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显色剂加入方式及结果计算方法对土壤磷酸酶测定结果的影响 被引量:4
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作者 贝美容 罗雪华 杨红竹 《热带农业科学》 2015年第1期62-66,共5页
为探讨有色显色剂的加液方式及加入量对显色后溶液吸收值的影响、标准曲线的绘制及结果计算方法对土壤磷酸酶测定值的影响,取广东橡胶园0~20 cm土样为材料,以磷酸苯二钠为基质,酶解土壤释放出酚,与显色剂氯代二溴对苯醌亚胺反应,以标准... 为探讨有色显色剂的加液方式及加入量对显色后溶液吸收值的影响、标准曲线的绘制及结果计算方法对土壤磷酸酶测定值的影响,取广东橡胶园0~20 cm土样为材料,以磷酸苯二钠为基质,酶解土壤释放出酚,与显色剂氯代二溴对苯醌亚胺反应,以标准曲线法求出样品测试液的酚浓度,比较以不同加液方式加入不同量的显色剂对溶液吸收值的影响,同时比较用直线或一元二次曲线等两种标准曲线回归方程对样品测试液酚浓度的影响。结果表明:以胶头滴管滴加或以移液枪用多次重复使用过的吸嘴加入显色剂,显色后溶液吸收值变异系数达3.33%~6.44%,而以活塞式定量加液器加入,其变异系数在1.28%以下,且随着加入量增大变异系数降低至0.51%,重现性好;当配制的标准曲线浓度范围较宽且相应吸收值较高(接近0.9),以曲线法求得的标准曲线回归方程决定系数(R2=0.999 8)大于直线回归的(R2=0.999 7),且曲线法求出的土壤无基质对照及试剂空白酚浓度比直线法更有实际意义。 展开更多
关键词 土壤磷酸酶 显色剂 定量加液器 标准曲线 结果计算
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畜禽产品兽药残留检测结果计算时需要注意的几个问题 被引量:1
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作者 杨修镇 杨林 +2 位作者 徐恩民 赵丰华 杨智国 《山东畜牧兽医》 2022年第1期33-35,共3页
畜禽产品兽药残留检测结果计算和表述方式的选择,对出具正确的检测结论有重大影响。本文简要介绍了检测结果计算和表述的类型特点,探讨了通过标准曲线进行适当加权、选择浓度接近的标样进行单点校准等方式来降低计算结果出现偏离的风险... 畜禽产品兽药残留检测结果计算和表述方式的选择,对出具正确的检测结论有重大影响。本文简要介绍了检测结果计算和表述的类型特点,探讨了通过标准曲线进行适当加权、选择浓度接近的标样进行单点校准等方式来降低计算结果出现偏离的风险,为相关人员和初学者提供参考。 展开更多
关键词 畜禽产品 兽药残留 结果计算
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关于稻谷不完善粒检验和结果计算方法的探讨
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作者 关福臣 高煜昌 《黑龙江粮食》 2014年第11期49-52,共4页
文章依据《GB5494》标准对稻谷脱壳后糙米中不完善粒检验结果计算。通过对稻谷与非假果类粮食的组成不同;稻谷与非假果类粮食检验方式有所不同;净稻谷糙米率与其中不完善粒稻谷糙米率不同;不完善粒稻谷中每个单项糙米率不同进行讨论分析... 文章依据《GB5494》标准对稻谷脱壳后糙米中不完善粒检验结果计算。通过对稻谷与非假果类粮食的组成不同;稻谷与非假果类粮食检验方式有所不同;净稻谷糙米率与其中不完善粒稻谷糙米率不同;不完善粒稻谷中每个单项糙米率不同进行讨论分析,提出了关于完善《GB5494》中稻谷不完善粒检验方法和结果计算建议。 展开更多
关键词 稻谷 不完善粒检验 结果计算
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国有资本保值增值结果计算与确认办法
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《财会月刊(合订本)》 2000年第14期C006-C007,共2页
第一章 总则 第一条 为加强国有资本监督管理,维护国家所有者权益,提高国有资本营运效益,规范国有资本保值增值考核工作,制定本办法。 第二条 国有资本保值增值结果计算与确认,是指国有资本的出资人或政府有关部门根据企业年度会计报表... 第一章 总则 第一条 为加强国有资本监督管理,维护国家所有者权益,提高国有资本营运效益,规范国有资本保值增值考核工作,制定本办法。 第二条 国有资本保值增值结果计算与确认,是指国有资本的出资人或政府有关部门根据企业年度会计报表资料,依法对列入考核范围的国家投资企业在一定经营期间所占有、使用的国有资本增值、保值或减值结果进行核实确认,并运用规定的方法分析判断国有资本运营效益及其所处行业水平,为实施企业考核工作提供准确的依据。 展开更多
关键词 国有资本 保值增值 结果计算 确认办法 考核指标
全文增补中
理论法与标准法计算环境介质中^(90)Sr检测结果比对
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作者 王瑞俊 段媛媛 +2 位作者 李周 保莉 宋沁楠 《核电子学与探测技术》 CAS 北大核心 2018年第2期289-292,共4页
土壤中90Sr的分析方法中给出的测量结果计算公式,是近似认为测量过程的中间时刻的计数率等同于整个过程的平均计数率,在此假设条件下得到的计算公式与实际测量过程存在一定的误差。理论上,在测量过程中考虑到90Y的衰变,应采用积分平均... 土壤中90Sr的分析方法中给出的测量结果计算公式,是近似认为测量过程的中间时刻的计数率等同于整个过程的平均计数率,在此假设条件下得到的计算公式与实际测量过程存在一定的误差。理论上,在测量过程中考虑到90Y的衰变,应采用积分平均值作为测量过程的平均值,得到的计算结果更为准确。对标准方法中的计算公式和理论方法在不同的测量时长的条件下进行了分析比较,结果发现,在测量时长较短时,两者误差很小;但在测量时长较长时,使用标准中的计算公式会引入较大误差,对于低水平放射性测量来讲,不能通过延长测量时间降低测量计数统计误差。 展开更多
关键词 90Sr分析 结果计算 统计误差
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基于神经网络算法的交通流量预测建模与计算 被引量:3
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作者 原二保 《现代电子技术》 北大核心 2020年第10期66-68,75,共4页
为了提高交通流量预测数据的准确度,文中利用神经网络算法提出一种短时交通流量的预测模型。通过分析交通流量的概念和特征,设计相应的预测评价体系,使用拉格朗日中值定理与小波变换,实现交通流量数据的插值、降噪和归一化。基于改进的... 为了提高交通流量预测数据的准确度,文中利用神经网络算法提出一种短时交通流量的预测模型。通过分析交通流量的概念和特征,设计相应的预测评价体系,使用拉格朗日中值定理与小波变换,实现交通流量数据的插值、降噪和归一化。基于改进的神经网络算法,建立和优化相应的预测数学模型。在评价体系的基础上,完成预测结果的计算与评估。仿真测试结果表明,改进神经网络算法的应用有效降低了预测结果的误差,提高了交通流量预测模型计算的准确度。 展开更多
关键词 交通流量预测 特征分析 预测结果计算 预测模型 评价体系设计 模型优化
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土壤有机质含量的测定 被引量:7
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作者 方能干 《现代农业科技》 2016年第8期207-208,共2页
总结了土壤地力等级评价中土壤有机质含量的测定方法,包括测定原理、仪器设备、试剂、操作步骤、结果计算及注意事项等,以供参考。
关键词 土壤 有机质含量 测定原理 操作步骤 结果计算 注意事项
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Stability of boundary pillars in transition from open pit to underground mining 被引量:11
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作者 赵兴东 李连崇 +1 位作者 唐春安 张洪训 《Journal of Central South University》 SCIE EI CAS 2012年第11期3256-3265,共10页
