Minmao Liao

Nonlinear Finite-Element Analysis of Critical Gusset Plates in the I-35W Bridge in Minnesota

Reported evidence suggests that failure of gusset plates initiated the collapse of the I-35W Bridge in Minneapolis, Minnesota. The particular gusset plates were at a panel point designated as U10. Therefore, an analytical investigation was conducted on the condition of the U10 gusset plates at the time of bridge collapse. The forces delivered to panel point U10 were reproduced using available information of the bridge. These forces were introduced to detailed nonlinear three-dimensional finite-element models to calculate stress and strain states of the gusset plates. The results indicate that substantial portions of the U10 gusset plates were yielded at the time of collapse, confirming earlier findings from federal and state investigations. Weight increase due to past deck reconstruction and construction material and equipment staged on the day of collapse, along with insufficient thickness of the gusset plate, were identified as the main contributing factors to the substantial yielding. The results also suggest that the interaction of compression and shear played an important role in the gusset plate failure.

Computation of Coefficients of Crack-Tip Asymptotic Fields Using the Weak Form Quadrature Element Method

AbstractCoefficients of crack-tip asymptotic fields are computed using a recently developed weak form quadrature element method (QEM), combined with the subregion generalized variational principle. The variational description of a crack is established by dividing the domain into two regions, the potential energy region and the complementary energy region. Then the weak form QEM is employed to derive a system of algebraic equations. The coefficients are extracted directly from solving the equations. The accuracy, efficiency, and parameter sensitivity of the proposed method are discussed by solving a number of benchmark examples. The computed results are in very good agreement with available analytical or numerical results. The involved parameters can be adjusted according to convergence requirements. Thus, the method enjoys the advantages of straightforwardness and self-adaptivity.

Toward a Fracture Mechanics--Based Design Approach for Unbonded Concrete Overlay Pavements

AbstractAn illustrative fracture mechanics–based design paradigm is proposed for unbonded concrete overlays (UBCOs), an increasingly popular pavement rehabilitation system, with the ultimate goal of establishing a more rational design procedure than those currently available. To illustrate the advantages of the fracture mechanics–based approach to design, specific attention is paid to one type of failure associated with pavement structures, reflection cracking. The design formulas derived from the results of a large number of crack propagation simulations of both the UBCO composite and a reference single-layer new pavement quantify the dependence of the required overlay thickness and load-carrying capacity on all relevant material and geometric parameters. Preliminary comparisons of the results with field observations suggest that the fracture mechanics paradigm offers a promising procedure for improved design of UBCOs.

Application of a Weak Form Quadrature Element Method to Nonlinear Free Vibrations of Thin Rectangular Plates

Geometrically nonlinear free vibrations of thin rectangular plates are studied using the recently developed weak form quadrature element method (QEM). The nonlinear von Karman plate theory is employed to express the strain-displacement relations. The weak form description of the plate is formulated on the basis of the variational principle. The integrals involved in the variational description are evaluated by an efficient numerical integration scheme, and the partial derivatives at the integration points are approximated by differential quadrature analogs. A system of algebraic equations is eventually derived, and the nonlinear frequencies and mode shapes are extracted from solving the equations. The efficiency of the method is demonstrated by a convergence study. The accuracy of the method is illustrated by comparing the computed nonlinear to linear frequency ratios with those available in the literature. The influences of the nonlinearity on higher order frequencies and mode shapes are exhibited as well.

Analysis of Critical Gusset Plates in the Collapsed I-35W Bridge

Investigation led by the National Transportation Safety Board (NTSB) suggests that inadequate design of gusset plates played a key role in the collapse of the I-35W Bridge in Minneapolis, Minnesota. The particular gusset plate connection was at a panel point designated as U10. Further understanding of the behavior of the U10 gusset plates is essential. In the present study, the U10 gusset plates were analyzed using detailed nonlinear finite element models. The forces delivered to panel point U10 were reproduced using available information of the bridge. These forces were, in turn, used to calculate possible stress and strain states of the U10 gusset plates. The results indicate that substantial portions of the U10 gusset plates were yielded at the time of collapse. Weight increase due to deck reconstruction, staged construction materials, and thermal effects, along with insufficient strength of the gusset plate, seem to be the main contributing factors to the substantial yielding. The results also suggest that the interaction of large compression and large shear should be addressed. This interaction is not well understood.

A Mesh Adaptive Procedure for Large Increment Method

A posteriorih-version mesh adaptive procedure is presented in the framework of large increment method (LIM) for elastic problems. In this mesh adaptive strategy, the classical Zienkiewicz–Zhu (ZZ) error estimator is adopted and a first class h-adaptive mesh refinement procedure is implemented. A major advantage of the proposed mesh adaptive procedure is that the numerical results from the previous mesh can be utilized to obtain the initial solution for the new mesh. Two-dimensional (2D) examples show that this initial solution is much closer to the real solution than the minimum norm solution used in the original LIM and the revised method can converge faster than the original method.

A weak form quadrature element method for nonlinear free vibrations of Timoshenko beams

Purpose – The purpose of this paper is to highlight the implementation of a recently developed weak form quadrature element method for nonlinear free vibrations of Timoshenko beams subjected to three different boundary conditions. Design/methodology/approach – The design of the paper is based on considering the geometrically nonlinear effects of axial strain, bending curvature, and shear strain. Then the quadrature element formulation of the beam is introduced. Findings – The efficiency of the method is demonstrated by a convergence study. Ratios of the nonlinear fundamental frequencies to the corresponding linear frequencies are extracted. Their variations with the ratio of amplitude to radius of gyration and the slenderness ratio are examined. The effects of the nonlinearity on higher order frequencies and mode shapes are also investigated. Originality/value – The computed results show fast convergence and compare well with available literature results.