Stair step height: Guide to Stair Riser Dimensions

Stair step riser height specifications & codes
- Allowable variation in stair step riser height by code & to avoid tripping
- Definition of & specifications for open riser & closed riser stairs
- Suggestions for adapting pre-fabricated stairways to the to the actual overall stairway height without violating building stair codes & standards
- Basic stair riser height dimensions required for safe stairs
- Different dimensions for open versus closed riser stairways
- Stair safety hazards, photos of defects & Sketches of stair design requirements
- Stair calculations: how to calculate custom stair tread & risers based on stair rise & run measurements
- Stair dimensions: width height &c - separate article
- STAIR HEADROOM - separate article
- STAIR RISER SPECIFICATIONS
- STAIR TREAD DIMENSIONS - separate article
Questions & Answers about stair and step riser heights and dimensions and building codes
References

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This article provides building code specifications, sketches, photographs, and examples of the proper stair step height or stair riser dimensions and other stair riser requirements for indoor or outdoor stairways. We compare the code requirements for closed riser and open riser stairs and we include other basic stair tread and riser dimensions. We also discuss the allowable variation in stair or step riser height between individual steps in a stairway. Sketch at page top courtesy Carson Dunlop Associates.

Stair Riser Dimensions, Specifications, Codes, Standards & Defects

Undersized stair tread depth (C) Daniel Friedman

Stair risers are detailed here. For a complete list of articles on stairs, railings, and ramps, their inspection, trip hazards, and good design, see STAIRS, RAILINGS, LANDINGS, RAMPS - INSPECTIONS, CODES. Or see these detailed articles on specifications for proper dimensions for stairs, railings, platforms

Stair dimensions: width height &c
  STAIR HEADROOM
  Stairway landings
  Stair Rise & Run Calculations
  Stair stringer defects
  Step riser dimensions
  STAIR TREAD DIMENSIONS
  Stair tread nose dimensions
HANDRAILS & HANDRAILINGS

Because more people are injured by trips and falls than other hazards, experts have looked closely at the specifications for stairs, steps, and rails to reduce the falling hazards. This work has been translated into stair and railing specifications that are similar among codes and countries (but not identical). -- IBC, IRC, BOCA, Kingston NY Stair Code, & other sources.

Definition of stair risers (stair riser height)

A stair riser (green arrow in our photo at above left) is the vertical distance (green arrow) between the walking surface of two stair treads (treads are what you step on) is the stair riser or riser height.

Stair riser heights The riser height shall be measured vertically between the leading edges of adjacent treads.

Stair treads: The stair tread is the horizontal walking surface (red arrow) of an individual step. The tread depth is measured from the forward edge of the step nose or edge of the step above out to the leading edge of the step being measured - the space beneath my foot in the photo at left. Stair tread depths shall be 11 inches (279 mm) minimum.The stair tread depth shall be measured horizontally between the vertical planes of the foremost projection of adjacent treads and at right angle to the tread's leading edge. Details about stair treads are found at STAIR TREAD DIMENSIONS and at Stair tread nose dimensions

Definition of & Detailed Specifications for Closed Riser Stairs

Closed riser stairs (demonstrated at left by the author's granddaughter Quinn Morgan Gilligan) include a vertical riser board (that my toe is kicking against). Stair risers are detailed at Step riser dimensions. Photo by permission.

Don't confuse step riser height (defined above) with stairway headroom - the vertical space between the walking surface of a stair tread and the ceiling or other obstruction overhead (defined further at STAIR HEADROOM).

If the vertical space is enclosed (see our Carson Dunlop sketch above), the enclosing board is called the stair riser.

Step riser specifications riser height (<= 7.75" or in some codes <= 7.0" or in Canada <=8.25") maximum and 4 inches (102 mm) minimum. This means your stair risers should be less than or equal to 7 3/4 inches. No taller. Some codes specify slightly taller stair risers, from 8" to 8 1/4" (Canada, for example).
Step riser height uniformity (<= 3/8" variation) - this means that more than 3/8 of an inch in variation of the height of steps from one step to another is a tripping hazard.
Step riser slope (out of vertical) (<= 30 deg measured from horizontal surface of the tread) - this stair specification means the rather obvious hazard that if stairs are pitched or sloped users are more likely to trip and fall. Outdoor stairs that are exposed to wet or icy conditions are an even more serious falling hazard if the stairs are sloped.
Step stair riser openings: open stair risers are permitted provided the opening will not pass a 4" sphere (child safety). This 4-inch opening dimension has the same basis as the rule that requires that the opening between stair balusters must be 4" or smaller.

