The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is th...The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is that the problem is statically indeterminate and therefore requires complementary information to obtain a unique solution. This paper reports 1) a comprehensive theoretical analysis of the three fundamental models based on treating the ladder as a single Euler-Bernoulli beam, and 2) a detailed experimental investigation of the forces of reaction as a function of applied load and location of load. In contrast to previous untested proposals that the solution to the ladder problem lay in the axial constraint on compression or the transverse constraint on flexure, the experimental outcome of the present work showed unambiguously that 1) the ladder could be modeled the best by a pinned support at the base (on the ground) and a roller support at the top (at the wall), and 2) the only complementary relation needed to resolve the static indeterminacy is the force of friction at the wall. Measurements were also made on the impact loading of a ladder by rapid ascent and descent of a climber. The results obtained were consistent with a simple dynamical model of the ladder as a linear elastic medium subject to a pulse perturbation. The solution to the ladder problem herein presented provides a basis for theoretical extension to other types of ladders. Of particular importance, given that accidents involving ladders in the workplace comprise a significant fraction of all industrial accidents, the theoretical relations reported here can help determine whether a collapsed structure, against which a ladder was applied, met regulatory safety limits or not.展开更多
传统电动汽车充电负荷建模通常采用对电动汽车个体进行抽样模拟的方式,未能从分析机理的角度描述电动汽车群体相互作用形成的宏观运行状态。为此,提出一种基于半动态交通均衡模型和组合荷电状态(combined states of the charge,CSOC)概...传统电动汽车充电负荷建模通常采用对电动汽车个体进行抽样模拟的方式,未能从分析机理的角度描述电动汽车群体相互作用形成的宏观运行状态。为此,提出一种基于半动态交通均衡模型和组合荷电状态(combined states of the charge,CSOC)概率计算的电动汽车充电负荷概率分布计算方法。首先,分析电动汽车的交通特性和充电特性,并提出一种可行路径集构建方法;然后,引入交通均衡理论进行电动汽车空间分布建模,建立考虑随机效用的半动态交通均衡模型,实现宏观交通流均衡分配。进一步地,从理论层面分析电动汽车群的荷电状态变化,建立基于CSOC的充电负荷概率分布计算模型。最后,分别在13节点路网和实际大路网中验证所提方法的有效性,并分析了电动汽车渗透率和路网结构对充电负荷概率分布的影响。展开更多
文摘The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is that the problem is statically indeterminate and therefore requires complementary information to obtain a unique solution. This paper reports 1) a comprehensive theoretical analysis of the three fundamental models based on treating the ladder as a single Euler-Bernoulli beam, and 2) a detailed experimental investigation of the forces of reaction as a function of applied load and location of load. In contrast to previous untested proposals that the solution to the ladder problem lay in the axial constraint on compression or the transverse constraint on flexure, the experimental outcome of the present work showed unambiguously that 1) the ladder could be modeled the best by a pinned support at the base (on the ground) and a roller support at the top (at the wall), and 2) the only complementary relation needed to resolve the static indeterminacy is the force of friction at the wall. Measurements were also made on the impact loading of a ladder by rapid ascent and descent of a climber. The results obtained were consistent with a simple dynamical model of the ladder as a linear elastic medium subject to a pulse perturbation. The solution to the ladder problem herein presented provides a basis for theoretical extension to other types of ladders. Of particular importance, given that accidents involving ladders in the workplace comprise a significant fraction of all industrial accidents, the theoretical relations reported here can help determine whether a collapsed structure, against which a ladder was applied, met regulatory safety limits or not.
文摘传统电动汽车充电负荷建模通常采用对电动汽车个体进行抽样模拟的方式,未能从分析机理的角度描述电动汽车群体相互作用形成的宏观运行状态。为此,提出一种基于半动态交通均衡模型和组合荷电状态(combined states of the charge,CSOC)概率计算的电动汽车充电负荷概率分布计算方法。首先,分析电动汽车的交通特性和充电特性,并提出一种可行路径集构建方法;然后,引入交通均衡理论进行电动汽车空间分布建模,建立考虑随机效用的半动态交通均衡模型,实现宏观交通流均衡分配。进一步地,从理论层面分析电动汽车群的荷电状态变化,建立基于CSOC的充电负荷概率分布计算模型。最后,分别在13节点路网和实际大路网中验证所提方法的有效性,并分析了电动汽车渗透率和路网结构对充电负荷概率分布的影响。
