A bracket mounting structure, for use with a slide rail, the bracket mounting structure comprising: a bracket including a longitudinal wall; a base disposed adjacent to the longitudinal wall and including a first space and a second space; a connecting member mounted in the first space; and a mounting member mounted in the second space, wherein the connecting member includes a screw thread feature; that the base, in the first space, includes a connecting structure and a hole having an auxiliary screw thread feature on a wall of the hole, wherein the hole and a through hole of the connecting member lie on the same longitudinal axis and the screw thread feature and the auxiliary screw thread feature are configured to connect with a threaded element (52, 56); and wherein the bracket mounting structure further comprises a first elastic member mounted on the connecting structure and received in the first space for applying an elastic force to the connecting member; wherein the connecting member includes a first portion, a second portion, and the through hole extending through the first portion and the second portion; wherein at least one of the first portion and the second portion includes the screw thread feature in the through hole; wherein, with the through hole penetrating the first portion and the second portion, the connecting member is configured to be used with a first threaded element and a second threaded element, which is longer than the first threaded element, and to pass through the through hole and to connect with the base; and wherein the screw thread feature is configured to connect with either the first threaded element or the second threaded element, wherein the second threaded element is further configured to connect with the auxiliary screw thread feature of the base after passing through the through hole. a bracket including a longitudinal wall; a base disposed adjacent to the longitudinal wall and including a first space and a second space; a connecting member mounted in the first space; and a mounting member mounted in the second space, wherein the connecting member includes a screw thread feature; that the base, in the first space, includes a connecting structure and a hole having an auxiliary screw thread feature on a wall of the hole, wherein the hole and a through hole of the connecting member lie on the same longitudinal axis and the screw thread feature and the auxiliary screw thread feature are configured to connect with a threaded element (52, 56); and wherein the bracket mounting structure further comprises a first elastic member mounted on the connecting structure and received in the first space for applying an elastic force to the connecting member; wherein the connecting member includes a first portion, a second portion, and the through hole extending through the first portion and the second portion; wherein at least one of the first portion and the second portion includes the screw thread feature in the through hole; wherein, with the through hole penetrating the first portion and the second portion, the connecting member is configured to be used with a first threaded element and a second threaded element, which is longer than the first threaded element, and to pass through the through hole and to connect with the base; and wherein the screw thread feature is configured to connect with either the first threaded element or the second threaded element, wherein the second threaded element is further configured to connect with the auxiliary screw thread feature of the base after passing through the through hole.