If the US and China specialize according to comparative advantage what will happen to the total output of steel and aluminum in the two countries?

In a theoretical situation, when two nations trade with one another using comparative advantage , the nation with the lesser opportunity cost in a certain product will produce that product. Example: Say the opportunity costs are as follows for the US and China:

China ~~~~~~~~~~~~~~~~~~~~~~ US
------- ~~~~~~~~~~~~~~~~~~~ ------
1 steel=10 aluminum ~~~~~~~1 steel=20 aluminum
1 aluminum= 20 steel ~~~~~~~1 aluminum=10 steel

In this scenario, China will export steel and the US will export aluminum. Since each nation is concentrating its efforts in one product, it will export less of the other product and let the other nation export that product. Example: China has decided to export steel since it has the comparative advantage, and has decided to import aluminum from the US since it is cheaper.

Hope this helps.