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What advantage does it provide? Explaining with a figure would be helpful.

I tried to draw a free body diagram and equated the sum of force and moments to zero, but still was not able to find out.

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enter image description here

  1. More compact configuration that fully utilizes the area of the leaf.

  2. Avoid stresses concentrated on a single plane that is likely to cause the base material to progressively fail in shear or split.

  3. The staggered arrangement is more stable. It provides better strength in resisting the incidental bending resulted from the weight of the door and missing/loose screw(s) on the door side leaf. (There is a couple in addition to the horizontal resistants of the bolts, albeit this advantage could be small and usually is unaccounted for.)

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Because the screws go into wood and if the screws are in line then the wood will most often split between the screws in the grain direction and then the screws come loose.

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Staggering the screws will

  • give a better chance for some of them to penetrate into solid grain. and discourage toilet paper perforation pattern.

  • Provide for larger torque resistance.

  • keeping the hinge from develoing a loose play, flapping out of door jamb plane. prhibiting door settling slanted out of its frame.

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Just adding to the rest of the answers, if the door hinge is thick enough to be assumed rigid, then the offset configuration offers better resistance to bending moments in at least two axis.

i.e: For the following reference system

enter image description here

Case Y-Axis bending moment Z-Axis bending
Front View enter image description here enter image description here
Top View enter image description here enter image description here

It is noteworthy, that for a pure pullout force (which is somewhat similar to the first case of Y-bending) the offset configuration will not have any additional advantage to the straight line.

So (just summing up) the zig-zag configuration offers:

  • Allows compact and uniform distribution of the loads both on the plate and on the frame. (This is particularly important in the case of wood frames, because of the grain).
  • Increases the bending resistance of the rivets (the effect is similar to the effect of the second moment of area in bending and torsion).
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It's so the screw heads on opposite leaves don't hit each other when the hinge is closed. The heads aren't always 100% flush.

Mechanically, this compromises some load cases, but not the limiting ones.

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    $\begingroup$ most hinges have the screw heads directly aligned $\endgroup$
    – Jasen
    Sep 19 at 5:41
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    $\begingroup$ No they don't. If you find one, throw it in the trash - it was made and sold by idiots. Hinge $\endgroup$
    – Phil Sweet
    Sep 19 at 14:21
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    $\begingroup$ I don't see how preventing the screw heads from touching actually solves the problem of the screws not being flush. My guess is that hinge is made that way because it has an even number of screw holes and thus when you rotate one leaf around you get the offset, and thus you only need to manufacture 1 type of leaf. When I look at hinges with an odd number of zigzaged holes they seem to line up, which suggests that the driving principle here is reducing the number of unique parts involved. $\endgroup$ Sep 19 at 16:24
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    $\begingroup$ If the heads aren't flush, you have crap workmanship. If non-flush heads interfere, then the tolerances on the door vs. frame are wrong - there should always be clearance. $\endgroup$ Sep 20 at 12:42
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    $\begingroup$ With most hinges, provided you use the screws that come with the hinge, the screw heads should end up flush with the hinge surface, since the holes are countersunk specifically for this reason. If your screw-heads aren't flush, either they're not screwed in all the way, or someone has replaced them with other screws not designed to go with that hinge. $\endgroup$ Sep 20 at 19:26

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