Simplified relationships between inelastic and elastic spectral acceleration demands for seismic design in New Zealand

Inelastic deformation ratio for seismic demands assessment of structures

Strength reduction factors which permit estimation of inelastic strength demands from elastic strength demands are evaluated. Results from various investigations of strength reduction factors carried out over the last 30 years are reviewed, and their results are presented in a common format which facilitates their comparison. The main parameters that affect the magnitude of strength reductions are discussed. The evaluation of the results indicates that strength reductions are primarily influenced by the maximum tolerable displacement ductility demand, the period of the system and the soil conditions at the site. Simplified expressions of strength reduction factors to estimate inelastic design spectra as functions of these primary-influencing parameters are presented.

This article describes a practical data-driven approach to increase revenue, identifying inelastic and elastic demand segments used to decide when to close classes. The method proposed defines class closure policies that will close the lower fares a specific number of days before the departure. By identifying the remaining inelastic and elastic demand, choice can be made when to close lower classes. This approach maximizes revenue from inelastic demand, when customers are forced to book at a higher fare, to exceed the loss of revenue from the rejected elastic demand. These class closure polices are defined at the detailed level of: (i) Origin/Destination, (ii) Point-of-sale, (iii) Date, (iv) Departure time, (v) Number of days before departure. This process reflects the function analysts perform manually, or via rules as determined in the revenue management system. Closer to departure, and as the share of inelastic demand increases, lower classes will close to create sell-up by inelastic demand. Generally analysts work by rule of thumb or based on ad hoc data analysis. The purpose of this article is to use data to define the class closure settings at a more detailed level than could be expected from a manual approach.

Modern seismic codes rely on performance-based seismic design methodology which requires that the structures withstand inelastic deformation. Many studies have focused on the inelastic deformation ratio evaluation (ratio between the inelastic and elastic maximum lateral displacement demands) for various inelastic spectra. This paper investigates the inelastic response spectra through the ductility demand µ, the yield strength reduction factor Ry, and the inelastic deformation ratio. They depend on the vibration period T, the post-to-preyield stiffness ratio α, the peak ground acceleration (PGA), and the normalized yield strength coefficient η (ratio of yield strength coefficient divided by the PGA). A new inelastic deformation ratio Cη is defined; it is related to the capacity curve (pushover curve) through the coefficient (η) and the ratio (α) that are used as control parameters. A set of 140 real ground motions is selected. The structures are bilinear inelastic single degree of freedom systems (SDOF). The sensitivity of the resulting inelastic deformation ratio mean values is discussed for different levels of normalized yield strength coefficient. The influence of vibration period T, post-to-preyield stiffness ratio α, normalized yield strength coefficient η, earthquake magnitude, ruptures distance (i.e., to fault rupture) and site conditions is also investigated. A regression analysis leads to simplified expressions of this inelastic deformation ratio. These simplified equations estimate the inelastic deformation ratio for structures, which is a key parameter for design or evaluation. The results show that, for a given level of normalized yield strength coefficient, these inelastic displacement ratios become non sensitive to none of the rupture distance, the earthquake magnitude or the site class. Furthermore, they show that the post-to-preyield stiffness has a negligible effect on the inelastic deformation ratio if the normalized yield strength coefficient is greater than unity.

While most of the existing work on public sector location models has been developed in the context of emergency facilities, the location problem of nonemergency facilities differs in the location objective and in the elastic nature of demand. The proper location objective under elastic demand is that of maximizing Consumers' Surplus (CS). Based on a proposed framework, we formulate the CS location objective under different demand functions, representing different demand behaviors. We prove that the CS function is convex and therefore the search for optimal locations can be restricted to nodes. We present integer programming formulations of the Maximum Consumers' Surplus Location problem (MCSLP) and its generalization which includes fixed facility cost. A computational analysis compares the location behaviors under elastic and inelastic demands, and investigates the effects of demand function (demand behavior) on location behavior.

