and the Mature Moments quartet.

Education/Credentials
I hold a Bachelor's degree in English and Math. I have completed many continuing education hours in the building trades. I hold a Master Carpenter card from the AGC, Associated General Contractors.

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