Does the Old Testament law prohibit marriage among step siblings?

I ask because I'm trying to understand whether the prohibition against sibling marriage is due to genetic or emotional reasons. Suppose Bob and Alice marry, have a daughter Eve, and some years later Alice dies. Suppose Chris and Diana marry, have a son Frank, and some years later Chris dies. Now, suppose Bob and Diana marry -- that would make Eve and Frank stepsiblings with no shared biological heritage. Would the Old Testament law, in this case, prohibit Eve and Frank's marriage?