Understanding Loads and Using Span Tables
Using span tables to size joists and rafters is a straightforward process when you understand the structural principles that govern their use.
Wood is naturally engineered to serve as a structural material: The stem of a tree is fastened to the earth at its base (foundation), supports the weight of its branches (column) and bends as it is loaded by the wind (cantilever beam). A complete analysis of wood’s mechanical properties is complex, but understanding a few basics of lumber strength will allow you to size joists and rafters with the use of span tables.
Let’s start by taking a broad view. The structural goal of a house is to safely transfer building loads (weights) through the foundation to the supporting soil. Remember when your science teacher said: every action has an opposite and equal reaction? Well every building load has an equal “reaction load”. If, when the loads of the house are combined, the house weighs more than the soil can support – the house will sink until it reaches a point at which the soil can support the load. This article will focus on how simple beams like joists and rafters react to loading.
Residential Loading
The house acts as a structural system resisting dead loads (weight of materials), live loads (weights imposed by use and occupancy), like snow loads and wind loads. Beams, studs, joists and rafters act as a structural skeleton and must be strong enough and stiff enough to resist these loads.
Strength and stiffness are equally important. For example, firstfloor ceiling plaster would crack as occupants walked across a secondfloor bedroom that was framed with bouncy floor joists. Perhaps the joists were strong enough if they didn’t break! But lack of stiffness leads to costly problems.
Stiffness of structural members is limited by maximum allowable deflection. In other words, how much a joist or rafter bends under the maximum expected load. Only live loads are used to calculate design values for stiffness.
Maximum deflection limits are set by building codes. They are expressed as a fraction; clear span in inches (L) over a given number. For example: a floor joist appropriately selected to span 10 feet with an L/360 limit will deflect no more than 120″/360 = 1/3 inches under maximum design loads. Drywall attached to the underside of this system is not expected to crack when the floor joist system deflects 1/3″.
Typical deflection limits referenced in code books are L/360, L/240 or L/180. These limits are based on live loads and activities experienced in specific rooms of a house. Examples of codeprescribed deflection limits and live load values are:

Living room floors L/360 & 40 psf

Bedrooms and habitable attic floors L/360 & 30 psf

Attic floors with limited storage L/240 & 10 psf.
Strength of a material is obviously important. Joists, and rafters must be strong enough not to break when loaded. Unlike stiffness, live loads and dead loads are added together to determine minimum design values for strength.
To determine the dead load value for a given floor or roof system, the weight of all permanently installed materials in a given component are added together. For a floor system you can find the individual weights of drywall, strapping, floor joists, subfloor, underlayment and carpet in an architectural handbook like Architectural Graphic Standards. But for most cases there is a cookbook solution. Simply reference the Tables published by the American Forest & Paper Association’s (AF&PA), American Wood Council (AWC). AF&PA’s Appendix A lists a variety of live and dead load combinations for floors, ceilings and rafters. For example, Appendix A indicates that one type of clay tile roof system has a live load value of 20 psf and a dead load value of 15 psf.
Factors That Influence
Many factors influence how a system responds to loading. It is important to realize that the way you select and use materials will control costs and performance.

Depth of structural members. Often, 2×10 joists spaced 24inches o.c. will provide a stronger and stiffer floor assembly than 2×8 joists of the same grade and species that are spaced 16inches o.c.

E value or modulus of elasticity of the individual elements. E is a ratio that relates the amount a given load causes a material to deform. A material with a higher E value is stiffer. For example: No.2 grade eastern white pine has an E value of 1,100,000 and No.2 hemfir has an E value of 1,300,000. Hemfir is a stiffer material.

Fb value or extreme fiber stress in bending. Loads cause beams, joists and rafters to bend. As a beam bends the outermost (extreme) fibers are compressed along the top edge. And at the same time, fibers stretch along the bottom edge. The outermost (extreme) wood fibers on the top and bottom surfaces are stressed more than those fibers in the middle. An Fb value indicates design strength for those extreme fibers. The higher the Fb the stronger the wood.

Lumber grade. A higher grade of a given species has a higher strength rating (Fb) and often has a higher stiffness value (E) too.

