For the purpose of building or keeping in repair such bridge or bridges, it shall be lawful for the county boards of such adjoining counties to enter into joint contracts. Such contracts may be enforced in law or equity against them jointly, the same as if entered into by individuals, and they may be proceeded against jointly, by any parties interested in such bridge or bridges, for any neglect of duty in reference to such bridge or bridges or for any damages growing out of such neglect. If either of such counties shall refuse to enter into contracts to carry out the provisions of this section for the repair of any such bridge or bridges, it shall be lawful for the other said counties to enter into such contract for all needful repairs and recover by suit from the county so in default such proportion of the cost of making such repairs as it ought to pay, not exceeding one-half of the full amount so expended. Whenever two or more counties have entered into a joint contract whereby one county assumes the responsibility for the separate maintenance and repair of the bridges upon specified portions of public roads upon or across county lines, it shall be the duty of the county agreeing to maintain and keep in repair any such bridge to promptly erect and maintain adequate barriers to prevent accidents, whenever the condition of any such bridge or the approaches thereto is dangerous to public travel, and to diligently proceed with the repair thereof. The performance of such duty by a county agreeing to maintain and keep in repair such bridge may be enforced by mandamus by any other county or counties which are parties to the contract.