Michael J. Tait

Parametric Study on the Response of Stable Unbonded-Fiber Reinforced Elastomeric Isolators (SU-FREIs)

Tests on stable unbonded (SU) square carbon fiber-reinforced elastomeric isolator (FREI) bearings were conducted to investigate their lateral and vertical response. The bearings are intended for seismic isolation of low-rise buildings including those of ordinary importance. To simulate the in-place application of SU-FREI bearings, the contact surfaces of the bearings were not bonded to the platens of the test machine. This unbonded application permitted stable rollover deformation to occur which enhances the bearings isolation efficiency. The bearings were shown to safely sustain large lateral displacements. When subjected to large lateral displacements, their originally vertical faces completely contacted the horizontal surfaces of the upper and lower platens, which created a stiffening response and ensured the stability of these very large displacements. The sensitivity of SU-FREI bearings to lateral displacement history and vertical pressure applied on the bearings were investigated. Regarding the latter parameter, it was found that the effect of variations in vertical pressure on the lateral response can be neglected when the SU-FREI bearings are subjected to relatively light vertical pressures such as considered for low-rise buildings.

Stability of fiber-reinforced elastomeric bearings in an unbonded application

Stable unbonded fiber-reinforced elastomeric isolators (SU-FREIs) are a viable device for seismic mitigation purposes in low-rise structures. SU-FREI bearings consist of alternating layers of elastomer and fiber fabric with shape factor and aspect ratio such that stable rollover occurs during lateral displacement. This study investigates the stability of SU-FREI bearings through experimental testing. Two experimental test procedures are employed. The first investigates stability during incrementally increasing axial loads under lateral cyclic excitation, and the second investigates the ultimate shear properties of SU-FREI bearings through monotonic lateral displacement under design axial load. Dynamic stability testing reveals that the tested SU-FREIs remain stable at axial loads significantly greater than the design load under a wide range of cyclic lateral displacement amplitudes. In addition, an increase in axial load results in lower effective stiffness and greater effective damping in the SU-FREI bearings. Although rollout instability was not encountered during ultimate shear property testing, shear tests provide insight into the stiffening effect encountered as the originally vertical faces of the SU-FREI bearings make contact with the top and bottom contact supports.

Theoretical Modeling of TLD With Different Tank Geometries Using Linear Long Wave Theory

This study focuses on the modeling of tuned liquid dampers (TLDs) with triangular-bottom, sloped-bottom, parabolic-bottom, and flat-bottom tanks using the linear long wave theory. The energy dissipated by damping screens is modeled theoretically utilizing the method of virtual work. In this proposed model, only the fundamental sloshing mode is considered, and the assumption of small free surface fluid response amplitude is made. Subsequently, the equivalent mechanical properties including effective mass, natural frequency, and damping ratio of the TLDs, having different tank geometries, are compared. It is found that the normalized effective mass ratio values for a parabolic-bottom tank and a sloped-bottom tank with a sloping angle of 20 deg are larger than the normalized effective mass ratio values for triangular-bottom and flat-bottom tanks. An increase in the normalized effective mass ratio indicates that a greater portion of the water inside the tank participates in the sloshing motion. The derived equivalent mechanical models for the TLD tank geometries considered in this study can be used for the preliminary design of structural-TLD systems.

Experimental Performance of Steel Beams under Blast Loading

In this study, the dynamic response of typical wide-flange steel beams was experimentally evaluated under blast loading. A total of 13 beams were field tested using live explosives, where the charge size ranged from 50 to 250 kg of ammonium nitrate-fuel oil mixture, and the ground stand-off distance was from 7.0 to 10.3 m. Blast wave characteristics, including incident and reflected pressures, were recorded. In addition, time-dependent displacements, accelerations, and strains at different locations along the steel members were measured, and the postblast damage and mode of failure of the test specimens were observed. The blast load characteristics were compared with those obtained using the Technical Manual UFC 3-340-02 results. The displacement response results were used to validate the results obtained from a nonlinear dynamic analysis based on a single degree-of-freedom (SDOF) model. Results showed that the UFC 3-340-02 pressure predictions compare reasonably well with the measured pressure in the positive phase in terms of both the peak pressure and overall time variations. The SDOF model predicted the maximum displacements of beams in the elastic range reasonably well, but it overestimated them in the plastic range.

Performance Enhancement of Steel Columns Using Concrete-Filled Composite Jackets

This paper studies the cross-sectional behavior of steel columns strengthened with fiber-reinforced polymers (FRPs). The composite column is constructed by wrapping the steel I-section column with epoxy-saturated glass- and carbon-FRPs (GFRP and CFRP) sheets in the transverse direction and subsequently filling the voids between the FRP and the steel with concrete. Experimental tests were performed on stub columns under axial compression including one to three CFRP wraps. A corner treatment technique, to avoid stress concentration at the corners and to improve confinement efficiency, was also investigated. A simplified analytical model was developed to predict the axial behavior of the composite columns. Experimental results showed significant enhancement in the behavior of the composite columns primarily attributable to the confinement mechanism imposed by the FRP jacket and concrete. Increasing the corner radius resulted in higher compressive strength of the confined concrete and ultimate axial strain of the composite columns. Good agreement between the analytically developed axial load-displacement relationships and the test data indicates that the model can closely simulate the cross-sectional behavior of the composite columns.