Species of wood. All species are not created equal. For example southern pine is much stronger and stiffer than spruce.

Duration of load. How long will the members be loaded? Fulltime loading (floor joists) serves as the benchmark value. Benchmark values are multiplied by 1.15 to yield snowload values and by 1.25 for 7day loading. Don’t worry about the calculations! Tables automatically handle this adjustment. You just read the numbers under the appropriate column heading. For example: A select structural, southern pine 2×8 floor joist has a 2650 Fb. While the same grade and species 2×8 has a 3040 Fb when used as a roof rafter in snow country. E values are unaffected by duration of load.
What You Need
Alright, so now you want to use this information. First you need to get a few things: Code book; AF&PA’s Span Tables for Joists and Rafters (this assigns allowable spans to various combinations of E and Fb); and a copy of Design Values for Joists and Rafters (this has Fb and E values for various species, sizes and grades of dimension lumber).
The code book can be purchased through your local code official. Building codes provide you with information about required grades, spans, bearing, lateral support, notching, etc. Purchase CABO One and Two Family Dwelling Code,5203 Leesburg Pike, Suite 708, Falls Church, VA 22041. CABO is referenced in most local building codes as an acceptable option to the local code. This code book has one appendix with span tables for joists and rafters and another with design values for joists and rafters.
The other publications I mentioned are referenced by most codes and can be purchased from AF&PA’s American Wood Council, PO Box 5364, Madison, WI 537055364, 18008907732. Or they can be ordered online at: http://www.forestprod.org/awc
These documents provide an expanded view of spantable use through “explanation” and “commentary” sections at the beginning and end of the publications. I find the AWC documents easy to follow. The technical staff at AWC is eager and able to help you understand the documents if you get stuck. You can contact the AWC Helpdesk at 800AWCAFPA (2922372) or via email at awcinfo [Email address: awcinfo #AT# afandpa.org  replace #AT# with @ ]. Or visit their website at http://www.awc.org for more information.
There are other span tables and publications available too. Western Wood Products Association (WWPA) publishes tables, for example. But WWPA uses “base values” that make the job more complicated. Some designers may find WWPA’s tables useful. However, I think builders and architects are better served by AF&PA’s version.
PULLING IT ALL TOGETHER
Calculating Loads
For the most part, live load and dead load values for floor and roof systems are considered distributed loads. In other words, the weight is distributed or shared uniformly by the members in the floor or roof system. In order to establish proper sizes, grades and oncenter spacing of joists and rafters you first need to determine what loading is acceptable to the building code.
Use your code book here. Look up the allowable loads and deflection limits imposed by your local code. For example: Massachusetts code book includes the following information.
Dwellings 
live load (psf) 
dead load 
first floor 
40 
* 
second floor 
30 
* 
uninhabitable attics 
20 
* 
* weights listed in code book appendix
Deflection
The code section on working load deflection states: The deflection of floor and roof assemblies shall not be greater than L/360 for plastered construction; L/240 for unplastered floor construction; and L/180 for unplastered roof construction. So these are the limits set by the code.
You can also use AF&PA’s “Span Tables for Joists and Rafters”. This is the easiest way to determine allowable dead loads, live loads and deflection limits. This publication has a much more extensive offering of possible joist and rafter conditions.
Once you find the appropriate table in the book, you determine acceptable Fb and E values for your particular span condition. Span is the distance from face to face of the supports.(for joists: from basementside of sill to sillside of center girder.)
Rafters
Rafters are sized the same way as joists: Establish live load, dead load and deflection limits; use the appropriate rafter table to determine acceptable Fb and E values; and then select the appropriate species, size and grade from AF&PA’s Design Values for Joists and Rafters publication.
Sizing rafters differs from sizing joists in 2 ways:
1) The span of a rafter is not based on the measurement along its length. Rather, the span is based on the rafter’s “horizontal projection”. This is the horizontal distance from the inside surface of the supporting wall to the inside surface of the ridge board. So consider a simple gable roof on a 24foot wide ranch framed with 2×6 exterior walls and a 1 1/2 ridge: the span would be 11’5 3/4″.
2) You must determine the snow load for your region. This information is found in the code book. The snow load is treated as a live load when you use AF&PA’s tables. If your code book says your snow load is 40 psf, then you use the 40 psf live load rafter table. The fact that snow loads only act part of the year has been used to create the rafter tables.
Compression Perpendicular to the Grain
The loads carried by floor joists, ceiling joists and rafters are transferred through their end points to supporting walls and beams. The ends of these members must be able to “react” or resist these loads without crushing. AF&PA lists the required compression perpendicular to grain values for joists and rafters for various spans, oncenter spacing and loading conditions in its Span Tables for Joists and Rafters. AF&PA’s Design Values for Joists and Rafters lists compression perpendicular to grain design values for a variety of species. Just be sure the species design value exceeds the required compression perpendicular to grain value for your structural condition.
SUMMARY
Step by Step
Here is a checklist of steps to follow when using span tables
1) check plans to determine span and oncenter spacing (design conditions)
2) check codes for allowable live load, snow load, dead load and deflection
3) select appropriate span table
4) match span in table to design condition and determine minimum Fb and E values listed in the span table

