I'm not able to add a column on a database table

[barbiomalefico]

I need to add a new column in a DB.
I write this code but it doesn't works (i have removed try catch block):

OleDbDataAdapter SingleMDBAdapter ;
DataSet SingleMDBDataSet;
string strQuery = "SELECT * FROM ["+ActualTableName+"]";
SingleMDBAdapter = new OleDbDataAdapter(strQuery,SingleMDBConnection);
SingleMDBDataSet = new DataSet();
SingleMDBAdapter.Fill(SingleMDBDataSet);
if (SingleMDBDataSet.Tables[0].Columns.Contains("String1"))
{
   if (!SingleMDBDataSet.Tables[0].Columns.Contains("String2"))
   {
       SingleMDBDataSet.Tables[0].Columns.Add("String2");
       SingleMDBAdapter.Update(SingleMDBDataSet);
   }
}

This code doesn't raise any exception, simply it doesnot put the new column on my access DB.

Any suggestions?