Based on the height of back-filled materials, thickness of ore body, height of boundary pillar and dipping angle of ore body and water pressure, the safety factors of all the pillars are calculated with the limit equi... Based on the height of back-filled materials, thickness of ore body, height of boundary pillar and dipping angle of ore body and water pressure, the safety factors of all the pillars are calculated with the limit equilibrium method. The calculation results present that the safety factors of pillars in Sections 19, 20, 24, 28 are less than 1.3, and those of unstable sections are identified preliminarily. Further, a numerical investigation in Sections 18, 20, 22, 24, 25 and 28 implemented with numerical code RFPA20 is employed to further validate the pillar performance and the stability of stopes. The numerical results show the pillars in Sections 18, 22 and 24 are stable and the designed pillar size is suitable. The width of the ore body near Section 28 averages 20 m, failure occurs in the left stope, but the boundary pillars near Section 28 maintain good performance. The pillars in Sections 20 and 25 are unstable which are mainly affected by the Faults F8 and F18. The existence of faults alters the stress distribution, failure mode and water inrush pathway. This work provides a meaningful standard for boundary pillar and stope design in a mine as it transitions from an open pit to underground. 展开更多
关键词 boundary pillar STABILITY underground mining numerical simulation case study
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A strength reduction method based on double reduction parameters and its application 被引量:45
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作者 袁维 白冰 +1 位作者 李小春 汪海滨 《Journal of Central South University》 SCIE EI CAS 2013年第9期2555-2562,共8页
In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of... In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of the cohesion and friction angle on the stability of the same slope and is defective to some extent.Regarding this defect,a strength reduction method based on double reduction parameters,which adopts different reduction parameters,is proposed.The core of the double-parameter reduction method is the matching reduction principle of the slope with different angles.This principle is represented by the ratio of the reduction parameter of the cohesion to that of the friction angle,described as η.With the increase in the slopeangle,ηincreases; in particular,when the slope angle is 45°,tηis 1.0.Through the matching reduction principle,different safety margin factors can be calculated for the cohesion and friction angle.In combination with these two safety margin factors,a formula for calculating the overall safety factor of the slope is proposed,reflecting the different contributions of the cohesion and friction angle to the slope stability.Finally,it is shown that the strength reduction method based on double reduction parameters acquires a larger safety factor than the classic limit equilibrium method,but the calculation results are very close to those obtained by the limit equilibrium method. 展开更多
关键词 double reduction parameter strength reduction method matching reduction principle slope stability
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Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion 被引量:10
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作者 唐进元 刘艳平 《Journal of Central South University》 SCIE EI CAS 2013年第2期354-362,共9页
The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur inv... The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%. 展开更多
关键词 face gear contact stress finite element method loaded meshing simulation load distribution factor multi-tooth contact
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Wheel slip-sinkage and its prediction model of lunar rover 被引量:11
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作者 丁亮 高海波 +1 位作者 邓宗全 陶建国 《Journal of Central South University》 SCIE EI CAS 2010年第1期129-135,共7页
