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Efficient beams on two-parameter elastic foundation finite elements have recently been developed. The stiffness matrix and nodal loud vector of these elements have been derived on the basis of the exact displacement function obtained from the solution of the governing differential equation. Most of the existing elements are, however, either limited to certain combinations of beam and foundation parameters, or provide only the solution of the homogeneous form of the governing equation. In this paper a new finite element is derived which eliminates these limitations. The stiffness matrix, nodal load vector and shape function of the clement are derived using the differential equation of a beam on a two-parameter elastic foundation. The complete solution of the equation corresponding to the most common types of load is also presented. This permits the determination of the deflections and internal forces anywhere along a simple or continuous beam on two-parameter foundations.
Membrane fouling and draw solution recycle are two important challenges faced by forward osmosis (FO) process in treating wastewater. In this study, we innovatively designed a corrugated TFC FO membrane(#FO-C) by conducting interfacial polymerization (IP) on a commercial corrugated polyvinylidene fluoride (PVDF) substrate and utilized fertilizer as the draw solution to treat emulsified oily wastewater for mitigating membrane fouling and recovering draw solution simultaneously. The corrugated-pattern membrane, #FO-C, had a similar separation performance compared with conventional flat TFC membrane (#FO-F), demonstrating that the corrugated pattern makes a little difference on IP process. Inspiringly, compared with #FO-F, #FO-C tested at parallel and vertical modes exhibited lower decrease of water flux in oily wastewater treatment when used 1 M (NH4)2SO4 (SOA) and three different types of oily wastewater (prepared by neutral and negatively/positively charged surfactants) as draw and feed solutions, respectively. In addition, the declined permeability of #FO-C could easily recover with performing surfactant cleaning and osmosis backwashing, which that of #FO-F only recovered partially. The result of computational fluid dynamics (CFD) simulation illustrated that the corrugated pattern of #FO-C would bring about vortex and higher shear stresses, which effectively alleviate the foulant deposition of on the membrane surface. Moreover, the diluted fertilizer draw solution was utilized to irrigate the plants directly and presented a promising result, readily achieving the recovering of draw solution. This work provides a promising strategy for meeting the challenges in FO process, having an important reference value. Graphical abstract
Premature debonding of externally bonded FRP laminate from retrofitted reinforced concrete (RC) members can lead to inefficient use of FRP and can limit the level of strength increase that can be achieved. In this investigation, π-CFRP anchors are used in an attempt to delay the onset of premature debonding and to achieve higher strength in beams retrofitted with a 1.2 mm thick and 50 mm wide CFRP laminate. This investigation consisted of testing six large scale T-beams with a 4500 mm span, 400 mm height and 500 mm flange width under four-point bending. Two beams were tested without retrofit as control beams, one beam with the laminate epoxy bonded to the beam and the remaining three beams with the laminate epoxy bonded and anchored using CFRP π-anchors. One of the beams with 30 anchors exhibited a 46% increase in the debonding load over the beam without anchors while the laminate attained a maximum strain equal to 80% of its ultimate strain capacity, a 94% increase compared to the maximum strain reached in the companion beam strengthened with only the epoxy bonded laminate. The displacement ductility ratio of the latter beam at debonding exceeded 4. The results demonstrate the π-anchoring system effectiveness and a feasible way for efficiently utilizing strong and thick laminates in strengthening RC members.
A hybrid reinforcement system is proposed which consists of a low modulus polymeric reinforcement combined with CFRP, and which is believed to overcome the lack of ductility in FRP reinforced concrete members. Three 4.2 m long and 400 mm deep, high strength concrete inverted T-beams were designed using this new concept and were tested under four point bending. Two of the beams contained hybrid reinforcement while the third contained only CFRP reinforcement (control beam). The control beam failed suddenly, following the rupture of the CFRP reinforcement. The beams with hybrid reinforcement failed in a ductile manner at 63% higher load and they had at least three times more deflection at failure than the control beam. In the later beams, deflections substantially increased following the rupture of CFRP, but the moment of resistance of the beams decreased marginally. Upon release of the load, the hybrid reinforced beams rebounded and had very little deflection under self-weight.
