They don't want scrap metal in the curbside recycling. From the city website the acceptable metals are:
aluminum drink cans
aluminum baking tins
steel or tin food cans and lids
empty aerosol cans
I don't think the wood would be acceptable in the green/composting bin. The website says they don't want treated wood. The only types of wood on the acceptable list are chopsticks, popsicle sticks, and yard trimmings.