In order to investigate wheel slip-sinkage problem, which is important for the design, control and simulation of lunar rovers, experiments were carried out with a wheel-soil interaction test system to measure the sink... In order to investigate wheel slip-sinkage problem, which is important for the design, control and simulation of lunar rovers, experiments were carried out with a wheel-soil interaction test system to measure the sinkage of three types of wheels in dimension with wheel lugs of different heights and numbers under a series of slip ratios (0-0.6). The curves of wheel sinkage versus slip ratio were obtained and it was found that the sinkage with slip ratio of 0.6 is 3-7 times of the static sinkage. Based on the experimental results, the slip-sinkage principle of lunar's rover lugged wheels (including the sinkage caused by longitudinal flow and side flow of soil, and soil digging of wheel lugs) was analyzed, and corresponding calculation equations were derived. All the factors that can cause slip sinkage were considered to improve the conventional wheel-soil interaction model, and a formula of changing the sinkage exponent with the slip ratio was established. Mathematical model for calculating the sinkage of wheel according to vertical load and slip ratio was developed. Calculation results show that this model can predict the slip-sinkage of wheel with high precision, making up the deficiency of Wong-Reece model that mainly reflects longitudinal slip-sinkage. 展开更多
关键词 lunar rover slip-sinkage loose lunar soil stress distribution slip ratio
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Critical safe distance design to improve driving safety based on vehicle-to-vehicle communications 被引量:5
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作者 陈晨 吕宁 +2 位作者 刘雷 裴庆祺 李晓记 《Journal of Central South University》 SCIE EI CAS 2013年第11期3334-3344,共11页
A critical safe distance(CSD)model in V2V(vehicle-to-vehicle)communication systems was proposed to primarily enhance driving safety by disseminating warning notifications to vehicles when they approach calculated CSD.... A critical safe distance(CSD)model in V2V(vehicle-to-vehicle)communication systems was proposed to primarily enhance driving safety by disseminating warning notifications to vehicles when they approach calculated CSD.By elaborately analyzing the vehicular movement features especially when braking,our CSD definition was introduced and its configuration method was given through dividing radio range into different communication zones.Based on our definition,the needed message propagation delay was also derived which could be used to control the beacon frequency or duration.Next,the detailed CSD expressions were proposed in different mobility scenarios by fully considering the relative movement status between the front and rear vehicles.Numerical results show that our proposed model could provide reasonable CSD under different movement scenarios which eliminates the unnecessary reserved inter-vehicle distance and guarantee the safety at the same time.The compared time-headway model always shows a smaller CSD due to focusing on traffic efficiency whereas the traditional braking model generally outputs a larger CSD because it assumes that the following car drives with a constant speed and did not discuss the scenario when the leading car suddenly stops.Different from these two models,our proposed model could well balances the requirements between driving safety and traffic throughput efficiency by generating a CSD in between the values of the two models in most cases. 展开更多
关键词 vehicle-to-vehicle communication systems collsion avoidance saftey distance
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Experimental and field study on dissipation coefficient of supersaturated total dissolved gas 被引量:10
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作者 冯镜洁 李然 +1 位作者 马倩 王乐乐 《Journal of Central South University》 SCIE EI CAS 2014年第5期1995-2003,共9页
