Per the National Design Specification for Wood Construction (NDS) 2012, Section the minimum penetration (not including the length of the tapered tip) of the lag screw into the main member for single shear connections or the side member for double shear connections shall be four times the diameter, Pmin = 4Ø. A 1/2″ lag screw would therefore need roughly 4 * 1/2″ = 2″ penetration.
However, if you have 4Ø, that  does not mean full capacity for the connection because in the tables of LAG SCREWS: Design Values, you will find footnote 3 which states that when the penetration is between 4Ø<=p<8Ø the lateral design loads values (Z) shall be multiplied by p/8Ø (penetration factor) or shall be calculated using the provisions of Section 11.3.
At first look in Section 11.5 Adjustment Factors for Dowel-Type Fasteners in lateral loads, there is no Cd (penetration Depth Factor) applied but the footnote referenced above refers to a specific section in order to calculate it.
Information provided by Zach Rubin, E.I.


Apr 18, 2016   6911    Codes & Standards, Engineering Principles    
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