How is Zakat calculated on shares, and is it permissible to give it to a needy brother for building a new house?

There is no impediment to giving zakat to a brother to complete the construction of his house, provided two conditions are met: that he does not possess another dwelling sufficient for him and his family, and that he is unable to secure housing, even through rent that does not burden him. If these two conditions are met, then zakat is permissible; otherwise, it is not permissible to give it to him.