Dynamic Response of a Rigid Slab Supported by Four Rigid Cylinrical Rocking and Wobbling Columns

Rajah, Sharveen; Bachmann, Jonas A.; Vassiliou, Michalis F.; Stojadinović, Božidar

doi:10.7712/120117.5625.18529

Cited by 2 publications

(2 citation statements)

References 44 publications

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“…Based on the assumptions presented in Section 3, the equations of motion of the system are

\begin{matrix} lefttrue \\ \ddot{θ} = - {\overset{p}{true}}^{2} (sin (α - θ) + cos (α - θ) (\frac{{\ddot{u}}_{g}}{g} cos φ + \frac{{\ddot{v}}_{g}}{g} sin φ)) + \\ + {\overset{φ}{true}}^{2} (\begin{matrix} left \\ sin θ {sin}^{2} α (4 γ + \frac{3}{2}) + cos α sin α (4 γ + 1) (1 + cos θ - 2 {cos}^{2} θ) + \\ sin θ cos θ (\frac{4}{3} {cos}^{2} α - \frac{5}{4} {sin}^{2} α + 4 γ ({cos}^{2} α - {sin}^{2} α)) \end{matrix}) \frac{12}{48 γ + 15 + {cos}^{2} a} \end{matrix}

\begin{matrix} lefttrue \\ (\begin{matrix} left \\ (\frac{4}{3} {cos}^{2} a - \frac{5}{4} {sin}^{2} α + 4 γ ({cos}^{2} α - {sin}^{2} α)) \cdot {sin}^{2} θ + \\ (3 + 8 γ) (1 - cos θ) {sin}^{2} α + 2 sin α cos α sin θ (1 + 4 γ) \cdot (1 - cos θ) \end{matrix}) \cdot \ddot{φ} + \\ + (\begin{matrix} left \\ (3 + 8 γ) {sin}^{2} α sin θ + (8) \end{matrix}) \end{matrix}

…”

Section: Description Of the Proposed 3d Modelmentioning

confidence: 99%

Seismic response of a wobbling 3D frame

Vassiliou

2017

Earthq Engng Struct Dyn

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Summary This paper investigates the 3D response of a slab supported by wobbling columns. The columns are not allowed neither to slide nor to roll out of their initial position. An analytical model is proposed, the equations of motion are derived, and they are solved numerically. The paper concludes that the addition of the slab makes the columns more stable. In fact, the system is almost equivalent to the response of a solitary column with the same aspect ratio yet larger size. However, it is also shown that the system is less stable than its planar counterpart and that planar analysis can only qualitatively describe the behavior of 3D structures. A case study shows that the concept could be used as a seismic isolation technique for bridges. However, more research need to be performed on defining proper intensity measures for uplifting structures, as it is shown that there is large record‐to‐record variability, even when intensity measures developed for rocking structures are used.

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“…Based on the assumptions presented in Section 3, the equations of motion of the system are

\begin{matrix} lefttrue \\ \ddot{θ} = - {\overset{p}{true}}^{2} (sin (α - θ) + cos (α - θ) (\frac{{\ddot{u}}_{g}}{g} cos φ + \frac{{\ddot{v}}_{g}}{g} sin φ)) + \\ + {\overset{φ}{true}}^{2} (\begin{matrix} left \\ sin θ {sin}^{2} α (4 γ + \frac{3}{2}) + cos α sin α (4 γ + 1) (1 + cos θ - 2 {cos}^{2} θ) + \\ sin θ cos θ (\frac{4}{3} {cos}^{2} α - \frac{5}{4} {sin}^{2} α + 4 γ ({cos}^{2} α - {sin}^{2} α)) \end{matrix}) \frac{12}{48 γ + 15 + {cos}^{2} a} \end{matrix}

\begin{matrix} lefttrue \\ (\begin{matrix} left \\ (\frac{4}{3} {cos}^{2} a - \frac{5}{4} {sin}^{2} α + 4 γ ({cos}^{2} α - {sin}^{2} α)) \cdot {sin}^{2} θ + \\ (3 + 8 γ) (1 - cos θ) {sin}^{2} α + 2 sin α cos α sin θ (1 + 4 γ) \cdot (1 - cos θ) \end{matrix}) \cdot \ddot{φ} + \\ + (\begin{matrix} left \\ (3 + 8 γ) {sin}^{2} α sin θ + (8) \end{matrix}) \end{matrix}

…”

Section: Description Of the Proposed 3d Modelmentioning

confidence: 99%

Seismic response of a wobbling 3D frame

Vassiliou

2017

Earthq Engng Struct Dyn

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“…They concluded that even though the 2D approximation is not conservative, 3D objects still present remarkable stability when excited dynamically. Rajah et al (2017) extended the 3D model of Vassiliou et al (2017b) to study the behavior of a slab supported on wobbling columns. As in the case of the planar rocking frame, the presence of the slab increases the stability of the system, even though it raises its center of mass.…”

Section: Rocking Piers Conceptmentioning

confidence: 99%

Comparative Assessment of Two Rocking Isolation Techniques for a Motorway Overpass Bridge

Agalianos

Psychari

Vassiliou

et al. 2017

Front. Built Environ.

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Rocking isolation of structures is evolving as an alternative design concept in earthquake engineering. The present paper investigates the seismic performance of an actual overpass bridge of the Attiki Odos motorway (Athens, Greece), employing two different concepts of rocking isolation: (a) rocking of the piers on the foundation (rocking piers); and (b) rocking of the pier and foundation assembly (rocking footings) on the soil. The examined bridge is an asymmetric 5-span system having a continuous deck and founded on surface foundations on a deep clay layer. The seismic performance of the two rocking-isolated bridges is comparatively assessed to the existing bridge, which is conventionally designed according to current seismic design codes. To that end, 3D numerical models of the bridge-foundation-abutment-soil system are developed, and both static pushover and non-linear dynamic time history analyses are performed. For the latter, an ensemble of 20 records (10 ground motions of 2 perpendicular components each) that exceed the design level are selected. The conventional system collapses in 5/10 of the (intentionally severe) examined seismic excitations. The rocking piers design alternative survives in 8/10 of the cases examined, with negligible residual deformations. The safety margins of the rocking footings design concept are even larger, as it survives in all cases examined. Both rocking isolation concepts are proven to offer increased levels of seismic resilience, reducing the probability of collapse and the degree of structural damage. Nevertheless, in the rocking piers design alternative high stress concentrations at the rotation pole (pier base) are developed, indicating the need for a special design of the pier ends. This is not the case for the rocking footings concept, which however is subject to increased residual settlements but no residual rotations.

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Dynamic Response of a Rigid Slab Supported by Four Rigid Cylinrical Rocking and Wobbling Columns

Abstract: Abstract. Letting columns uplift has been proposed as an earthquake response modification

Cited by 2 publications

References 44 publications

Seismic response of a wobbling 3D frame

Seismic response of a wobbling 3D frame

Comparative Assessment of Two Rocking Isolation Techniques for a Motorway Overpass Bridge

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