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Re: How to Frame an Arch

From: bjwalsh88@sbcglobal.net
Category: Wallboard/Veneer Plaster
Remote Name: 68.255.172.32
Date: 19 Nov 2005
Time: 12:38 PM

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Question: We want to open the wall from the dining room to family room with an open arch. We have plenty of space and think it could be more than six ft. wide. Please give us any info you think we need to proceed with this project. I prefer a plastered arch rather than a paneled square. Thanks!

Builders Websource® Answer: Framing an arch is relatively straightforward, but it does require forethought and a little math. If your ceiling height is 8' (typical), the arch will be relatively shallow in order to leave room for the header while still leaving sufficient clearance for the passthrough. The first step is to determine whether the wall is load bearing or not. A load bearing wall is one that transfers load from a 2nd floor, a roof post, or any other load (including even ceiling joists). If the wall is load bearing, you'll need a structural engineer to determine the size of the header. Assuming you have double top plates (3"), In most cases, a 4x12 header is typically sufficient to support a 6-foot opening, but this would drop the top of the arch to approximately 6'-9" which is getting pretty low. If you have determined that the wall is not a load-bearing wall, then you'll be able to get by with a more shallow header, possibly a 4x8 or 4x10.

Before you add the arch, complete the square portion of the frame with the header including a king stud on each side of the header plus at least one jack stud to support each side of the header -- just as if you were framing for a door or window. For extra strength, consider adding metal straps and/or plates to secure the header. Assuming your wall is 2x4 construction, rip a piece of 2x4 down to 2x3 size, or simply purchase one stick of 2x3 (actual dimensions will be 1.5 x 2.5 inches). Nail this in the middle of the bottom portion of the header across the entire length of the opening. You should have a 1/2" inset along both sides of the header bottom. Depending on the depth of the arch, add another piece of 2x3 along each side of the arch. For example this piece might be 6"-9" long. For the sake of discussion, let's assume that the arch opening (clear) from the face of one jack stud to the next is 6'.  And suppose the depth of the arch from the bottom of the 2x3 on the header is 6". Cut two pieces rectangular pieces of plywood exactly 6'-3" wide by 7.5" high. This leaves 1-1/2" on the top and 1-1/2" on each side to nail to the 2x3 stringers.

Now for the tricky part. You'll need to draw an arc on the plywood that mathematically conforms to the correct width and depth. That means you need to compute the actual radius of the arch based on a preset width and depth. Using a little math, you can derive the following formula for the radius based on Pythagorean's theorem:

r2 = (r-y)2 + (x/2)2 where: r = arch radius,  y = arch depth, and x = clear arch width

Solving this equation for the radius "r" yields:

r = (y/2) + x2/(8*y)

Plugging in hypothetical measurements (let's do it in feet where x = 6' and y = 0.5'):
r = (0.5/2) + 62/(8*0.5) = 0.25 + 36/4 = 9.25 feet or 9'-3"

Now, here comes the fun part. Find a clean, flat surface, such as your garage floor. Layout your cut plywood and using a string with a 9'-3" length, draw an arch (using a pencil) along the desired trajectory. Remember that the plywood has an extra 1-1/2" on three sides, so make sure you leave that intact. The string acts as a giant compass. Secure the pivot end of the string with a nail or have some hold it while you draw out the line. It's critical that the center of the plywood be aligned with the string, otherwise your arch will be lopsided.

Once you've penciled in your line, cut along the line with a circular saw or jig saw. Nail both pieces of 1/2" plywood into place on each side of the opening. The surface of the plywood should now be flush with the face of the studs on both sides of the archway. To provide extra support and a nailing surface along the bottom side of the archway, cut short pieces of leftover 2x3 and nail them into place along the inside contour of the arch, making sure the face of the blocks are flush with underside opening. This will provide a nailing surface for drywall and/or plaster. If you like, use bullnose drywall corners along the contour of the entire arch sides and opening (be sure to fill them solid so they don't get dinged easily). When it's all done, it will look first-rate, adding a touch of class to your opening. Here's a tip: If you like the look of a thicker arch, you could also buildup the opening with 2x4 material along the outer face of the arch opening (sides) and 2 layers of 3/4" plywood cut to the right radius along the arch opening. This makes the arch look substantial, creating an elegant touch.

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