Stairs 8: Lapeyre or Alternating Tread Stairs

I received an interesting email from a member who was enquiring about Lapeyre Stairs, which I wasn't familiar with at the time. These may be the answer to some of you with limited run for regular stairs, especially for a loft area.

He asks, "I'm looking for information on Lapeyre stairs. Some people call them Monk's stairs. They are the steep alternating stairway that allows for angles over 50 degrees. Do you know how to calculate the rise and run for these type of stairs? Here are a couple of pics that show what I'm referring too."

This shows a metal version, notice how the treads alternate on each side. Make sure you start off correctly.

Here is a wooden version. The handrails are quite low compared to the metal steps.

Notice how the stringer goes up above the floor level to support the handrails. Also that the top step is flush with the floor level.

This was new to me, so when in doubt, I always draw a picture. To calculate the rise and run wouldn't be hard, though. I confered with Dan, my webmaster and brother. Dan loves a good math puzzle. I also enquired on the web at a site that was suggested to me by the member who lives in Washington State.

Below is a summary of Washington's specifications on Alternating Tread Stairs:

Alternating Tread-Type Stairs

Alternating tread-type stairs have a series of steps between 50 and 70
degrees from horizontal, attached to a center support rail in an
alternating manner so that a user of the stairs never has both feet
at the same level at the same time.

1 Alternating tread-type stairs shall be designed, installed, used,
and maintained in accordance with approved manufacturer's specifications,
and shall have the following:

(a) Stair rails on all open sides;

(b) Handrails on both sides of enclosed stairs;

(c) Stair rails and handrails of such configuration as to provide an

(d) A minimum of 17 inches between handrails;

(e) A minimum width of 22 inches overall;

(f) A minimum tread depth of 8 inches;

(g) A minimum tread width of 7 inches; and

(h) A maximum rise of 9 1/2 inches to the tread surface of the next
alternating tread.

2 Alternating tread-type stairs shall not have more than a 20-foot
continuous rise. Where more than a 20-foot rise is necessary to reach
the top of a required stair, one or more intermediate platforms shall
be provided.

3 Stairs and platforms shall be installed so the top landing of the
alternating tread stair is flush with the top of the landing platform.

4 Stair design and construction shall sustain a load of not less than five
times the normal live load, but never less strength than to carry safely
a moving concentrated load of 1,000 pounds.

5 Treads shall be equipped with slip-resistant surfaces.

6 Where a platform or landing is used, the width shall not be less
than the width of the stair nor less than 30-inch depth in the
direction of travel. Stairs shall be flush with the top of the landing
platform.

Our member continues, "It's ironic that it's for Washington state (WA) since that's where I'm located. It seems to be okay to use one of these as long as it isn't the primary means to access another level UNLESS it's to storage or a loft. Mine would be to a loft so I should be okay. From floor level to floor level is 8' 3" and the upper floor thickness is 8.5". I'd really like to keep the total run to as close to 3' as possible. Thank you."

Here is the layout for his stairs according to my drawing:

All I knew at first was that the height of the triangle was 99" (total rise) and the angle I wanted was 70 degrees, from the Washington State building code.

I know that the length of the staircase (the hypoteneuse in the diagram) is 99 inches divided by sin 70 = 105.35 inches.

Then I solved for the base of the triangle using Pythagorus's theorem (the height times itself plus the base times itself equals the hypoteneuse times itself) to get 36.03 inches. Wow exactly what he wanted.

I then divided up 105.35 inches into 11 rises at 9.58 inches each. The maximum rise according to Washington State codes is 9.5 inches. So I went the other way and got an angle of 71 degrees with 104.5 inches. I figured they wouldn't belly-ache about 1 degree if he was getting this inspected. Our cutoff saws call 90 degrees 0 so 71 degrees is 19 on the cutoff saw. This gives you the bottom angle as well as the angle of each step.

The total run is 36", but the total distance used is 36 + 9 (tread depth) = 45. That is what the opening in the floor should be. This gives a bit extra, so you won't be hugging the stairs when climbing them. Remember that this set of "stairs" is really a ladder and the conventional way of laying out stairs is not appropriate here. Remember also that the top tread is flush with the upper floor. This is specified in the Washington State code, too.

Total rise is 99" Total run is 36". Length of stringers is 140.5", allowing about 36" for the stringer to go above the top floor level to attach handrails. This is the same idea as pushing up the ladder above the roof to give something to hold onto while getting on and off the ladder. 11 risers at 9.5" equals 104.5". Stringers to be made from 2x10x12' long, ripped to 8 7/16". Treads are 9" wide.

I allowed the tread 1" longer so he can dado the stringers 1/2" on each side. This will be stronger than just the treads screwed to the stringers as in the picture. Also, I told him to put the handrails on the inside of the stringer, as specified by Washington State code, not like the picture, which has theirs on the outside. The end cuts and treads are on a 19 degree angle, so the length will fit. Where the 5" side of the tread is on the stringer, just rip a small filler to fill the dado. A blind dado would also work, here. The treads on the angle should be a bit longer than the width of stringer to fill in the dado nicely and overhang the stringer a bit.

Here is my drawing for the "stairs" :

And a drawing of the actual tread, the one above and below will be reversed:

Apply the theory as above to your particular set of stairs. I remind you that these should not be used throughout your house, just in areas with limited runs, such as bedroom lofts or attics.

Try the math first and if you are having trouble, you know I'm not far away along the cyber highway.

Dave