I've an adsense account. Now one of family member wants to create another one. That account will be used by a single pc. Does it violates terms?
If both of accounts have separate address
No. That is like asking "will my bank allow 2 different people living at the same address have separate accounts".
If you each use your own gmail account it will be fine. In fact, it is possible for an individual to have multiple adsense accounts...as long as they have multiple gmail addresses - and who doesn't ;o)