The elevated supersaturation of total dissolved gas (TDG) downstream of a high-dam spill has deleterious effects on fish in a large range. A one-dimensional (l-D) longitudinal model is optimal for the prediction o... The elevated supersaturation of total dissolved gas (TDG) downstream of a high-dam spill has deleterious effects on fish in a large range. A one-dimensional (l-D) longitudinal model is optimal for the prediction of supersaturated TDG dissipation over a long distance. The key issue of the model is to determine the dissipation coefficient accurately. In agreement with field observations and experiment data, dimensional analysis and regression were performed to propose a formula for estimating the dissipation coefficient of supersaturated TDG in various rivers and reservoirs, and it involves the effects of the turbulence intensity, the hydro-pressure and the solid-liquid interface. The friction velocity, water depth, hydraulic radius and Froude number are independent variables in the formula which are easy to determine in practical applications. The 1-D longitudinal model is implemented to calculate the dissipation of TDG in a reach of the Jinsha River. Good agreement is found between the calculated results and field data for both the dissipation coefficient and the dissipation process. 展开更多
关键词 total dissolved gas dissipation coefficient longitudinal model HYDRODYNAMICS
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A computational method for post-construction settlement of high-speed railway bridge pile foundation considering soil creep effect 被引量:12
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作者 冯胜洋 魏丽敏 +1 位作者 何重阳 何群 《Journal of Central South University》 SCIE EI CAS 2014年第7期2921-2927,共7页
Based on reasonable assumptions that simplified the calculational model,a simple and practical method was proposed to calculate the post-construction settlement of high-speed railway bridge pile foundation by using th... Based on reasonable assumptions that simplified the calculational model,a simple and practical method was proposed to calculate the post-construction settlement of high-speed railway bridge pile foundation by using the Mesri creep model to describe the soil characteristics and the Mindlin-Geddes method considering pile diameter to calculate the vertical additional stress of pile bottom.A program named CPPS was designed for this method to calculate the post-construction settlement of a high-speed railway bridge pile foundation.The result indicates that the post-construction settlement in 100 years meets the requirements of the engineering specifications,and in the first two decades,the post-construction settlement is about 80% of its total settlement,while the settlement in the rest eighty years tends to be stable.Compared with the measured settlement after laying railway tracks,the calculational result is closed to that of the measured,and the results are conservative with a high computational accuracy.It is noted that the method can be used to calculate the post-construction settlement for the preliminary design of high-speed railway bridge pile foundation. 展开更多
关键词 high-speed railway bridge pile foundation post-construction settlement Mesri creep model simplified computational method
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Upper bound analytical solution for surrounding rock pressure of shallow unsymmetrical loading tunnels 被引量:7
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作者 雷明锋 彭立敏 +2 位作者 施成华 谢友均 谭立新 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第6期2339-2347,共9页
By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle ... By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle of virtual power, the upper bound solution for surrounding rock pressure of shallow unsymmetrical loading tunnel was derived and verified by an example. The results indicate that the calculated results of the derived upper bound method for surrounding rock pressure of shallow unsymmetrical loading tunnels are relatively close to those of the existing "code method" and test results, which means that the proposed method is feasible. The current code method underestimates the unsymmetrical loading feature of surrounding rock pressure of shallow unsymmetrical loading tunnels, so it is unsafe; when the burial depth is less or greater than two times of the tunnel span and the unsymmetrical loading angle is less than 45°, the upper bound method or the average value of the results calculated by the upper bound method and code method respectively, is comparatively reasonable. When the burial depth is greater than two times of the tunnel span and the unsymmetrical loading angle is greater than 45°, the code method is more suitable. 展开更多
