It is unlawful to start or maintain an uncontained open fire in the city during the fire season unless a permit for such fire has first been issued by the fire chief; provided, that under no conditions shall any uncontained open fire be started or maintained at any time within the fire limits of the city. No fire shall be started or maintained and no burning shall be done at any time within any building or structure undergoing construction, demolition, or structural repair or alteration, if the building or structure or any part thereof is made of or contains wood, paper or any other combustible material, unless a fire permit therefor has first been issued by the fire chief.