Performance Evaluation of a Prestressed Belitic Calcium Sulfoaluminate Cement (BCSA) Concrete Bridge Girder

Belitic calcium sulfoaluminate (BCSA) cement is a sustainable alternative to Portland cement that offers rapid setting characteristics that could accelerate throughput in precast concrete operations. BCSA cements have lower carbon footprint, embodied energy, and natural resource consumption than Portland cement. However, these benefits are not often utilized in structural members due to lack of specifications and perceived logistical challenges. This paper evaluates the performance of a full-scale precast, prestressed voided deck slab bridge girder made with BCSA cement concrete. The rapid-set properties of BCSA cement allowed the initial concrete compressive strength to reach the required 4300 psi release strength at 6.5 h after casting. Prestress losses were monitored long-term using vibrating wire strain gages cast into the concrete at the level of the prestressing strands and the data were compared to the American Association of State Highway and Transportation Officials Load and Resistance Factor Design (AASHTO LRFD) predicted prestress losses. AASHTO methods for prestress loss calculation were overestimated compared to the vibrating wire strain gage data. Material testing was performed to quantify material properties including compressive strength, tensile strength, static and dynamic elastic modulus, creep, and drying and autogenous shrinkage. The material testing results were compared to AASHTO predictions for creep and shrinkage losses. The bridge girder was tested at mid-span and at a distance of 1.25 times the depth of the beam (1.25d) from the face of the support until failure. Mid-span testing consisted of a crack reopening test to solve for the effective prestress in the girder and a flexural test until failure. The crack reopen effective prestress was compared to the AASHTO prediction and AASHTO appeared to be effective in predicting losses based on the crack reopen data. The mid-span failure was a shear failure, well predicted by AASHTO LRFD. The 1.25d test resulted in a bond failure, but nearly developed based on a moment curvature estimate indicating the AASHTO bond model was conservative.

Curvature estimates for stable free boundary minimal hypersurfaces

In this paper, we prove uniform curvature estimates for immersed stable free boundary minimal hypersurfaces satisfying a uniform area bound, which generalize the celebrated Schoen–Simon–Yau interior curvature estimates up to the free boundary. Our curvature estimates imply a smooth compactness theorem which is an essential ingredient in the min-max theory of free boundary minimal hypersurfaces developed by the last two authors. We also prove a monotonicity formula for free boundary minimal submanifolds in Riemannian manifolds for any dimension and codimension. For 3-manifolds with boundary, we prove a stronger curvature estimate for properly embedded stable free boundary minimal surfaces without a-priori area bound. This generalizes Schoen’s interior curvature estimates to the free boundary setting. Our proof uses the theory of minimal laminations developed by Colding and Minicozzi.

Properly embedded minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$

We prove that every properly embedded minimal annulus in $\mathbb{S}^2\times\mathbb{R}$ is foliated by circles. We show that such minimal annuli are given by periodic harmonic maps $\mathbb{C} \to \mathbb{S}^2$ of finite type. Such harmonic maps are parameterized by spectral data, and we show that continuous deformations of the spectral data preserve the embeddedness of the corresponding annuli. A curvature estimate of Meeks and Rosenberg is used to show that each connected component of spectral data of embedded minimal annuli contains a maximum of the flux of the third coordinate. A classification of these maxima allows us to identify the spectral data of properly embedded minimal annuli with the spectral data of minimal annuli foliated by circles.

Optimal Control

Chapter 8 focuses on nonlinear optimal control and its applications. The chapter begins by introducing the fundamentals of optimal control and prototypical problem formulations. This is followed by the treatment of first-order necessary conditions including the Pontryagin minimum principle, dynamic programming, and the Hamilton–Jacobi–Bellman equation. Singular arcs and bang–bang controls are relevant in the solution of many minimum-time and minimum-fuel problems and so these issues are discussed with the help of examples that have been worked out in detail.This chapter then turns towards direct and indirect numericalmethods suitable for solving large-scale optimal control problems numerically.The chapter concludes with an example relating to the calculation of an optimal track curvature estimate from global positioning system (GPS) data.