The sizing of wood beams can be accomplished in several ways. There is a great deal of information available on the web such as calculators and tabulated data to help you select appropriate sized wood members for simple loading conditions. This article will focus on using American Wood Council (AWC) Span Tables in conjunction with the Massachusetts State Building Code to size sawn lumber joists. This information is most relevant to residential dwellings.
Needed Information:
Span tables are a very effective and simple way of sizing joists. You will need the following information to determine joists sizes:
1. Length of span (distance between face of end supports)
2. Uniform live load to be supported
Typical Minimum Live Load Values:
(From Mass Building Code Seventh Edition – 780 CMR Table 5301.5)
Use | Live Load (psf) |
Attics without Storage | 10 |
Attics with storage | 20 |
Sleeping rooms | 30 |
Rooms other than sleeping rooms | 40 |
Decks | 40 |
Exterior balconies | 60 |
3. Deflection limit
Typical Minimum Deflection Limits:
(From Mass Building Code Seventh Edition – 780 CMR Table 5301.5)
Structural Member | Deflection Limit |
Rafters with slope > 3/12 with no attached finished ceiling | L/180 |
Floors and plastered ceilings | L/360 |
All other structural members | L/240 |
4. Uniform dead load to be supported
The following tables provide typical dead load values for common building materials. The dead load values from these table should be added together depending on the construction. When in doubt, it is always better to overestimate.
Typical Minimum Design Dead Load Values – Wood Joist Floor with ¾” Plywood Subfloor:
(From ASCE 7-10 Table C3-1)
Design Dead Load (psf) | |||
Joist Size (in.) | 12-in. Spacing | 16-in. Spacing | 24-in. Spacing |
2 x 6 | 6 | 5 | 5 |
2 x 8 | 6 | 6 | 5 |
2 x 10 | 7 | 6 | 6 |
2 x 12 | 8 | 7 | 6 |
Typical Minimum Design Dead Load Values – Floor Finishes:
(From ASCE 7-10 Table C3-1)
Floor Finish | Design Dead Load (psf) |
Concrete fill finish (per inch thickness) | 12 |
Hardwood flooring, 7/7-in. | 4 |
Linoleum or asphalt tile, ¼” | 1 |
Slate (per mm thickness) | 15 |
Solid flat tile on 1-in. mortar base | 23 |
Typical Minimum Design Dead Load Values – Ceilings Finishes:
(From ASCE 7-10 Table C3-1)
Ceiling Finish | Design Dead Load (psf) |
Acoustical fiber board | 1 |
Gypsum board (per 1/8-in. thickness) | 0.55 |
Plaster on wood lath | 8 |
Suspended metal lath and cement plaster | 15 |
Suspended metal lath and gypsum plaster | 10 |
Wood furring suspension system | 2.5 |
Plywood (per 1/8-in. thickness) | 0.4 |
Typical Minimum Design Dead Load Values – Other Dead Loads for Consideration:
(From ASCE 7-10 Table C3-1)
Other Components | Design Dead Load (psf) |
Mechanical Duct Allowance | 4 |
Cellular glass insulation (per 1-in. thickness) | 0.7 |
Fibrous glass insulation (per 1-in. thickness) | 1.1 |
Fiberboard insulation (per 1-in. thickness) | 1.5 |
Sizing the Beam:
After you have selected the appropriate loads and deflection requirements from the tables above, it is now time to size your beam using the Span Tables from the AWC. A free download of the span tables can be found at this link:
http://www.awc.org/codes-standards/spantables
To use the span tables, you first need to find the right table. As an example, let’s say that I am sizing a floor joist with the following criteria:
Length of Span = 14 feet
Uniform Live Load = 40 psf
Deflection Limit = L/360
Uniform Dead Load = 20psf
Use the table of contents to find the appropriate table based on your design criteria. My example corresponds to table F-5. Let’s say that based on dimensional requirements for my project, I want to use a 2×10 spaced at 16” on center.
In the span table find where it says 2×10 for the joist size and go to the row for 16” spacing. Move across the row to the right until you come to a column with a span length that is greater than or equal to what you need. In this case, it was exactly 14’-0”. At the top of the column you will find the required modulus of elasticity for the beam to meet deflection requirements. In this case, it is 1,000,000 psi. Next go the bottom portion of the table, labeled as “F_{b}”, in the same column and row level as your selected span to find the required bending stress. In this case, it is 1,101 psi.
Now that you have the required elastic modulus and bending stress you can find the appropriate species and grade of lumber in the AWC National Design Specification (NDS) Supplement. This information can be found at this link:
http://www.awc.org/pdf/codes-standards/publications/nds/AWC-NDS2015-Supplement-ViewOnly-1411.pdf
For this example, let’s assume that Spruce–Pine-Fir is available to us. Find the Spruce–Pine– Fir section of Table 4A in the NDS Supplement.
Recall that from the span tables we required a minimum elastic modulus value of 1,000,000 psi to meet deflection requirements. Based on Table 4A shown above, all grades of Spruce-Pine-Fir meet the minimum requirement. The minimum bending stress value from the span tables is 1,101psi. From Table 4A, only the Select Structural Grade of Spruce-Pine-Fir meets the minimum requirement for bending strength therefore a Select Structural – Spruce Pine-Fir 2×10 spaced at 16” on-center would be acceptable for use.
Closing Notes:
The span tables from NDS are an easy way of sizing wood beams for simple situations. More complex situations may require the use of the NDS design formulas and more in depth engineering. When in doubt it is always best to contact an engineer. Note that the example shown above is only one way to size a beam using span tables. In the example, we started with the beam size because we knew what beam size we wanted to use. You could always start with the span length and find the appropriate size beam. An iterative process is sometimes required to find a combination that will work for your project.