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Joining two 10 ft 6x6s of dry pressure treated with half lap (not tapered) and 3/8" lag bolts with washers (not machine bolts). For strength, what is the optimal length of half lap and what is the optimal ratio of thicknesses? Would it be different for 4x4s?

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In a "half" lap joint, the thickness should always be half of the material for the most strength. You're reducing the strength of the board because you're removing thickness, and the joint will only be as strong as the weakest piece. If you made the thickness ratio 25%/75%, then the 25% side would be the weakest.

Lap joints are used often for 90 degree joints, and in this case, the length of the joint is equal to the width of the board so all the edges match up. In a end-to-end joint, the same ratio can be used to provide adequate gluing, nailing, or bolting area. Less length might not provide enough area for bolts, and more area isn't going to add more strength because the weak point still comes from the fact that you just cut out half the thickness of the board.

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Picture: http://timberframehq.com/simple-half-lap-joint/

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    If I do the 50/50 then the lag bolts will have only 2" to grab in the 6x6 (5" lag, lap thickness 2.75), and 1" in the 4x4 (3" lag, 1.75" lap thickness) (1/4" of the tip has neglible holding power). If the length was 12" rather than 5.5", there would be much less torque (for in-plane bending), or pull-out (for perpendicular bending). – user25678 Sep 28 '17 at 20:47
  • @user25678, why not use carriage bolts that would go all the way through? – JPhi1618 Sep 28 '17 at 21:24
  • can't. as specified in OP, lag bolts not machine bolts. – user25678 Sep 28 '17 at 21:40
  • @user25678 , you are OP, and I thought more detail was in order because bolts would increase the strength quite a bit. – JPhi1618 Sep 29 '17 at 13:26

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