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The unrestrained torsional analysis of bars is an important theme in elasticity theory, first solved by Saint-Venant using semi-inverse methods. It has been considered and solved by several others using analytical methods and numerical procedures due to the importance in the design of machine parts under torsional moments. In this paper, the Saint Venant torsion problem is solved for rectangular prismatic bars using Galerkin-Kantorovich variational method (GKVM). The work presents a detailed theoretical framework of the problem, deriving using first principles considerations the stress compatibility equation in terms of the Prandtl stress function ϕ(x, y). The derived domain equation which is required to be satisfied over the rectangular cross-sectional domain is a partial differential equation of the Poisson type. GKVM is adopted as the solution method for finding the solution to the domain equation. The unknown Prandtl stress function ϕ(x, y) is assumed, following Kantorovich method to be a product of an unknown function for f(x) sought to minimize the Galerkin-Kantorovich variational functional (integral) (GKVF) and a known function (y2 - n2) which satisfies the boundary conditions at all boundary points in the y-direction, that is, at y = ±b. The resulting GKVF is a simplified functional whose integral is a second order inhomogeneous ordinary differential equation (ODE) in f(x). The integrand is solved to find f(x) leading in a full determination of the Prandtl stress function. The expression for stresses, torsional moments and torsional parameters are then found and they satisfy the boundary conditions and the domain equation. The results for the torsional moments and torsional parameters are identical to previous results obtained using double finite sine transform method (DFSTM), and analytical methods. The merit of GKVM is that it has led to the exact solution of the unrestrained torsion problems. [ABSTRACT FROM AUTHOR]

Conventional reinforced concrete shear walls are vulnerable to strong earthquakes with significant residual deformations, which substantially affect structural service and can even lead to structural collapse. Superelastic shape memory alloys (SMAs) are advanced materials that can realize strain recovery upon unloading. If SMAs can be used as reinforcing bars in structures, they can undergo large deformation without permanent deformation. This study presents a complementary and synergistic material system that integrates SMA with damage-tolerant engineered cementitious composites (ECCs) to minimize residual displacement and mitigate concrete damage. This study explored the seismic performance of shear walls using SMA and ECC in the plastic hinge region. Reverse cyclic loading tests were performed on four specimens to demonstrate the feasibility of this method. The specimens included a conventional steel-reinforced concrete shear wall (SW-R-C), steel-reinforced ECC shear wall (SW-R-ECC), SMA-reinforced concrete shear wall (SW-SMA-C), and SMA-reinforced ECC shear wall (SW-SMA-ECC). The results show that the SW-SMA-C specimen exhibited remarkable self-centering capability of more than 85% even after a large deformation, compared to SW-R-C. Furthermore, reduced damage and better ductility were observed in the SW-SMA-ECC specimen in addition to reduced residual displacement. The proposed approach indicated that SMA combined with ECC is more effective in mitigating plastic hinge damage and minimizing residual displacements, which could improve the seismic performance of shear walls. [ABSTRACT FROM AUTHOR]

Strongly weathered phyllite is a metamorphic soft rock widely distributed in the central and western regions of China. Due to its inadequate engineering properties, the direct use of this material as a roadbed filler is not feasible and requires improvement. In this paper, calcium acetate Ca(CH 3 COO) 2 , magnesium acetate Mg(CH 3 COO) 2 and calcium chloride CaCl 2 are prepared to improve the filler by microbially induced carbonate precipitation (MICP). The effects of different calcium and magnesium sources on porosity, water absorption, uniaxial compressive strength, crack propagation time and failure patterns are investigated. The results show that CaCl 2 and Ca(CH 3 COO) 2 exhibit the most significant enhancement effect in reducing porosity and water absorption, increasing the uniaxial compressive strength by over 30%, delaying the time of failure occurrence and reducing the number of tensile cracks significantly. X-ray diffraction (XRD), scanning electron microscopy (SEM) and pore size distribution analyses reveal disparities among the rock samples. CaCl 2 and Ca(CH 3 COO) 2 have greater efficacy than Mg(CH 3 COO) 2 in terms of improvement, as they generate relatively many carbonate precipitates to bind the phyllite filler and reduce the size and quantity of pores. To avoid the corrosion of Cl- ions when adding reinforcement bars in actual engineering, Ca(CH 3 COO) 2 is an ideal calcium source for improving the strongly weathered phyllite filler. • The physical and mechanical properties of strongly weathered phyllite filler can be improved after modification. • The physical properties and strength of modified sample have a relationship with carbonate content and crystal morphology. • Calcium acetate is suggested for use as the calcium source to improve the strongly weathered phyllite filler. [ABSTRACT FROM AUTHOR]