Summarizing proper stair dimensions for Closed Riser Stairs

Closed riser stairs include a board or other solid material that encloses the vertical space between stair treads.

Stair riser height: ideal: 7 3/4, or in some jurisdictions 8 to 8 1/4" tall. Some older homes include a very steep stairway to access the home's attic. The stairs were very tall or "steep" when there was simply not enough horizontal space for a longer and less steep stairway. It may be impractical to fix this condition by a new stairway for the same reason - there just isn't enough space. Be sure to reduce the falling hazard at steep stairs by providing good lighting and secure handrails. (See Attic stairs)
Stair tread nosing: required, 1" to 1 1/2" projection beyond the riser face
Stair tread run (or horizontal depth): 8 1/4 to 9"
Stair tread thickness: 1" or greater, tread is supported by the riser.

Definition of & Detailed Specifications for Open Riser Stairs

If the vertical space between stair treads is open (see our photo at left) the space is still a stair riser, but it's an "open riser".

Or simply put, open riser stairs have no enclosure (my toe, shown above would be facing into open space).

Open stair risers with a more than 4-inch opening are a child hazard, as we detail below.

Summarizing proper stair dimensions for Open Riser Stairs

Open riser stairs (shown at right in the sketch above) do not include a solid board or other material that fully encloses the open space between stair treads.

Open riser stair treads should be to 9 1/4" in depth and will typically be greater at shorter stair riser heights.
Open riser stair treads must be at least 1 1/2" thick because the tread, not supported by a riser, may otherwise split.
Open riser stairs are allowed a"back slope of at most 1 1/2". Take a look at the sketch of stair specifications at the top of this page.

Because there is no solid vertical riser to enclose the space between stair treads, the concept of a stair tread "nose" does not apply.

But if stair treads are constructed so that the front edge of a tread is more than 1 1/2" behind the back edge of the stair tread below, the treads can become a trip hazard.

Are These Stairs Open Riser or Closed Riser Design?

Closed riser stairs Maria Mitchell Observatory Vassar College (C) Daniel Friedman

The lovely stairway shown at left rises to the main entry for the Maria Mitchell Observatory on the Vassar College Campus, Poughkeepsie, New York.

But are these open risers or closed riser stairs?

They are closed riser stairs (except for that broken missing riser at the first step) because the cast iron gridwork defines the limits of placement of the leading toe of a foot of someone ascending these steps.

Therefore the rules for stair nose design and projection apply to these steps.

Stair Riser Defects in Height, Slope, Consistency

Quick Summary of Stair Riser or Height Hazards

As we explained above, the most common stair riser defects likely to lead to a fall include:

Stair risers of uneven height between various steps in the stairway. This means that there should be no step to step walking surface height variation greater than 0.375 inches
Stair risers of improper height, too tall - as we cite above the definition of steps that are "too tall" varies by jurisdiction but 7" is a good design number in the U.S. , or 8" max in Canada.
Stair risers of improper height, too short - under 4" in step height.

What happens if you make any step riser less than 4" is that walkers tend to trip over the mini-step as an obstruction rather than recognizing it as a step up. While we never recommend building a known trip hazard, if a an existing walkway cannot avoid step risers less than 4" high, because it is a trip hazard (and probably a code violation in most jurisdictions) you can at least reduce the risk by using clear color changes to give a visual clue marking the changes in height. See Color / Lighting Cues Avoid Trip Hazards
Stair risers, or the vertical distance between the stair treads, that are too tall are difficult to climb and are a falling or trip hazard.
Stair risers that are too short can also be a trip hazard if the stair treads themselves (the walking surface of the stair or step) are not large enough. As we discuss below, generally as we reduce the stair riser height below about 6-inches, we need to increase the "depth" (front to back distance) of the stair tread.
Stair risers that are uneven or irregular in height are also a serious trip and fall hazard. That's because when people walk up and down stairs we are mostly on "auto pilot" - our brains assume that each step height will be the same as the one we took just before. So a "surprise" such as a step that is taller or shorter, can make us fall - a particular hazard for the elderly, children, or people who are physically disabled and have trouble climbing stairs. (Also see ELDERLY & VETERANS HOME SAFETY).