NOTE: you will have options for oncenter spacing and size
5) select appropriate species and grade from values listed in design values table

NOTE: you will have options regarding species and grade providing you with an economic opportunity
6) determine required compression perpendicular to grain design value in table
7) verify that the compression perpendicular to grain design value for the species selected in step 5 meets the required design value determined in step 6
EXAMPLE: A Test Case
Test your skill. Let’s work through an example that illustrates the steps involved in using the tables. Let’s say you’re building a 16foot addition and have to select the correct size and species of lumber for the floor joists. The joists will be 16 inches oncenter. Their design span, the exact length from face to face of the supports, is 15 feet 1 inch (see illustration – Figure #1)

When sizing joists, use the clear span – the 
Steps
Floor Joists
Step 1 Check The Code: First check the local code for allowable live load, dead load, and deflection (see Figure #2). For this example I’ll use the CABO One and Two Family Dwelling Code , which serves as the model for many state and local codes. This sets an allowable firstfloor live load of 40 psf, a dead load of 10 psf, and a deflection of L/360.
MINIMUM UNIFORMLY DISTRIBUTED LIVE LOADS 

Use 
Live Load 
Balconies (exterior) 
60 
Decks 
40 
Fire escapes 
40 
Garages (passenger cars only) 
50 
Attics (no storage with roof slope no steeper than 3 in 12) 
10 
Attics (limited attic storage) 
20 
Dwelling Units (except sleeping rooms) 
40 
Sleeping Rooms 
30 
Stairs 
40 
ALLOWABLE DEFLECTION OF STRUCTURAL MEMBERS 

Structural Member 
Allowable Deflection 
Rafters with slope > 3/12 and no ceiling load 
L/180 
Interior walls and partitions 
L**/180 
Floors and plastered ceilings 
L/360 
All other structural members 
L/240 
Notes: L = span length, L** = vertical span 
Step 2 Span Table: Select the appropriate table in Span Tables for Joists and Rafters . The Table of contents indicates that Table F2 watches these loading conditions. Using Table F2 (Figure #3), check each lumber size to see if a 16inch spacing will permit a span of 15 feet 1 inch. Start with the “16.0” line in the “Spacing” column at the left of the table, then go to the right until you reach an appropriate span at least 15 feet 1 inch in this case). Then drop down to find the appropriate Fb Value for the span.
As the table shows, no 2×8’s meet the span and spacing requirements, but a 2×10 with an E of 1,300,000 psi and Fb of 1093 psi can span 15 feet 3 inches – more than enough. A 2×12 with an E of 800,000 psi and Fb of 790 psi also works, since it can span 15 feet and 10 inches.
FLOOR JOISTS WITH L/360 DEFLECTION LIMITS 

DESIGN CRITERIA: 

Joist Size (in.) 
Spacing (in.) 
Modulus of Elasticity, E, in 1,000,000 psi  
0.8 
0.9 
1.0 
1.1 
1.2 
1.3 
1.4 
1.5 
1.6 

2×6 
12.0 
86 
810 
92 
96 
99 
100 
103 
106 
109 
16.0 
79 
80 
84 
87 
810 
91 
94 
96 
99 

