No building or structure, or any part thereof, shall hereafter be built within the City unless a permit therefor shall first be obtained by the owner or his agent from the Building Inspector. No construction shall be commenced prior to the issuance of such permit. Commencement of construction shall include such acts as beginning excavation or constructing forms for cement work. See Chapter 140, Building Construction, of this Code. The Building Inspector may grant variances from the terms of this chapter in those cases where a setback, side yard or rear yard variance would clearly be consistent with those existing in the neighborhood. Where an existing older residence constructed before October 22, 1987, is being rebuilt after a fire or is being converted to a duplex and lacks the minimum square feet of living area and land area required in the zoning district as prescribed in this chapter, the Council may grant a special exception waiving the requirements for a certain minimum square feet of floor space or land area so as to allow such reconstruction or conversion; provided, however, that granting of such special exception will not be contrary to the public interest.