The Planning Commission shall be the Board of Zoning and Building Code Appeals. All meetings of the Board shall be public. In addition to any other powers granted by ordinance, the Board shall have power to hear and determine appeals from refusal of building and zoning permits and to permit exceptions to and variations from the zoning and building code regulations in individual cases as may be required to afford justice and avoid unreasonable hardship to property owners in accordance with standards established by ordinance of Council.