Unsafe Deck, Deck Stairs & Deck & Stair Railing Example

Nothing is right about the exterior stairs shown in our photo (at left ) from a 1991 home inspection:

This stair stringer is too-deeply notched and could split;
The stair risers are too high, as our client is showing with our tape.
The stair treads are too narrow.
There is no railing at all along these stairs (and the height above ground is more than 36" which means that in just about every jurisdiction stair railings would be required by the building code)
The deck and platform railing is open with no balusters.

See Deck & Porch Steps or Stairs for more details.

...

Frequently Asked Questions (FAQs) about stair and step riser height codes and requirements

Question: Using pre-fab stairs - Is there an exception to the riser height variation for the very first step of the staircase?

Is there an exception to the riser height variation for the very first step of the staircase? Let me attempt to clarify the question. I have a deck (exterior porch) for which the distance from the top of the deck to the slab which forms the footing for the set of stairs is just shy of the 5 steps within a pre-fabricated 5 step stair stringer which can be purchased at a Home Depot or Lowes, for example.

If I attach the pre-made stringer from the deck to the slab, ensuring that the top of the deck to the next stair down is the same height as the rest, then the riser height from the slab to the first stair is greater than a 3/8' variation from the rest of the riser heights by 1/8th of an inch (ie. it's 1/2 inch shorter than the rest of the stairs - I actually need to remove a half inch from the bottom most stair of the stringer to fit). If this is a violation of code, than it means I need to cut my own customer stringer. Just verifying. Any feedback is appreciated. - Dan

Reply: no stair step riser height variation greater than 0.375 inches is allowed

Dan,

There is no exception for individual stair steps, first, bottom, top, or other. A difference in riser height can be a serious trip hazard at any location on a stairway.

Quoting from the article text above on stair and step height regularity and the amount of variation in stair step riser height that is allowed (presumably to avoid a trip hazard)

"Stair risers of uneven height - no variation greater than 0.375 inches is allowed"

Minor Adjustments can fit a factory-built stair to the specific overall stair rise

As I read your note, you have just a 1/2" error to make up between the total elevation difference between the deck surface and the ground surface if you use a pre-fabricated stair way.

If you can split the adjustment between the top and bottom stair risers by trimming the stringer top and bottom, you'll have just 1/4" or 0.25" of riser height variation (one at stair top and one at stair bottom) - thus minimizing the trip hazard risk of the uneven risers and the variation will be within standards.

Watch out: be sure to measure the height difference (deck surface to ground surface) at a projected point along a horizontal line from the edge of the deck out to the location, in horizontal distance, of the front edge of the nose of the very first or lowest step of the stairway. That will avoid any error in calculating total stairway height due to any slope in the actual ground surface.

If you need a greater adjustment in the stair height between the ground surface and the deck surface in order to avoid having to re-cut a whole new pair of stair stringers, sometimes that can be accommodated by changing the height of the surface of the concrete or other masonry platform that many building departments and local codes require be placed as a landing at the bottom of the stairs.

Question: how do we set the step riser height for a very low angle staircase?

Perhaps one of the experts here could give advise on this. What are the rules for a low angle staircase? I am planning an exterior (built on grade) staircase on a slope too steep for a ramp.

My rise is 78 in. over 28 ft. and there is additional room for a landing at top and bottom. I am considering 3 ½” risers and 16” treads (using commonly available cement block). What rules-of-thumb should I follow to build a comfortable walk-able low angle staircase? If there is some formula to the ideal cadence; I would form this in concrete in order to achieve it. I do not want to feel like I am taking “baby steps” or alternately taking a “step-and-a-half” all the way up and down. - Tom 6/23/12

Reply: Here is a simple approach to calculating the stair rise & run for a low slope stairway

Great question. Bernie Campbalik who taught us carpentry, including stair building, used a rule of thumb that basically makes the run longer when the rise is shorter. I've seen several rules such as the sum of one tread and one riser should always be equal or greater than 17; I think we need to dig out some texts on stair design such as those in the references. The concept is that a low rise stair usually has, just as you suggest, a tread that provides a "longer" walking surface. Up to a point. If we make the rise too short, say an inch, it's not a step at all, it's a trip hazard.

