Selecting 1st and 3rd Tuesdays
This code works by passing a date value, such as "getdate()", to a function.

Works great.  Not my work.

Source:  http://mikedefehr.com/2011/07/25/finding-the-nth-weekday-of-a-given-month/

CREATE FUNCTION nth_weekday_of_month_fn ( 
@dt DATETIME, 
@dow VARCHAR(10), 
@num INT 
) 
RETURNS DATETIME 
AS 
BEGIN

DECLARE @RetDate DATETIME;

WITH MonthDays AS 
( 
SELECT DATEADD(DAY,number-1,DATEADD(MONTH,DATEDIFF(MONTH,0,@dt),0)) AS
MonthDate 
FROM MASTER..spt_values 
WHERE number &gt; 0 
   AND TYPE = 'P' 
) 
, WeekDays AS 
( 
SELECT *, ROW_NUMBER() OVER(ORDER BY MonthDate) DayIndex 
FROM MonthDays 
WHERE YEAR(@dt) = YEAR(MonthDate) 
   AND MONTH(@dt) = MONTH(MonthDate) 
   AND DATENAME(dw,MonthDate) LIKE @dow + '%' 
) 
SELECT @RetDate = MonthDate 
FROM WeekDays 
WHERE DayIndex = @num RETURN (@RetDate) END 
GO


For 1st and 3rd Tuesdays of current month:

SELECT dbo.nth_weekday_of_month_fn(GETDATE(),'Tuesday',1) 
SELECT dbo.nth_weekday_of_month_fn(GETDATE(),'Tuesday',3)