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I have to build a box to extend the length of a projector bracket:

enter image description here

The projector bracket weighs 7kg and has an arm of about 500mm. The projector weighs another 5kg.

The box has a depth of 140mm. That is the length by which I need to extend the length of the projector arm because the wall on which the bracket is mounted is recessed by 140mm behind the image surface.

Does one of the following two ways of joining offer a stronger structure?

enter image description here

I don't have tools to make complex joints. I can only screw ½" plywood at right angles.

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    $\begingroup$ Are you going to glue & screw the joints or just screw them together? If you're concerned about the strength of the joint, proper gluing in addition to screws is advisable. $\endgroup$ – user16 Mar 16 '19 at 16:53
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In addition to the excellent suggestion of glue with the screws, consider to add a batten or bracing at the corners, as per the diagram below.

box support

The red squares would run the width of your box and allow you to drive the screws through the thickness of the plywood and into long grain of the battens, rather than into edge grain of the other plywood. This will give you the best possible strength in the simplest manner.

The ends of the boxes should also have battens and be screwed in place. The box ends will provide torsion strength which is going to be a substantial portion of the design success.

I'm not sure why, but one red square is missing from the drawing. The four box end battens are omitted for clarity.

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