Statics: Horizontal Movements of Structures Induced by Vertical Loads

A grandstand

Fig. 12-10: Typical mode of vibration of a frame model of a cantilever grandstand showing coupled vertical and front-to-back movements [12.3]

Fig. 12-10 shows coupled vertical and front-to-back movement of the cross-section of a grandstand in one typical mode of vibration. It can be seen that the front-to-back movements of the grandstand are larger than the vertical movements of the two tiers for this particular mode. This mode shape indicates that resonance in the front-to-back direction would occur if one of the frequencies of vertical loading on a tier was close to the natural frequency associated with the mode, even though the vertical movement will be small. It has been observed at a pop concert that a stand moved much more significantly in the front-to-back direction than in the vertical direction although the human loading was primarily in the vertical direction.