SUMMARYRecent advances in the literature regularize the strain-softening response of force-based frame elements by either modifying the constitutive parameters or scaling selected integration weights. Although the former case maintains numerical accuracy for strain-hardening behavior, the regularization requires a tight coupling of the element constitutive properties and the numerical integration method. In the latter case, objectivity is maintained for strain-softening problems; however, there is a lack of convergence for strain-hardening response. To resolve the dichotomy between strain-hardening and strain-softening solutions, a numerically consistent regularization technique is developed for force-based frame elements using interpolatory quadrature with two integration points of prescribed characteristic lengths at the element ends. Owing to manipulation of the integration weights at the element ends, the solution of a Vandermonde system of equations ensures numerical accuracy in the linear-elastic range of response. Comparison of closed-form solutions and published experimental results of reinforced concrete columns demonstrates the effect of the regularization approach on simulating the response of structural members.

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SUMMARYRecent literature shows the choice of an integration method in the state determination of force-based frame finite elements has a significant influence on the computed element response. To assess the modeling uncertainty associated with integration methods in force-based elements, analytical sensitivity of onedimensional interpolatory quadrature is developed via direct differentiation of the governing Vandermonde equations. Comparisons with finite difference calculations show that the combination of the Vandermonde equation sensitivity with equations that govern force-based element response sensitivity leads to an accurate approach to stand-alone response sensitivity analysis. Consistent with previous findings for material, load, and geometric parameters in finite element response sensitivity analysis, sensitivity with respect to parameters associated with the integration method in force-based elements improves the efficiency of gradient-based algorithms where the locations and/or weights of the integration method are treated as uncertain random variables.

Bridges are usually designed and evaluated on the basis of member strength and serviceability criteria; however, they are expected to have sufficient levels of reserve strength and multiple paths to resist collapse should any of their members get damaged or exceed their nominal strength capacity. The ability of a structural system to redistribute the load around damaged members is referred to as structural redundancy. To account for bridge redundancy during the design and safety evaluation process, the AASHTO load and resistance factor design and load and resistance factor rating provide a preliminary set of load modifiers or system factors, most of which were developed based on the code writer’s judgment and experience. This paper evaluated the redundancy of prestressed concrete box girder bridges under vertical loads and lateral loads. Pushover and pushdown analyses were performed by using frame and grillage models in SAP2000. The grillage models were validated by more advanced finite element models built in ABAQUS. The effects of different damage scenarios and types of connections between the box girder and columns on the structural redundancy level were investigated. On the basis of those results, a set of system factors for prestressed concrete box bridges accounting for the system redundancy is proposed. The proposed system factors can be used during the design and safety assessment of prestressed concrete box girder bridges subjected to transient lateral load and vertical vehicle load.