This work is aimed at studying the strengthening of reinforced concrete (R. C.) beams using prestressed glass fi- ber-reinforced polymer (PGFRP). Carbon fiber-reinforced polymer (CFRP) has recently become popular for ...This work is aimed at studying the strengthening of reinforced concrete (R. C.) beams using prestressed glass fi- ber-reinforced polymer (PGFRP). Carbon fiber-reinforced polymer (CFRP) has recently become popular for use as repair or rehabilitation material for deteriorated R. C. structures, but because CFRP material is very stiff, the difference in CFRP sheet and concrete material properties is not favorable for transferring the prestress from CFRP sheets to R. C. members. Glass fi- ber-reinforced polymer (GFRP) sheets with Modulus of Elasticity quite close to that of concrete was chosen in this study. The load-carrying capacities (ultimate loads) and the deflections of strengthened R. C. beams using GFRP and PGFRP sheets were tested and compared. T- and ⊥-shaped beams were used as the under-strengthened and over-strengthened beams. The GFRP sheets were prestressed to one-half their tensile capacities before being bonded to the T- and ⊥-shaped R. C. beams. The prestressed tension in the PGFRP sheets caused cambers in the R. C. beams without cracks on the tensile faces. The PGFRP sheets also enhanced the load-carrying capacity. The test results indicated that T-shaped beams with GFRP sheets increased in load-carrying capacity by 55% while the same beams with PGFRP sheets could increase load-carrying capacity by 100%. The ⊥-shaped beams with GFRP sheets could increase load-carrying capacity by 97% while the same beams with PGFRP sheets could increase the loading-carrying capacity by 117%. Under the same external loads, beams with GFRP sheets underwent larger deflections than beams with PGFRP sheets. While GFRP sheets strengthen R. C. beams, PGFRP sheets decrease the beams’ ductility, especially for the over-strengthened beams (⊥-shaped beams).展开更多
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej′er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0〈p≤1/2.
A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the founda...A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.展开更多
Let （Ω, F, P） be a probability space and L0（F,R） the algebra of equivalence classes of real- valued random variables on （Ω, F, P）. When L0（F,R） is endowed with the topology of convergence in probability, we ...Let （Ω, F, P） be a probability space and L0（F,R） the algebra of equivalence classes of real- valued random variables on （Ω, F, P）. When L0（F,R） is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0（F, R） to L0（F,R）. As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module （S, ｜｜·｜｜） is random uniformly convex iff LP（S） is uniformly convex for each fixed positive number p such that 1 〈 p 〈 ＋∞.展开更多
基金Supported by the Science Research Foundations for the Doctoral Program of Guilin University of Electronic Technology under Grant(UF09007Y)the Guangxi Natural Science Foundations under Grant(2010GXNSB013049)the National Natural Science Foundations under Grant(11101100,71001015)
文摘This work is aimed at studying the strengthening of reinforced concrete (R. C.) beams using prestressed glass fi- ber-reinforced polymer (PGFRP). Carbon fiber-reinforced polymer (CFRP) has recently become popular for use as repair or rehabilitation material for deteriorated R. C. structures, but because CFRP material is very stiff, the difference in CFRP sheet and concrete material properties is not favorable for transferring the prestress from CFRP sheets to R. C. members. Glass fi- ber-reinforced polymer (GFRP) sheets with Modulus of Elasticity quite close to that of concrete was chosen in this study. The load-carrying capacities (ultimate loads) and the deflections of strengthened R. C. beams using GFRP and PGFRP sheets were tested and compared. T- and ⊥-shaped beams were used as the under-strengthened and over-strengthened beams. The GFRP sheets were prestressed to one-half their tensile capacities before being bonded to the T- and ⊥-shaped R. C. beams. The prestressed tension in the PGFRP sheets caused cambers in the R. C. beams without cracks on the tensile faces. The PGFRP sheets also enhanced the load-carrying capacity. The test results indicated that T-shaped beams with GFRP sheets increased in load-carrying capacity by 55% while the same beams with PGFRP sheets could increase load-carrying capacity by 100%. The ⊥-shaped beams with GFRP sheets could increase load-carrying capacity by 97% while the same beams with PGFRP sheets could increase the loading-carrying capacity by 117%. Under the same external loads, beams with GFRP sheets underwent larger deflections than beams with PGFRP sheets. While GFRP sheets strengthen R. C. beams, PGFRP sheets decrease the beams’ ductility, especially for the over-strengthened beams (⊥-shaped beams).
基金supported by Shota Rustaveli National Science Foundation grant no.13/06(Geometry of function spaces,interpolation and embedding theorems)
文摘The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej′er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0〈p≤1/2.
文摘A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.
基金Supported by National Natural Science Foundation of China (Grant No. 10871016)
文摘Let （Ω, F, P） be a probability space and L0（F,R） the algebra of equivalence classes of real- valued random variables on （Ω, F, P）. When L0（F,R） is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0（F, R） to L0（F,R）. As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module （S, ｜｜·｜｜） is random uniformly convex iff LP（S） is uniformly convex for each fixed positive number p such that 1 〈 p 〈 ＋∞.
