What is the background behind footnote “m” of IBC 2012 table 721.1 (2) which states:
“m For studs with a slenderness ratio, le/d, greater than 33, the design stress shall be reduced to 78 percent of allowable F′c. For studs with a slenderness ratio, le/d, not exceeding 33, the design stress shall be reduced to 78 percent of the adjusted stress F′c calculated for studs having a slenderness ratio le/d of 33.”
Most North American fire tests on wood stud wall assemblies were conducted between 1950 and 1975. During that time, the standard wall configuration was a 10 foot x 10 foot wall using 2x4 Select Structural grade Douglas Fir-Larch or 2x4 #1 Dense grade Southern Pine studs. These grades were chosen to allow a single, highly-loaded test to be used for all lower grade studs.
In 1982, the design values for compression perpendicular-to-grain stress (Fc-perp) were increased due to changes made to ASTM D245 Standard Practice for Establishing Structural Grades and Related Allowable Properties for Visually Graded Lumber. D245 provisions were changed so that reference Fc-perp design values were derived from Fc-perp test results at 0.04" deformation rather than at proportional limit which had previously been used. Because of this change, designs which had previously been limited by Fc-perp, such as bearing wall assemblies, were then limited by other criteria.
The National Forest Products Association (NFPA) staff was asked if the wall assembly fire resistance tests conducted between 1950 and 1975 were valid since the loads on the walls were now often limited by the calculated buckling stress, FcE, rather than the calculated bearing. Recognizing that the fire resistance of an assembly under a given load would not change just because the reference basis of the design value had been changed, the maximum calculated load capacity of the assembly using the old and new criteria were calculated and compared based on the 1982 design values for Fc-perp.
Using the Fc-perp design values which have been in place since 1982, the calculated load capacity of 2x4 wall assemblies are typically limited by column buckling in the strong axis direction. Several design assumptions were resolved for the final comparison. First, the actual stud length for a 10 foot wall was assumed to be 115.5 inches (120-3*1.5). Also, since it was unclear which grades of lumber were used in the fire tests, staff compared Select Structural, #1, #2 and #3 grades and found that the most conservative assumption was to use design values for Select Structural for the comparisons.
Finally, the adjustment factor was calculated as follows:
Most wall assembly tests that are the basis of the 1 and 2-hour wood wall assemblies in the International Building Code (IBC) were 10' walls using 2x4 studs. From the above calculation, it was valid (though conservative) to limit the capacity of those wall assemblies to 78% of the adjusted allowable compression design value at a Le/d ratio of 33. Since 1999, AWC has conducted multiple wall assembly tests that permit the use of 2x4 and 2x6 wall assemblies at full design load (100% of designs per the 2005 National Design Specification (NDS) and later versions). These assemblies have been included in the IBC and are described in DCA3 at awc.org/Publications/dca/dca3.