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  • stair stringers

    Hi, Having problems calculating tapered stairs for my porch. The top tread is appx 80" in width.
    The bottom tread is appox. 30" in width.
    I'm using 5 treads. How do I calculate the two outside tapered stringers for the tread dim. The three non-tapered stringers have 6.75" rise & 10" treads.

  • #2
    Are both sides tapered? Or just one side?

    You seem to be saying that you are using 5 treads and five stringers. Two stringers are tapered while three are not. I’m not sure what you mean by this. Are you really packing five stringers into 30 inches at the bottom? Do you mean that the three "non-tapered" stringers are evenly spaced in the middle and the two tapered stringers are on the outside? What are the dimensions of your stringers? How far in from the ends of the treads do you want the stringers?

    You also use "approx." measures. How "approx" do you mean?

    Are you looking for lengths of the stringers? Angles to set the miters? Widths of treads to cut? Dimensions and angles on treads to cut? How wide are the treads at the top? How wide are the treads at the bottom?

    Way too many questions and not nearly enough details to make these calculations.

    [ 09-26-2005, 10:19 AM: Message edited by: ianw2 ]
    Ian Wilson

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    • #3
      Thanks for the reply. Sorry for the amount of questions with not enough information. This is my first time on a BB. Let me try again, The stairs I'm building start with the top tread flush with the porch at 80"( I said approx. because I do not have the exact dim. with me, they are in another state)where I'm building these stairs.The bottom tread is 30" in width. Yes, the three stringers in the center are evenly spaced and straight as if the stairs had all treads at 30". Like a normal set of steps.I used an extra stringer in the middle for extra support.The two outside stringers would start at the bottom 30" and will be angled to the ends of the 80" dimensions at the top. I will use the normal overhang of .75 " or more on the treads. I know the length of the stringers & angles of the miters top and bottom. I will attach the bottom of the angled stringers to the outside of the center straight stringers.What I need to know is the run dimension of each tread on these angled stringers. The rise on the three center stringers is 6.75" with a 10" run.I assume that because the two outside stingers are at an angle, the run dimension needs to be greater. Thanks in advance for your patience with me and hopefully an answer to my question.

      [ 09-26-2005, 10:52 PM: Message edited by: MARK A. ]

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      • #4
        This should do it ....

        Comment


        • #5
          Wayne, Thanks for your help. I forgot about the Pythagorean theorem.This should do it as you said. My only problem is I forgot how to calculate the unknown angles. By your diagram I could'nt get the same angles as you did. Tried to look up in my old college books but to no avail. It has been many many years. I hate to ask, but, how about a little refresher. Thanks for your help either way.
          Mark A.

          [ 09-27-2005, 07:49 PM: Message edited by: MARK A. ]

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          • #6
            Thanks for stepping in, Wayne. It’s been really busy around here.

            If you think of the triangles created by the angle in the stringers, you get a triangle with a 25" base and a 50" side. The arctan of 25/50 = the angle at the bottom of the stairs. The arctan of 0.500 = 26.565 degrees or 26°33’54". (Tan = length of opposite side over the length of the adjacent side; Cos = length of adjacent side over length of hypotenuse; Sin = length of opposite side over length of hypotenuse---remember SOH CAH TOA from high school Trig? As a surveyor, I use this sort of math every day.))

            Since we’re dealing with a right triangle, the sum of the interior angles is 180°. So, 180-90-26.565 = 63.435 degrees or 63°26’06".

            There’s also a component to the angle contributed by the fact that this project is 3D. The contribution is relatively minor, though. You can set the toe of the stringer and scribe the vertical component to the angle for a better fit.

            I don’t have access to my CAD software at home. I’d have to "build" the stairs in 3D to come up with the compound angle.
            Ian Wilson

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            • #7
              The angle calculations are in the middle at the bottom. A/sin A etc.
              The angles of the triangle are labled A, B and C. The formula uses the lengths opposite the angles. A = 90 degrees, we know this because thats the way we build the inner stringer. the length opposite 90 is 55.9" calculated as C in the formula which is likely where the confusion begins. the formula should have said A = 55.9
              So A/sin of angle opposite to A = b/sin of angle opposite B
              A = 55.9
              Angle opposite A = 90 degrees
              B = 50
              Angle opposite of B is what we solve for.
              Sin of 90 = 1

              so 55.9/1 = 50/sin B

              or sin B = 50/55.9
              sin B = 0.8945

              To solve for B we need to take the ARCSIN of both sides (usually expressed as sin**-¹ on a calculator)

              B = 63.4**°

              Does that help?

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              • #8
                Ian & Wayne, Thank you both for your answers to my questions. You were both very helpful and refreshed my memory.I printed copies of the replys and put them in a safe place in case I get another brain fade.

                Thanks Again
                Mark A.

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