19.2 
73 
77 
710 
81 
84 
87 
89 
90 
92 

24.0 
69 
70 
73 
76 
79 
711 
82 
84 
86 

2×8 
12.0 
113 
118 
121 
126 
1210 
132 
136 
1310 
142 
16.0 
102 
107 
110 
114 
118 
120 
123 
127 
1210 

19.2 
97 
100 
104 
108 
110 
113 
117 
1110 
121 

24.0 
811 
93 
97 
911 
102 
106 
109 
110 
113 

2×10 
12.0 
144 
1411 
155 
1511 
165 
1610 
173 
178 
180 
16.0 
130 
136 
140 
146 
1411 
153 
158 
160 
165 

19.2 
123 
129 
132 
137 
140 
145 
149 
151 
155 

24.0 
114 
1110 
123 
128 
130 
134 
138 
140 
144 

2×12 
12.0 
175 
181 
189 
194 
1911 
206 
210 
216 
2111 
16.0 
1510 
165 
170 
177 
181 
187 
191 
196 
1911 

19.2 
1411 
156 
160 
167 
170 
176 
1711 
184 
189 

24.0 
1310 
144 
1411 
154 
1510 
163 
168 
170 
175 

F_{b} 
12.0 
718 
777 
833 
888 
941 
993 
1043 
1092 
1140 
16.0 
790 
855 
917 
977 
1036 
1093 
1148 
1202 
1255 

19.2 
840 
909 
975 
1039 
1101 
1161 
1220 
1277 
1333 

24.0 
905 
979 
1050 
1119 
1186 
1251 
1314 
1376 
1436 

Note: The required bending design value, F_{b}, in pounds per square inch is shown at the bottom of each table and is applicable to all lumber sizes shown. Spans are shown in feet – inches and are limited to 26′ and less. Check sourcesof supply for availability of lumber in lengths greater than 20′. 

EXCERPTED FROM SPAN TABLES FOR JOISTS AND RAFTERS, Copyright © 1993 AMERICAN FOREST & PAPER ASSN., WASHINGTON, D.C. 
Step 3 Wood Design Values: Now you must select a wood species and grade that meets the required Fb and E values, and that’s available in your area. For this, use the tables in Design Values for Joists and Rafters. For this example, I’ve excerpted the relevant sections from tables for hemfir, Douglas firlarch, and sprucepinefir (Figure 4). In hemfir, either a No.1 2×10 or a No. 2 2×12 would work. In Douglas firlarch, either a No 2 2×10 or a No. 2 2×12 works. In sprucepinefir, No. 1 7 2 2×10 or 2×12 would do the job.
DESIGN VALUES FOR JOISTS AND RAFTERS 

These F_{b} values for use where repetative members are spaced not more than 24 inches. For wider spacing, the F_{b} values shall be reduced 13%. Values for surfaced dry or surfaced green lumber apply at 19% maximum moisture content in use. 

Species and Grade 
Size 
Design Value in Bending (F_{b}) 
Modulus of Elasticity (E) 

Normal Duration 
Snow Loading 
7 Day Loading 

HEMFIR 

Select Structural 
2×10 
1770 
2035 
2215 
1,600,000 
No. 1 & Btr. 
1330 
1525 
1660 
1,500,000 

No. 1 
1200 
1380 
1500 
1,500,000 

No. 2 
1075 
1235 
1345 
1,300,000 

No. 3 
635 
725 
790 
1,200,000 

Select Structural 
2×12 
1610 
1850 
2015 
1,600,000 
No. 1 & Btr. 
1210 
1390 
1510 
1,500,000 

No. 1 
1095 
1255 
1365 
1,500,000 

No. 2 
980 
1125 
1385 
1,300,000 

No. 3 
575 
660 
720 
1,200,000 

DOUGLAS FIRLARCH 

Select Structural 
2×10 
1835 
2110 
2295 
1,900,000 
No. 1 & Btr. 
1455 
1675 
1820 
1,800,000 

