(a) The owner, occupant, or person having charge or management of any parcel of land situated within the City and abutting upon any public alley or street, shall trim and keep trimmed all trees growing on such premises, or between the property line and the center of such abutting alley or street, the branches of which trees overhang any part of the pavement or sidewalk of the public alley or street, such trees to be so trimmed and kept trimmed so that the lowermost branches thereof shall be a height of fifteen and one-half feet above the level of that part of the pavement of any sidewalk, alley or street so overhung by such branches. However, the provisions of this section shall not apply to trees so small that the branches thereof do not materially obstruct public travel and which cannot be so trimmed without serious injury thereto.