Reader Follow-Up:

Dan, Thanks for your response. I now think any rule can at best only make general recommendations for all the low-slope possibilities.
I figured that if I could determine the optimum number of steps to comfortably traverse the distance of the slope of my proposed staircase I would then know the correct number of treads.

So I marked off the landing locations and simply walked up and down the slope while counting the number of steps I took as I did so. I repeated this a few times adjusting my gait somewhat and arrived at an average number.

In this case I took 14 steps to travel the slope which equates to 14 treads - 24” long. Then since the landing counts as one of the treads; I divided the rise by 14 which give me a riser height of 5.57”.

I also counted steps made on level ground over the same distance as the length of the stair and came up with 12 so I think 14 is conservative considering the slope but about right for my needs. I am not in a hurry to build but before I do I would still like to hear a professional opinion or two on this. Another possibility might include a landing midway up thus making all the treads shorter? Your input is appreciated.

Reply: stair design basics: calculating step riser height, step tread depth, total rise, total run, intermediate platform lengths

Tom,

I think a sketch of what you're up to would be helpful - if you want to send one use the CONTACT US link at page top/bottom. Meanwhile I'll provide two of my own: a "theoretical stairway" and then the "actual calculated stairway" at the end of these notes, based on the figures you provided.

Please see the details about how to calculate step or stair rise & run over at Stair Rise & Run Calculations where we discuss this topic nearly to death.

...

