I received 2 SSA-1099 forms but only entered 1 when I filed my 2016 Tax Return. Tax due is still zero after correcting. Do I need to file an amended return form 1040x?

Adding the additional amount from the 2nd SSA-1099 form does not change tax due, which is still zero.  The only change on Form 1040A is Social Security Benefits (line 14a).  Taxable Social Security (line 14b) is still zero.  Amount of Tax Owed (Line 50) is still zero.