Horizontal Movements of Structures Induced by Vertical Loads
- Vertical loads acting on structures can induce horizontal movements. Exceptions are symmetric structures subject to symmetric vertical loads and (rarely) anti-symmetric structures subject to anti-symmetric loads.
- The magnitudes of the horizontal movements of structures in response to vertical loads depend on the load distribution and the structural geometry.
- When the frequency of a dynamic vertical load is close to one of the lateral natural frequencies of a structure, resonance in the lateral direction of the structure can occur.
Model Demonstrations
A symmetric frame


Fig. 12-7: A symmetric frame subjected to an asymmetric load
Fig. 12-7 shows a simple symmetric plastic frame unloaded (a) and carrying an asymmetrically concentrated load positioned close to the right hand column (b). It can be observed that the horizontal member deflects vertically and the loaded frame moves to the left. Note that the movement is to the left for the load placed to the right of the centre line of the frame. If the vertical load was a harmonic dynamic load and its frequency matched the natural frequency of the frame in its horizontal direction, resonance with significant horizontal movements of the frame would occur.
An anti-symmetric frame


Fig. 12-8: An anti-symmetric frame subjected to an asymmetric load
Fig. 12-8 shows a simple anti-symmetric plastic frame unloaded (a) and carrying an asymmetrically concentrated load positioned close to the right hand column (b). It can be observed that the horizontal member deflects vertically and the loaded frame moves to its left. Again the movement is to the left for the load placed to the right of the centre line of the frame.
An asymmetric frame


Fig. 12-9: An asymmetric frame subjected to an asymmetric load
Figure 12-9 shows a simple asymmetric plastic frame unloaded (a) and carrying a concentrated load positioned close to the right hand column. The horizontal member deflects vertically and it can be observed that the loaded frame moves to the left. Again the movement is to the left for the load placed to the right of the centre line of the frame.
Practical Examples
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.
A building floor




A 9 m by 6 m test panel of a large composite floor is shown in Fig. 12-11. The structural response of the panel was measured for a group of 64 students jumping following a music beat (Fig. 12-12). At the centre of the test floor panel, the vertical acceleration was recorded for just over 16s, as was the horizontal acceleration in the direction orthogonal to the direction in which the students were facing. The peak vertical acceleration was 0.48g and the corresponding horizontal acceleration 0.03g. The autospectra for these records are shown in Fig. 12-13 and the characteristic response can be seen in both directions. The test area was part of the much larger flooring system (Fig. 12-11) and the vertical human loading was thus applied asymmetrically on the structure as a whole, which induced the horizontal motion of the whole building system.
Rail bridges:
Horizontal movements of some railway bridges have been observed as trains passed over them. Because of the increasing speed of trains a number of bridges have had to be re-assessed for safety. As there are often two or more rail tracks on a bridge, the loading from any one train is effectively applied in an asymmetrical manner on the structure generating lateral horizontal movements of the bridge. There will also be some horizontal forces generated by lateral movement of the railway vehicles, even along straight tracks. With the increasing speed of trains, the vertical loading frequency will increase and this may be a problem if resonance occurs, i.e. if one of the train load frequencies in the vertical direction is close to one of the lateral natural frequencies of the bridge. It is therefore necessary to check horizontal as well as vertical natural frequencies of bridges to ensure that both are above the likely loading frequencies associated with trains running at higher speeds.
References
12.1 Dallard, P, Fitzpatrick, T, Flint, A, Low, A, Smith, R R and Willford, M, (2000), Pedestrian induced vibration of footbridges, The Structural Engineer, Vol.78, No.23/24, pp.13-15.
12.2 Ji, T, Ellis, B R and Bell, A J, (2003), Horizontal movements of frame structures induced by vertical loads. Structures and Buildings, the Proceedings of the Institution of Civil Engineers, Vol.156, No.2, pp141-150.
12.3 Mandal, P and Ji, T, (2004), Modelling dynamic behaviour of a cantilever grandstand, Structures and Buildings, The Proceedings of the Institution of Civil Engineers, 157(3) p.173-184.