and beams and by bending deformation of the whole frame caused by axial deformation of the posts normally the vibration of a building consists of the total of the aforementioned two deformations and the greater the height of a slender building relative to its width the greater is the bending deformation of the whole frame many conventional variable stiffness structures cope with the vibration of a building by controlling the stiffness of the whole frame on each story which requires a complicated control to cope with the bending deformation according to the present embodiment a rod like control member extending over at least a plurality of stories is provided along the posts of the multi storied building and upper and lower portions of the control member are respectively connected with portions of the building preferably with the uppermost and lowermost portions thereof a variable damping device capable of varying the connecting condition is provided on an intermediate portion or an end portion of the control member so that the stiffness of the building or the damping force is controlled by means of control of the bending deformation against the vibrational disturbance such as earthquake or wind referring to fig1 through 18 an interior steel round pipe 121 serving as the control member is installed inside a hollow rectangular post 122 of a high rise building the inside steel pipe 121 has the uppermost portion rigidly connected to cruciform vertical connecting plates 126a and to a rectangular diaphragm plate 125a the lowermost portion of pipe 121 is rigidly secured to cruciform vertical connecting plates 126b and to a rectangular diaphragm plate 125b.