No. 1 
1265 
1455 
1580 
1,700,000 

No. 2 
1105 
1275 
1385 
1,600,000 

No. 3 
635 
725 
790 
1,400,000 

Select Structural 
2×12 
1670 
1920 
2085 
1,900,000 
No. 1 & Btr. 
1325 
1520 
1655 
1,800,000 

No. 1 
1150 
1325 
1440 
1,700,000 

No. 2 
1005 
1155 
1260 
1,600,000 

No. 3 
575 
660 
720 
1,400,000 

SPRUCEPINEFIR 

Select Structural 
2×10 
1580 
1820 
1975 
1,500,000 
No. 1/No. 2 
1105 
1275 
1385 
1,400,000 

No. 3 
635 
725 
790 
1,200,000 

Select Structural 
2×12 
1440 
1655 
1795 
1,500,000 
No. 1/No. 2 
1005 
1155 
1260 
1,400,000 

No. 3 
575 
660 
720 
1,200,000 

EXCERPTED FROM DESIGN VALUES FOR JOISTS AND RAFTERS, Copyright © 1992 AMERICAN FOREST & PAPER ASSN., WASHINGTON, D.C. 
Step 4 Bearing Check: The final step is to make sure the lumber you’ve chosen meets the required design value for compression perpendicular to the grain. The loads carried by floor joists, ceiling joists, and rafters are transferred through their end points to supporting walls and beams. The ends of these members must be able to resist these loads without crushing.
Table 9.1 in Span Tables for Joists and Rafters (Figure #5) gives a required compression value of 237 psi for a span of 16 feet and bearing length of 1.5 inches. (the tables permit a bearing length of up to 3.5 inches, but since 1.5 is probably the worst case that you’ll encounter for joist or rafter bearing, it’s a safe value.) You can get the compression perpendicular to grain design value for various species selected from the addendum that comes with Design Values for Joists and Rafters. For instance, hemfir has an acceptable value of 405 psi, sprucepinefir of 425 psi.
SPAN TABLES FOR JOISTS AND RAFTERS 

Required compression perpendicular to grain values (F_{c}) in pounds per square inch for simple span joists and rafters with uniform loads 

Bearing Length, in. 

Span, ft. 
1.5 
2.0 
2.5 
3.0 
3.5 

8 
119 
98 
71 
59 
51 

10 
148 
111 
89 
74 
63 

12 
178 
133 
107 
89 
76 

14 
207 
156 
124 
104 
89 

16 
237 
178 
142 
119 
102 

18 
267 
200 
160 
133 
114 

20 
296 
222 
178 
148 
127 

22 
326 
244 
196 
163 
140 

24 
356 
267 
213 
178 
152 

Notes: 

1993 ADDENDUM TO DESIGN VALUES FOR JOISTS AND RAFTERS 

Species^{1} 
Compression design value, psi. “F_{c}“perpendicular to grain 

Douglas FirLarch 
625 

Eastern White Pine 
350 

HemFir 
405 

Southern Pine, Dense 
660 

Southern Pine, Select Structural No.1, No.2, No.3, Stud, Construction, Standard, Utility 
565 

Southern Pine, NonDense 
480 

SprucePineFir 
425 

SprucePineFir (south) 
335 

1. Design values apply to all grades for the species listed unless otherwise indicated in the table above. 

EXCERPTED FROM SPAN TABLES FOR JOISTS AND RAFTERS, Copyright © 1993 AMERICAN FOREST & PAPER ASSN., WASHINGTON, D.C. 
Ceiling Joists and Rafters
Ceiling joists are sized like floor joists except that deflection limits vary depending on whether the joists will be used for attic storage or will have a plaster or drywall finish. Check your code and follow the AF&PA tables accordingly.
When using the tables to size rafters, there are two points to keep in mind. First, remember that the rafter’s span is not its actual length, but its total horizontal projection (see Figure #6). Second, use the snow load value for your region in determining which rafter table to use. If your code book says your snow load is 40 psf, then you must use the 40 psf live load rafter table. The fact that snow loads only act part of the year has been taken into account in the rafter tables, but don’t forget to use the “Snow Loading” column to get the Fb design value.

Use the horizontal projection of a rafter, not 
Last updated: June 4, 2009