Does anyone know the formula for cutting stringers for staircases??
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I have made 3 sets, one in concrete, another in a rough outdoor setting to get up to a patio and a formal household stair case.
The only thing they have in common is they got better.
I used graph paper to draw it out. Once you have that you can get the angle and calculate your stretch and rise from there.
ok take the total height from floor up to next level in inches and divide either 7 to eight into and see how many steps you would need...hope you understand how to use carpenters square...but a tread with can be no less than 10...riser height 7-8"
Before you do anything with stairs and landings, check with your local building department to see if you need a building permit. Also ask about code requirements for staircase width, headroom, unit rise, unit run, landing sizes, and, fire blocking.
RISE AND RUN CALCULATIONS
The following formula is used to calculate rise and run. Numbers in parentheses are sample values used to demonstrate calculations.
• Measure the total rise between the finish floors (108 inches). If the finish floors are not yet installed, allow for their thicknesses when measuring.
• Divide the total rise by 7 inches (a comfortable unit rise) to arrive at an approximate number of stair risers (108 / 7 = 15.43 risers).
• Round this number either up or down to the nearest whole number and divide the total rise again by this new number to determine the average unit rise (108 inches / 15 risers = 7.2-inch average unit rise).
• Convert this decimal number back into a fraction. Enter this number onto your worksheet under average unit rise (7.2 inches = 7 3/16 inches).
• Using the rise/run formula, calculate an average unit run by subtracting the average unit rise from 18 inches (18 inches - 7 3/16 inches = 10 13/16 inches).
• Now convert the average unit run to a decimal equivalent (10 13/16 inches = 10.8 inches). Multiply the unit run by the number of stair risers to get the total run of the staircase (10.8 inches x 15 = 162 inches total run).
• Determine stringer lengths with this formula: (total rise) 2 + (total run) 2 = stringer length 2 (1082 + 1622 = 37,908). Figure the square root of the answer (square root of 37,908 = 194.7 inches), and divide it by 12 inches to convert it to feet (194.7 inches / 12 inches = 16.2 feet). Then add 10 percent, and round up to the nearest foot to find out the correct length 2x12 to buy (16.2 feet + 1.6 feet = 17.8 feet; rounding up = 18-foot 2x12s).
• Determine the amount of riser and tread materials needed:
(15 risers x 36 inches x 7.2 inches = 3,888 square inches) + (15 treads x 36 in. x [10.8 in. + 1.2 in. nosing] _ 6,480 sq. in.) = 10,368 square inches = 72 square feet (three 4x8 sheets).
Note: There are 32 square feet in a 4x8 sheet of plywood and 144 square inches in one square foot. So 32 x 144 = 4,608 square inches per 48 sheet of plywood. If you're using dimensional lumber, round to the nearest 2-foot increment. If you're using plywood, plan the tread cuts across the grain for strength.
I hope this helps,stringers are sometimes very difficult to build,here is where i obtain the info...
1. Determine heights of finished floor, deck, or sidewalk surfaces. This determines the rise of each step.
The distance from the deck surface to the floor, sidewalk or deck surface below is called the total rise.
Then some math must be done. If a certain riser height is preferred (say 6 inches), then divide the total run by the preferred riser height. Or... use the riser height of the pre-cut stair treads, otherwise use a good starting number like 7 inches.
This gives the number of risers (steps) needed. Let's use an example of 27 inch total rise. 27" divided by 6" gives us 4½ steps. Oops... you can't have half a step. We can have either 4 or 5 risers.
27" divided by 4 gives a riser height of 6.75 inches.
27" divided by 5 gives a riser height of 5.4 inches, which is kinda short. So 4 risers will be our choice.
Note that the number of risers is not necessarily the same as the number of steps. You always get one free riser. Suppose a house has one room that is 7 inches lower than the next room, you don't need any stairs... you just have a step down to the next platform. A deck could be built this way, with several different levels, each 6 to 8 inches lower than the previous. That's a lot of trouble to avoid building stairs, though.
2. Determine the thickness of stair tread material.
On most decks this is simply one inch, the thickness of standard 5/4x6 deck boards.
But... there are extra-thick deck boards available (I keep running into these darned things), and there are synthetic decking materials that can be any thickness the manufacturer wants.
3. Lay out the heights of the UPPER SURFACES of the stair treads.
These are the surfaces you walk on, and the surfaces that the building inspector measures from.
First... We subtract the riser height from the finished deck surface, which gives the location of the top of the upper tread.