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Best Practices Guide to Residential Construction, by Steven Bliss. John Wiley & Sons, 2006. ISBN-10: 0471648361, ISBN-13: 978-0471648369, Hardcover: 320 pages, available from Amazon.com and also Wiley.com. See our book review of this publication.
Eric Galow, Galow Homes, Lagrangeville, NY. Mr. Galow can be reached by email: ericgalow@gmail.com or by telephone: 914-474-6613. Mr. Galow specializes in residential construction including both new homes and repairs, renovations, and additions.
[3] "The Elimination of Unsafe Guardrails, a Progress Report," Elliott O. Stephenson, Building Standards, March-April 1993
[4] "Are Functional Handrails Within Our Grasp" Jake Pauls, Building Standards, January-February 1991
[5] Access Ramp building codes:
- UBC 1003.3.4.3
- BOCA 1016.3
- ADA 4.8.2
- IBC 1010.2
[6] Access Ramp Standards:
- ADA (Americans with Disabilities Act), Public Law 101-336. 7/26/90 is very often cited by other sources for good design of stairs and ramps etc. even where disabled individuals are not the design target.
- ANSI A117.4 Accessible and Usable buildings and Facilities (earlier version was incorporated into the ADA)
- ASTM F 1637, Standard Practice for Safe Walking Surfaces, (Similar to the above standard
[7] The Circular Staircase, Mary Roberts Rinehart
[8] Construction Drawings and Details, Rosemary Kilmer
[9] Falls and Related Injuries: Slips, Trips, Missteps, and Their Consequences, Lawyers & Judges Publishing, (June 2002), ISBN-10: 0913875430 ISBN-13: 978-0913875438
"Falls in the home and public places are the second leading cause of unintentional injury deaths in the United States, but are overlooked in most literature. This book is unique in that it is entirely devoted to falls. Of use to primary care physicians, nurses, insurance adjusters, architects, writers of building codes, attorneys, or anyone who cares for the elderly, this book will tell you how, why, and when people will likely fall, what most likely will be injured, and how such injuries come about. "
[10] Mobile Home Inspections common defects unique to factory built housing, inspection methods
[11] The National Institute of Standards and Technology, NIST (nee National Bureau of Standards NBS) is a US government agency - see www.nist.gov
- "A Parametric Study of Wall Moisture Contents Using a Revised Variable Indoor Relative Humidity Version of the "Moist" Transient Heat and Moisture Transfer Model [copy on file as/interiors/MOIST_Model_NIST_b95074.pdf ] - ", George Tsongas, Doug Burch, Carolyn Roos, Malcom Cunningham; this paper describes software and the prediction of wall moisture contents. - PDF Document from NIS
[12] Slips, Trips, Missteps and Their Consequences, Second Edition, Gary M. Bakken, H. Harvey Cohen,A. S. Hyde, Jon R. Abele, ISBN-13: 978-1-933264-01-1 or ISBN 10: 1-933264-01-2, available from the publisher, Lawyers ^ Judges Publishing Company,Inc., www.lawyersandjudges.com sales@lawyersandjudges.com and also from the InspectAPedia Bookstore (Amazon.com)
[13] Slips, Trips, Missteps and Their Consequences, Gary M. Bakken, H. Harvey Cohen, Jon R. Abele, Alvin S. Hyde, Cindy A. LaRue, Lawyers and Judges Publishing; ISBN-10: 1933264012 ISBN-13: 978-1933264011
[14] The Stairway Manufacturers' Association, (877) 500-5759, provides a pictorial guide to the stair and railing portion of the International Residential Code. [copy on file as http://www.stairways.org/pdf/2006%20Stair%20IRC%20SCREEN.pdf ] -
[15] How to Clean Moldy Wood Framing & Sheathing How to clean/seal mold from/on exposed lumber or plywood subfloor or roof sheathing indoors - some suggestions based on our field and laboratory research
[16] Mold-Resistant Building Practices, advice from an expert on how to prevent mold after a building flood and how to prevent mold growth in buildings by selection of building materials and by anti-mold construction details.
[17] Steps and Stairways, Cleo Baldon & Ib Melchior, Rizzoli, 1989.
[18] The Staircase, Ann Rinaldi
[19] Common Sense Stairbuilding and Handrailing, Fred T. Hodgson
[20] The Art of Staircases, Pilar Chueca
[21] Building Stairs, by pros for pros, Andy Engel
[22] A Simplified Guide to Custom Stairbuilding, George R. Christina
[23] Basic Stairbuilding, Scott Schuttner
[24] The Staircase (two volumes), John Templar, Cambridge: the MIT Press, 1992
[25] The Staircase: History and Theories, John Templar, MIT Press 1995
[26] Steps and Stairways, Cleo Baldon & Ib Melchior, Rizzoli, 1989.
[27] "The Dimensions of Stairs", J. M. Fitch et al., Scientific American, October 1974.
[28] Stair & Walkway Standards for Slipperiness or Coefficient of Friction (COF) or Static Coefficient of Friction (SCOF)
- ANSI A1264.2
- ANSI B101
- ASTM D-21, and ASTM D2047
- UL-410 (similar to ASTM D-21)
- NSFI 101-B (National Floor Safety Institute)
- NSFI Walkway Auditing Guideline (WAG) Ref. 101-A& 101-B (may appear as ANSI B101.0) sets rules for measuring walkway slip resist
- OSHA - (Dept of Labor CFR 1910.22 does not specify COF and pertains to workplaces) but recognizes the need for a "qualified person" to evaluate walkway slipperiness
- ADA (relies on the ANSI and ASTM standards)
[29] A. Sacher, International Symposium on Slip Resistance: The Interface of Man, Footwear, and Walking Surfaces, Journal of Testing and Evaluation (JTE), ISSN: 1945-7553, January 1997 [more focused on slipperiness of polished surfaces
[30] Algae is widely recognized as a slippery surface - a Google web search for "how slippery is algae on steps" produced more than 15,000 results on 8/29/12)
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[33] Coefficient of friction of algae on surfaces [like stair treads]: Delphine Gourdon, Qi Lin, Emin Oroudjev, Helen Hansma, Yuval Golan, Shoshana Arad, and Jacob Israelachvili, "Adhesion and Stable Low Friction Provided by a Subnanometer-Thick Monolayer of a Natural Polysaccharide", Langmuir, 2008 pp 1534-1540, American Chemical Society, retrieved 8/29/2012,
Abstract: Using a surface forces apparatus, we have investigated the adhesive and lubrication forces of mica surfaces separated by a molecularly thin, subnanometer film of a high-molecular-weight (2.3 MDa) anionic polysaccharide from the algae Porphyridium sp. adsorbed from aqueous solution. The adhesion and friction forces of the confined biopolymer were monitored as a function of time, shearing distance, and driving velocity under a large range of compressive loads (pressures). Although the thickness of the dilute polysaccharide was <1 nm, the friction was low (coefficient of friction = 0.015), and no wear was ever observed even at a pressure of 110 atm over 3 decades of velocity, so long as the shearing distances were less than twice the contact diameter. Atomic force microscopy in solution shows that the biopolymer is able to adsorb to the mica surface but remains mobile and easily dragged upon shearing. The adhesion (adsorption) of this polysaccharide even to negatively charged surfaces, its stable low friction, its robustness (high-load carrying capacity and good wear protection), and the weak (logarithmic) dependence of the friction force on the sliding velocity make this class of polyelectrolytes excellent candidates for use in water-based lubricant fluids and as potential additives to synovial fluid in joints and other biolubricating fluids. The physical reasons for the remarkable tribological properties of the ultrathin polysaccharide monolayer are discussed and appear to be quite different from those of other polyelectrolytes and proteins that act as thick “polymer brush” layers.
[34] Jinjin Li, Yuhong Liu, Jianbin Luo, Pengxiao Liu, and Chenhui Zhang, "Excellent Lubricating Behavior of Brasenia schreberi Mucilage" Langmuir 2012 28 (20), 7797-7802
[35] Jason R. Stokes, Lubica Macakova, Agnieszka Chojnicka-Paszun, Cornelis G. de Kruif, and Harmen H. J. de Jongh, "Lubrication, Adsorption, and Rheology of Aqueous Polysaccharide Solutions, Langmuir 2011 27 (7), 3474-3484
[36] "Coefficients of Friction for Ice", The Physics Factbook™, Glenn Elert, Ed., retrieved 8/29/12, original source: http://hypertextbook.com/facts/2004/GennaAbleman.shtml
[37] "Coefficients of Friction for Ice", The University of the State of New York Reference Tables for Physical Setting/Physics. New York: The State Education Department, 2002. Op. Cit.
[38] Serway Physics for Scientists and Engineers 4th edition (p. 126.)
[39] "How Slippery Is It", retrieved 8/29/12, original source http://www.icebike.org/Articles/howslippery.htm
[40] John E. Hunter, "Friction Values", The Source, Society of Accident Reconstructionists, Winter 1998. Study of frictional values of car tires involved in collisions on snow or ice covered roadways.
[41] Frictional Coefficients of some Common Materials and Materials Combinations, The Engineering Toolbox, retrieved 8/29/2012, original source: http://www.engineeringtoolbox.com/friction-coefficients-d_778.html [copy on file as Friction and Coefficients of Friction.pdf ]
[42] Stairways and Ladders, A Guide to OSHA Rules, OSHA, U.S. Department of Labor, 3124-12R 2003 - Web Search 05/28/2010 original source: http://www.osha.gov/Publications/osha3124.pdf. OSHA regulations govern standards in the construction industry and in the workforce Quoting from OSHA whose focus is on workplace safety and so excludes discussion of falls and stair-falls in private homes:

