Does a shared custody arrangement change child support?

I currently have every other weekend visits with my children because I live 3 hours away from them. I will soon be moving to Cleveland where they live to be closer to them. I want to file for shared custody as soon as I move. Is there anything I have to show a court to gain shared custody other than that I will then be close enough to them to manage a 50/50 custody schedule? I can get them to school and their extracurricular activities. Also, I currently pay full child support to my ex. If I do gain shared custody, will that change my child support obligation? Do I have to ask for the child support change at the same time I request equal custody rights?