A buckstay connecting system includes a socket part that is fixed to the horizontal buckstay being separated from a lower end of the vertical buckstay between the lower end of the vertical buckstay and the horizontal buckstay, and an insertion part that is fixed to a lower portion of the vertical buckstay, is inserted into the socket part so as to be able to slide in a vertical direction, inhibits the horizontal buckstay from being inclined, and is allowed to be fastened to the socket part.