One of the cross beams of my bed's box spring snapped a few weeks ago, causing the bed to sag a bit on one side. So I screw this into the original beam, or do I combine it with another piece of wood.
Buy one the correct size apply wood glue and screw it every inch or two. Also you can apply wood glue at the split and use a bar clamp to hold it all together until it dries.
Very important to glue it the entire length and also glue the cracked split section well then clamp that section. It will be stronger but may pose problems getting it secured well where the wood with the glue won't be going anywhere. I'm not sure how much weight or pressure that area takes but this is clearly not a perfect fix.
They come in 8ft 10ft and 12ft lengths if it was me I would cover as large a area as I can.