For purposes of preserving the integrity of the Official Map, no permit shall be issued for any building or structure in the bed of any street or public drainageway, flood control basin or public area reserved pursuant to §
96-32 of this chapter, as shown on the Official Map or shown on a plat filed pursuant to this chapter before adoption of the Official Map, except as provided herein. Whenever one or more of parcels of land upon which is located the bed of such mapped street or public drainageway, flood control basin or public area reserved pursuant to §
96-32 hereof cannot yield a reasonable return to the owner unless a building permit is granted, the Board of Adjustment may, in a specific case, by an affirmative vote of a majority of the full authorized membership of the Board, direct the issuance of a permit for a building or structure in the bed of such mapped street, public drainageway, flood control basin or public area reserved pursuant to §
96-32 hereof, which will as little as practicable increase the cost of opening such street or tend to cause a minimum change of the Official Map; and the Board shall impose reasonable requirements as a condition of granting the permit so as to promote the health, morals, safety and general welfare of the public. Sections
96-64 through
96-67 of this chapter shall apply to applications or appeals pursuant to this section.