Earthquake Response Spectra Analysis of Bridges considering Pounding at Bilateral Beam Ends Based on an Improved Precise Pounding Algorithm

Asynchronous vibration was generated between the main bridge and approach spans or abutments due to differences in stiffness and mass during an earthquake, thus further leading to pounding at the bilateral beam ends. By taking a T-shaped rigid frame bridge as an example, the bilateral pounding model was abstracted, and the earthquake response spectra considering pounding at the bilateral beam ends were studied, including the maximum displacement spectrum, the acceleration dynamic coefficient spectrum, the pounding force response spectrum, and the response spectrum for the number of pounding events. An improved precise pounding algorithm was proposed to solve the dynamic equation of the bilateral pounding model. This algorithm is based on the precise integration method for solving the second-order dynamic differential equation and reduces the order thereof by introducing a new velocity vector and uses the series method to find the nonhomogeneous term. The system matrix is simpler, and the inversion of the system matrix can be avoided. On this basis, a multipoint earthquake-induced pounding response spectrum program was developed. A total of 18 seismic waves from Class II sites were selected, and the response spectra of 18 waves were analyzed using this new program. Furthermore, the effects of structural stiffness, mass, stiffness of contact element, pounding recovery coefficient, and peak ground acceleration (PGA) on the earthquake response spectrum were studied. Through the analysis of earthquake response spectra and a parametric study, the phenomenon of earthquake-induced pounding of bridges was clarified to the benefit of the analysis and engineering control of earthquake-induced pounding of bridges.

Increasing Student Understanding of Response Spectra: An Argument for the Inductive Learning Approach

Creating and interpreting earthquake response spectra are important fundamentals in earthquake engineering education. We argue that an effective approach for teaching the fundamentals of earthquake response spectra is to use an inductive learning approach in an interactive classroom, which is well supported by engineering education literature. To demonstrate this approach we use desktop learning modules that exhibit response spectra concepts. Preliminary data based on post-class interviews with instructors support our opinion. Notably, all interviewed instructors have chosen to adopt the inductive learning approach when teaching response spectra concepts in future iterations of their classes.

Erdbebenantwortspektren einer weichen Bodenschicht auf einem Halbraum/Earthquake response spectra of a soft soil layer underlain by a halfspace

Weiche Bodenschichten, wie sie beispielsweise als Tonschichten über steifen Sedimentböden auftreten, beeinflussen die Form eines horizontalen Erdbeben-Antwortspektrums aufgrund von resonanzartigen Effekten der einfallenden SH-Wellen erheblich. Daher werden etwa im EC 8 (deutsches NAD) für weiche Böden mit Scherwellengeschwindigkeiten unter 150 m/s besondere Untersuchungen gefordert. Auf der Grundlage einer intensiven Parameterstudie wurden für das Modell einer homogenen viskoelastischen Bodenschicht auf einem homogenen viskoelastischen Halbraum Gleichungen zur Beschreibung des zugehörigen horizontalen Beschleunigungsantwortspektrums entwickelt. An der Oberfläche des Halbraums wurde ein Antwortspektrum nach EC 8, Boden-/Untergrundklasse C-S angenommen. Die mit den Gleichungen erhaltenen Antwortspektren stimmen mit den nach der Theorie für eindimensionale Scherwellen erhaltenen Ergebnissen gut überein. Sie können unmittelbar zur Ermittlung der Erdbebenbeanspruchungen von Gebäuden auf einer weichen Bodenschicht nach EC 8 verwendet werden.