Simplified analysis of a low-rise building seismically isolated with stable unbonded fiber reinforced elastomeric isolators

The seismic response of an ordinary low-rise base isolated (BI) structure, employing stable unbonded-fiber reinforced elastomeric isolator (SU-FREI) bearings, is predicted by using two different simplified analytical models. Subsequently, the accuracy of the two models is evaluated by using measured test results from a shake table study. Two models simulate the nonlinear experimental lateral load–displacement hysteresis loops of these bearings. The experimental hysteresis loops were obtained from cyclic shear tests on prototype bearings under a constant compression load. Because of the nonlinear lateral response behavior of the SU-FREIs, these models are employed in an iterative time-history analysis approach, enabling the model variables and the calculated peak lateral displacement of the bearings to converge to their unique values. Analysis results show that the presented simplified models may be used effectively in seismic response prediction of ordinary low-rise buildings that are seismically isolated...

On coupon colorings of graphs

Abstract Let G be a graph with no isolated vertices. A k -coupon coloring of G is an assignment of colors from [ k ] ≔ { 1 , 2 , … , k } to the vertices of G such that the neighborhood of every vertex of G contains vertices of all colors from [ k ] . The maximum k for which a k -coupon coloring exists is called the coupon coloring number of G , and is denoted χ c ( G ) . In this paper, we prove that every d -regular graph G has χ c ( G ) ≥ ( 1 − o ( 1 ) ) d / log d as d → ∞ , and the proportion of d -regular graphs G for which χ c ( G ) ≤ ( 1 + o ( 1 ) ) d / log d tends to 1 as | V ( G ) | → ∞ . An injective k -coloring of a graph G is an assignment of colors from [ k ] to the vertices of G such that no two vertices joined by a path of length two in G have the same color. The minimum k for which such a coloring exists is called the injective coloring number of G , denoted χ i ( G ) . In this paper, we also discuss injective colorings of Hamming graphs.

Equivalent Linearized Mechanical Model for Tuned Liquid Dampers of Arbitrary Tank Shape

This paper presents a model to describe the behavior of sloshing in a general tank with a uniform fluid depth. An equivalent linearized mechanical model is developed for a tuned liquid damper (TLD) with arbitrary tank geometry. The finite element method is employed to determine the mode shapes of the sloshing fluid. In general, the mode shapes of arbitrary tanks will have response components in the x- and y-directions. The mode shapes enable the generalized properties of the sloshing fluid to be determined; these properties are subsequently used to establish equivalent mechanical properties. The nonlinear damping of slat-type damping screens is linearized, permitting it to be included in the model as amplitude-dependent viscous damping. The proposed model is in excellent agreement with existing linearized models for the special cases of rectangular and circular tanks. Sinusoidal shake table tests are conducted on tanks with chamfers placed in selected corners. In the literature, no experimental testing has focused on tanks of arbitrary shape with a constant fluid depth. The proposed model is in good agreement with the experimental results for the mode dominated by motion in the direction of excitation. However, the model is found to underestimate the response of the mode which is dominated by motion perpendicular to the excitation direction. The linearized mechanical model developed can serve as a useful preliminary TLD design tool.

Equivalent mechanical models of tuned liquid dampers with different tank geometries

This paper focuses on the development of equivalent mechanical models for tuned liquid dampers (TLDs) with rectangular, vertical-cylindrical, horizontal-cylindrical, and hyperboloid (conical) tank shapes under external excitation in the transverse direction. Potential flow theory is utilized to obtain the free-surface response amplitude and the corresponding velocity of the sloshing liquid and Lagrange’s equations are used to determine the generalized properties. Morison’s equation and the virtual work method are used to estimate an equivalent viscous damping ratio based on the screen loss coefficient. The equivalent mechanical properties derived in this paper model the fundamental sloshing mode only and are restricted to small response amplitudes. Subsequently, the equivalent mechanical properties including effective mass, natural frequency, and damping ratio of the TLDs, having different tank geometries, are compared. It is found that the effective mass values for horizontal-cylindrical and hyperboloid ...

Variations on a theme of Graham and Pollak

Abstract Graham and Pollak proved that one needs at least n − 1 complete bipartite subgraphs (bicliques) to partition the edge set of the complete graph on n vertices. In this paper, we study the generalizations of their result to coverings of graphs with specified multiplicities and to complete uniform hypergraphs. We also discuss the recently disproved Alon–Saks–Seymour Conjecture (which proposed a generalization of the previous result of Graham and Pollak) and compute the exact values of the ranks of the adjacency matrices of the known counterexamples to the Alon–Saks–Seymour Conjecture. The rank of the adjacency matrix of a graph G is related to important problems in computational complexity and provides a non-trivial lower bound for the minimum number of bicliques that partition the edge set of G .