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I am building a headboard for a bed, and want to put an MDF sheet inside a dado in 4x4 cedar boards, as shown in the image: enter image description here

Should I make the MDF free floating in case it swells? Or glue it to the cedar inside the dado?

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In general the dimensional movements in man-made sheet goods are absolutely minimal, in fact they are taken to be zero in most situations. It's not quite zero but it's so small it might as well be and is commonly ignored, same as longitudinal movement in solid wood is.

This is precisely why you can get away with 'picture framing' even quite large panels of MDF and HDF, chipboard and ply without any movement concerns. As in e.g. workshop tables and workbenches:

MDF workbench tops

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