ABSTRACT

The geometry of skewed and curved bridges can cause complexity of their dynamic response and difficulty of analysis against earthquakes. In addition, when vibration occurs in the curved bridges, due to their specific geometry, the vertical, flexural, and torsional vibrations of the deck are coupled. The present study was carried out aiming to investigate the effect of non-uniform vertical excitation of the bridge piers with various vertical/horizontal acceleration ratio (V/H) on the pounding phenomenon in concrete curved bridges subjected to near-source earthquakes. For this purpose, the analytical method was employed using the expansion of the functions of structural dynamics on a two-span continuous concrete bridge model, consisting of continuous flexural/torsional beam elements for the deck, springs for the rubber bearings, and rods as the bridge piers. The non-uniform vertical excitations of the piers were induced to the whole system by the harmonic functions in the form of transient wave transfer functions, and then the equations of the entire system were solved using the Eigen functions. The induced waves can cause separation of the box girder deck from the rubber bearing along with the vertical and horizontal displacement as well as the torsion of the box girder around the longitudinal axis of the bridge. After each separation, the deck returns back and hit the rubber bearing, resulting in a vertical pounding force on the bearing and the pier. The analyses results show that when the curved beam is subjected to a non-uniform vertical excitation with a various V/H, the lateral displacement of the deck are up to 21% larger than when the bridge is excited by considering a value of V/H = 2/3. The results also show when the excitation frequencies are different in different piers of the bridge, the pounding force can be increased up to three times, for some specific curvature angle, comparing to the case of equal excitation frequency in all piers.

摘要

倾斜和弯曲桥梁的几何形状会导致其动力响应的复杂性和抗震分析的难度。此外，当弯曲桥梁发生振动时，由于其特定的几何形状，桥面的垂直、弯曲和扭转振动是耦合的。本研究旨在研究不同垂直/水平加速度比（V/H）下桥墩的非均匀垂直激励对混凝土弯桥近源地震冲击现象的影响。为此，该分析方法采用了在两跨连续混凝土桥梁模型上扩展结构动力学函数的方法，该模型由桥面的连续弯曲/扭转梁单元、橡胶支座的弹簧、和杆作为桥墩。通过谐波函数以瞬态波传递函数的形式将桥墩的非均匀竖向激励引入整个系统，然后利用本征函数求解整个系统的方程。诱发的波浪会导致箱梁桥面与橡胶支座分离，以及箱梁围绕桥梁纵轴的垂直和水平位移以及扭转。每次分离后，甲板返回并撞击橡胶支座，从而在支座和桥墩上产生垂直冲击力。分析结果表明，当弯曲梁受到不同V/H的非均匀垂直激励时，考虑到 V/H = 2/3 的值，桥面的横向位移比激发桥时大 21%。结果还表明，当桥梁不同桥墩的激振频率不同时，与所有桥墩相同激振频率的情况相比，对于某些特定曲率角，冲击力可提高3倍。