I am trying to create a calculated member with multiple dimensions as
conditions.

Same thing can be acheived by below SQL Script.

SELECT SUM(f.Amt)
FROM Fact f
inner join dimension1 d1 on d1.d1_ID = f.d1_ID
inner join dimension2 d2 on d2.d2_ID = f.d2_ID
inner join dimension3 d3 on d3.d3_ID = f.d3_ID
where d2.Num = 20 and d3.index >=100 and d3.index <=500

Num is a column in d2 table and index is a column in d3 table.

Please advise.

Thanks,
Dana