关键词 TUNNEL shallow buried tunnel unsymmetrical loading ultimate analysis method upper bound solution
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Similarity measure design and similarity computation for discrete fuzzy data 被引量:7
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作者 LEE Sang-Hyuk PARK Wook-Je JUNG Dong-yean 《Journal of Central South University》 SCIE EI CAS 2011年第5期1602-1608,共7页
The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The useful... The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The usefulness of the proposed similarity measure was verified.The results show that the proposed similarity measure could be applied to ordinary fuzzy membership functions,though it was not easy to design.Through conventional results on the calculation of similarity for fuzzy membership pair,fuzzy membership-crisp pair and crisp-crisp pair were carried out.The proposed distance based similarity measure represented rational performance with the heuristic point of view.Furthermore,troublesome in fuzzy number based similarity measure for abnormal universe of discourse case was discussed.Finally,the similarity measure computation for various membership function pairs was discussed with other conventional results. 展开更多
关键词 similarity measure fuzzy number DISTANCE similarity evaluation fuzzy membership function
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Kinematical analysis of highway tunnel collapse using nonlinear failure criterion 被引量:9
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作者 杨小礼 杨子汉 +1 位作者 潘秋景 李育林 《Journal of Central South University》 SCIE EI CAS 2014年第1期381-386,共6页
For different kinds of rocks,the collapse range of tunnel was studied in the previously published literature.However,some tunnels were buried in soils,and test data showed that the strength envelopes of the soils foll... For different kinds of rocks,the collapse range of tunnel was studied in the previously published literature.However,some tunnels were buried in soils,and test data showed that the strength envelopes of the soils followed power-law failure criterion.In this work,deep buried highway tunnel with large section was taken as objective,and the basic expressions of collapse shape and region were deduced for the highway tunnels in soils,based on kinematical approach and power-law failure criterion.In order to see the effectiveness of the proposed expressions,the solutions presented in this work agree well with previous results if the nonlinear failure criterion is reduced to a linear Mohr-Coulomb failure criterion.The present results are compared with practical projects and tunnel design code.The numerical results show that the height and width of tunnel collapse are greatly affected by the nonlinear criterion for the tunnel in soil. 展开更多
关键词 upper bound theorem tunnel collapse highway tunnel nonlinear failure criterion
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Experimental study and analysis on fatigue stiffness of RC beams strengthened with CFRP and steel plate 被引量:13
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作者 卢亦焱 胡玲 +1 位作者 李杉 王康昊 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第3期701-707,共7页