Then... Then we subtract the riser height again from that first line (the top surface line) to get the top surface of the second tread. And so on...
Laying this out is much easier on paper (or a CAD system) than trying to create layout lines on the actual project. I suppose you could draw layout lines on the deck support posts, or you could drive some stakes into the ground and mark them.
4. Subtract the thickness of the stair treads to determine the horizontal cut lines that will be marked on the stair stringers.
If using pre-cut stringers, hold the stringers in a position so the highest horizontal cut meets this line. Of course, the stringer must be held with the horizontal cuts level, or else your stairs will suck.
5. Determine a starting point for the outer (front) surface of the risers.
On many decks and porches, the top riser will determine the starting point, because the top riser is often the outer joist of the deck structure.
6. Determine the final position of the top tread:
The important geometry is the location of the front edge of the first tread.
Common tread materials for exterior decks are:
Two 5/4x6 deck boards, which gives a tread width of about 11 inches.
Two 2x6's which gives a tread width of about 11 inches.
2x12, which gives a tread width of about 11¼ inches.
2x10, which gives a tread width of about 9¼ inches. This certainly works for indoor treads but may not be acceptable for deck stairs.
In this example we'll use a pair of 5/4x6 deck boards, which creates treads one inch thick and 11 inches wide.
7. Subtract the nose overhang distance to get the location of the front of the next riser.
The nose is usually one inch. Nose distances of 3/4" to 1¼" are usually acceptable.
8. Subtract the riser material thickness to get the vertical cut line for the stair stringers.
Riser materials are usually:
1x6 or double 1x4 treated wood (3/4" thick)
5/4x6 deck boards (1" thick or more)
Sometimes 2x lumber is used (1½" thick)
See the next drawing for this...
9. Repeat steps 6, 7 and 8 for all the other treads.
In other words, now that the first riser outer surface has been determined, the tread width can be laid out in front:
This gives us the location of the front edge of the second tread.
Back off the nose overhang to get the outer surface of the next riser
Back off the riser thickness to get the vertical cut line on the stringer.
------------------------------...
10. Convert stair layout to stringer cutting layout:
Draw a line to connect all the points on the stair stringers. Note that this is parallel to the "nose line" of the finished stairs, but is not the same as the nose line.
Make another line parallel to the first line, 11.25 inches apart. This denotes the width of a 2x12, the standard material used for stair stringers.
In the drawing below, note some interesting patterns:
The 7.75" top vertical dimension is not part of the stringer... this is a dimension that locates the position of the top of the stringer relative to the deck surface.
The middle vertical dimensions (6.75") are the riser heights.
The lower vertical dimension (5.75") is just the riser height minus the tread thickness.
The 10.00" horizontal dimensions are the "effective tread width". This is the actual tread width minus the nose overhang distance. If you took a "bird's eye view" of the steps from above, you would see only 10 inches of the 11 inch treads.
The 9.25" horizontal dimension is the effective tread width minus the 0.75" thickness of the riser. When the risers are nailed onto the front edges, the effective tread width will return to 10 inches. And all the remaining tread supporting areas will simply "shift forward" by 0.75", if that makes any sense.
One benefit of a simple 2-dimensional CAD program is that you get easy (and very accurate) measurements of the overall length, and the angle between the stringer bottom and horizontal. Note that some of the tread cut-out angles are the same 34 degree angle, and the other lines are the complement of that angle, 56 degrees. You remember the Complementary Angle Theorem from high school math, don't you?
It's kinda intuitive... if a line is 34 degrees above horizontal, then the angle between that line and vertical is just 90-34, or 56 degrees.
A really powerful benefit of CAD software is the ability to quickly get distances from the end of the board to the stair "points" on the stringer. From these points the angled cuts can be laid out, and inaccuracies are held to a minimum.
This is NOT how most carpenters lay out stair stringers. The traditional practice has been to use a rafter framing square with little hexagonal brass buttons (sold separately) that are clamped onto the framing square to establish fixed dimensions. I'm not sure I can explain this process... you can read about it in the book Basic Stairbuilding by Scott Schuttner, from Taunton Press, which should be available at Home Depot.
11. Build Stairs
Note that many decks are not built with the decking overhanging the edge by one inch, so stairs built against such a deck may have a missing nose at the top. This is not normally a problem.
The procedure for building stairs is typically:
Install the stringers. Stringers would be fastened at the top, to the deck. It may also be desirable (or required by code) to fasten the lower end of the stringers to posts in the ground.
Install the riser boards.
Install the treads.
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