For LRFD in the 2005 NDS^®, why does the φ factor cancel out when adjusting nominal resistances using the LRFD Format Conversion Factor, K_F , and the resistance factor, φ?

• The resistance factor, φ is used to adjust the LRFD design value for variability. However, reference design values in the NDS are based on near-minimum values and thus are already adjusted for variability. In order to be used with conventional LRFD design procedures, the NDS reference design values (ASD based), must be divided by the resistance factor. The NDS Format Conversion Factor, K_F , explicitly divides a constant conversion factor by the resistance factor consistent with the format used in ASTM D5457 Standard Specification for Computing Reference Resistance of Wood-Based Materials and Structural Connections for Load and Resistance Factor Design. However, explicitly dividing by the resistance factor in the calculation of the format conversion factor, and then multiplying by the resistance factor in LRFD design procedures, has proven to be disconcerting to many NDS users. For this reason, revision of the format conversion factor is being considered whereby final values of K_F will be tabulated in-lieu of equations having the format of: K_F = 2.16/φ or K_F = 1.875/φ
  
  An example of what is meant by “cancel out” is shown as follows for determination of the adjusted LRFD bending design value, F_b’:

  F_b’ = (F_b)(2.16/φ_b)(φ_b)(all other applicable adjustments)

  where

  F_b = reference bending design value in the NDS
  2.16/φ_b = Format conversion factor for bending
  φ_b = resistance factor for bending