The objective of this work is to investigate the fatigue behavior of reinforced concrete(RC) beams strengthened with externally bonded carbon fiber reinforced polymer(CFRP) and steel plate. An experimental investigati... The objective of this work is to investigate the fatigue behavior of reinforced concrete(RC) beams strengthened with externally bonded carbon fiber reinforced polymer(CFRP) and steel plate. An experimental investigation and theoretical analysis were made on the law of deflection development and stiffness degradation, as well as the influence of fatigue load ranges. Test results indicate that the law of three-stage change under fatigue loading is followed by both midspan deflection and permanent deflection, which also have positive correlation with fatigue load amplitude. Fatigue stiffness of composite strengthened beams degrades gradually with the increasing of number of cycles. Based on the experimental results, a theoretical model by effective moment of inertia method is developed for calculating the sectional stiffness of such composite strengthened beams under fatigue loading, and the calculated results are in good agreement with the experimental results. 展开更多
关键词 carbon fiber reinforced polymer steel plate composite strengthening technique reinforced concrete beams fatigue stiffness
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Analytical approach and field monitoring for mechanical behaviors of pipe roof reinforcement 被引量:4
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作者 王海涛 贾金青 康海贵 《Journal of Central South University》 SCIE EI CAS 2009年第5期827-834,共8页
Considering the delay effect of initial lining and revising the Winkler elastic foundation model,an analytical approach based on Pasternak elastic foundation beam theory for pipe roof reinforcement was put forward. Wi... Considering the delay effect of initial lining and revising the Winkler elastic foundation model,an analytical approach based on Pasternak elastic foundation beam theory for pipe roof reinforcement was put forward. With the example of a certain tunnel excavation,the comparison of the values of longitudinal strain of reinforcing pipe between field monitoring and analytical approach was made. The results indicate that Pasternak model,which considers a more realistic hypothesis in the elastic soil than Winkler model,gives more accurate calculation and agrees better with the result of field monitoring. The difference of calculation results between these two models is about 7%,and Pasternak model is proved to be a better way to study the reinforcement mechanism and improve design practice. The calculation results also reveal that the reinforcing pipes act as levers,which increases longitudinal load transfer to an unexcavated area,and consequently decreases deformation and increases face stability. 展开更多
关键词 tunnel heading pipe roof reinforcement Pasternak elastic foundation beam field monitoring
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Characteristics of supersonic flow in new type externally pressurized spherical air bearings 被引量:2
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作者 WANG Fu-sheng BAO Gang 《Journal of Central South University》 SCIE EI CAS 2012年第1期128-134,共7页
In order to predict accurately the characteristics of supersonic flow in new type externally pressurized spherical air bearings under large bearing clearance and high air supply pressure, which could decrease their lo... In order to predict accurately the characteristics of supersonic flow in new type externally pressurized spherical air bearings under large bearing clearance and high air supply pressure, which could decrease their load carrying capacity and stability, a CFD-based analysis was introduced to solve the three-dimensional turbulent complete compressible air flow governing equations. The realizable κ-ε model was used as a turbulent closure illustrate that the interaction exists between shock waves The supersonic flow field near air inlets was analyzed. The flow structures and boundary layer, and the flow separation is formed at the lower comer and the lower wall around the point of a maximum velocity. The numerical results show that the conversion from supersonic flow to subsonic flow in spherical air bearing occurs through a shock region (pseudo-shock), and the viscous boundary layer results in the flow separation and reverse flow near the shock. The calculation results basically agree with the corresponding experimental data. 展开更多
关键词 supersonic flow spherical air bearings Mach number shock wave
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