OSHA estimates that there are 24,882 injuries and as many as 36 fatalities per year due to falls from stairways and ladders used in construction. Nearly half of these injuries are serious enough to require time off the job--11,570 lost workday injuries and 13,312 non-lost workday injuries occur annually due to falls from stairways and ladders used in construction. These data demonstrate that work on and around ladders and stairways is hazardous. More importantly, they show that compliance with OSHA's requirements for the safe use of ladders and stairways could have prevented many of these injuries. -osha.gov/doc/outreachtraining/htmlfiles/stairlad.html
[43] International Building Code, Stairway Provisions, Section 1009: Stairways and Handrails, retrieved 8/29/12, original source: http://www.amezz.com/ibc-stairs-code.htm [copy on file as IBC Stairs Code.pdf]
[44] Model Building Code, Chapter 10, Means of Egress, retrieved 8/29/12, original source: http://www2.iccsafe.org/states/newjersey/NJ_Building/PDFs/NJ_Bldg_Chapter10.pdf, [copy on file as NJ_Bldg_Chapter10.pdf] adopted, for example by New Jersey. International Code Council, 500 New Jersey Avenue, NW, 6th Floor, Washington, DC 20001, Tel: 800-786-4452

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Best Practices Guide to Residential Construction, by Steven Bliss. John Wiley & Sons, 2006. ISBN-10: 0471648361, ISBN-13: 978-0471648369, Hardcover: 320 pages, available from Amazon.com and also Wiley.com. See our book review of this publication.
Decks and Porches, the JLC Guide to, Best Practices for Outdoor Spaces, Steve Bliss (Editor), The Journal of Light Construction, Williston VT, 2010 ISBN 10: 1-928580-42-4, ISBN 13: 978-1-928580-42-3, available from Amazon.com
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