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This paper presents detailed analysis of the results of field tests on 13 full scale wide flange steel beams subjected to blast loads generated by the detonation of up to 250kg of ANFO explosive. The experimental results are analyzed using an equivalent Single-Degree-of-Freedom (SDOF) model of a beam, which includes material nonlinearity and strain rate effects. To account for strain rate effect on beam stiffness and strength, its full moment-curvature response is determined by dividing its cross-section into a number of layers and a strain rate-dependent stress-strain relationship, based on the Cowper–Symonds strain rate model, is used to capture the nonlinear stress distribution over the section. To determine the effects of higher modes of vibration and the variation of beam mechanical properties along its length on its dynamic response, the test beams are also analyzed using a Multi-Degree-of-Freedom (MDOF) model involving beam finite elements. Each element has two nodes and three degrees of freedom and is again divided into a number of layers to capture the strain rate effect and nonlinear stress distribution over its depth. The predicted displacements and strains by the two models are compared with the corresponding experimental data and the results show that for the given beams, the time-dependant deformations, internal forces, and moments can be adequately predicted by either model because the first mode of vibration is found to dominate their response; however, the use of a constant strain rate through the so-called Dynamic Increase Factor (DIF) can lead to highly conservative estimate of the actual strength of such members.
The authors are to be congratulated for their comprehensive research work on the use of RCA as aggregate in structural grade concrete [1], but some of their conclusions with regard to the effect of aggregate type and RCA content on the fresh and hardened properties of concrete made with coarse RCA, termed RAC for brevity, need discussion.
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Advanced composite materials, also known as fibre reinforced plastics or polymers (FRP), are providing the construction industry with new materials for the construction of new buildings and bridges or for the repair of existing ones. The FRP currently used in construction comprise high strength fibres of glass, aramid and/or carbon, embedded in thermoset polymer matrices, such as epoxy, polyester and vinylester. While the high strength, corrosion resistance and light weight of FRP make them highly attractive construction materials, they also pose new challenges to the structural engineering and construction industry which must be overcome before FRP becomes a routine construction material. This paper examines both the opportunities and the challenges that material producers, structural designers and the construction industry in general must countenance before FRP can become a true alternative to steel, concrete and other traditional construction materials.
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The rigid‐ice model of frost heave is one of the most comprehensive frost‐heave models but is restricted to one‐dimensional cases in its present form. In this paper, the model is extended to two‐dimensional problems. The complete formulation of the partial differential equations governing heat, moisture and ice transport in freezing soils is provided. The equations are subsequently solved using the Galerkin finite element method in space and the finite difference method in time. A computer program is developed for the two‐dimensional rigid‐ice model. A case of freezing around chilled gas pipeline is solved and the numerical results are compared with experimental values, with good agreement between the two sets of results.
One-seventh scale direct models of single-cell and two-cell prestressed concrete box girder bridges, tested to destruction at McGill University, are analyzed by the nonlinear finite element technique. The nonlinear program NONLACS, utilized in the analysis, is described in detail together with the material models employed. The objective of the current study is to demonstrate the capabilities of the finite element program NONLACS in predicting the ultimate strength and complete response of prestressed concrete box girder bridges at all stages of loading up to the ultimate load. The load–deflection curves, concrete and steel stresses, and deflected shapes of the bridges at different load levels are compared with the corresponding experimental data. The results verify the applicability of the nonlinear finite element method as an economical and expedient alternative, in some cases, to expensive experimental work aimed at the investigation of the complete response of complex structures to applied loads. Key words: box girder bridges, concrete, concrete and steel strains, experimental data, finite element, load–deflection characteristics, nonlinear analysis, prestressing.