Retailers commonly offer discounts to encourage consumers to purchase more products thereby increasing retailers’ revenues. This article focuses on modeling the seller pricing decisions by using agent-based approach when the price, as a tool of revenue management, decreases. Considering the seller as an agent who uses price changes to maximize its total revenues, the objective of this research is to find the proper seller’s decision about the rate of discount on products in 3 different scenarios. In the first scenario, all products’ price elasticity of demand are the same and the products have relatively elastic demand. In the second scenario, all goods have the same price elasticity of demand and have relatively inelastic demands. The third scenario presents a combination of the first and the second scenarios in which the price elasticity of demand of products are different and goods with elastic and inelastic demand are placed next to each other. Also, all goods in each scenario are substitutes. In the first scenario, reducing the price causes the downward trend in rate of profit even though the discount could increase the revenue. In the second scenario, the agent behaves differently which offering the discount does not increase the revenue. In the third scenario, the products’ discount increases the revenue with a slope less than the first scenario. Also, the discount for all products doesn’t cause income growth. Therefore, some goods without any discount remain in shelf. Consequently, the proposed model in this research shows the proper rate of discount on each product in different product layouts.

Inelastic seismic energy spectra for soft soils: Application to Mexico City

IN a recent article in The Journal of Industrial Economics, Richard H. Holton suggested that the elasticity of demand is the main consideration determining whether or not a new item will be added to the assortment carried by a retail store. 'To qualify for admission to the product-mix ... a candidate item mu-st [my italic] have a relatively inelastic demand. It is this requirement which seems to be of overwhelming importance in influencing the choice of new lines'.' It is true that, in the case of supermarkets, the store-type specifically considered by Holton, most of the recent (principally non-food) additions to the product-line have had high percentage margins and therefore, it may be inferred, rather inelastic demands, at the price set. But it seems misleading to attribute the addition of such items to this low elasticity, which is only one of the factors relevant to the decision whether or not to add an item. Consider two new item candidates for a store's assortment and assume that the acquisition cost of a unit of each is the same, and constant. Assume, as seems reasonable, that operating costs are not affected by the addition of either item, so that the acquisition cost of each is its marginal cost, and these are, therefore, for the two items identical and constant. For each item there is a family of demand curves relating quantity sold to the price, the demand curves moving to the right, as the amount of space allocated to the item is increased. Suppose a given amount of space is available for a new product. The profit-maximizing price for each item can then be determined. Although the product with the less elastic demand (at the price selected) will produce a greater profit per unit of product sold, the product with the more elastic demand may well produce a greater profit for the amount of space allotted to it. If this is so, the profitmaximizing retailer should add, if it is in fact profitable to add a new item, the item with the more elastic demand. Whether or not it is profitable to add a new item to a retailer's assortment will depend upon the relationship between the gross profit increment attributable to the new item and the opportunity cost of adding the new item; this opportunity cost will be the decrement in gross profit that results when the space made available to the

Real-time pricing of electricity is theoretically more economically efficient than flat rate pricing. However, a switch from flat-rates to real-time rates means that many consumers will lose the cross-subsidy they are receiving under the flat rate, and may see an increase in their bills even if they have elastic demand. We use hourly load data from 1260 Commonwealth Edison residential customers on a standard flat rate electricity tariff from 2007 and 2008. We calculate which customers would have been better off and which customers would not under real time pricing with both elastic and inelastic demand and look at the general characteristics of these customers. We find that if customers do not respond to prices under RTP, then only 35% of customers save money, while the remainder loses. The greatest potential for savings is from reduction in capacity costs.

This paper present a new semi-analytical approach aims to estimating the inelastic deformation ratio for SDOF bilinear systems. The new proposed approach combines both the inelastic and elastic maximum lateral displacement demands instead of combining the yield-strength reduction factor and the ductility factor. The new inelastic deformation ratio on one hand depends on the inelastic properties of systems (the period, the post-to-preyield stiffness ratio, the yield strength coefficient, the normalized yield strength coefficient), on the other hand the elastic spectral response acceleration \((S_{a} )\) that is presented in seismic design codes, such as the Federal Emergency Management Agency FEMA and Eurocode8. The results are compared to those of the Nonlinear Time History Analysis (NL-THA) and some existing formulations for three different reinforced concrete (R.C.) 2D-frames subjected to the record ground motion of El-Centro 1940 (N/S).KeywordsInelastic deformation ratioSeismic demandPushoverInelastic spectra

Near fault earthquake shaking may cause structures to experience inelastic displacement demands which are significantly greater than that expected from design level earthquakes. This paper describes the inelastic demands for elastic-perfectly plastic single-degree-offreedom oscillators to actual recorded earthquake motions. Inelastic response spectra from sites at known locations relative to the fault are used to quantify the inelastic demands in terms of a relationship between lateral force reduction factor, period and ductility. For medium and long period oscillators the severity of inelastic demand increased as the distance along the fault from the epicenter in the direction of rupture increased. Short period oscillators were relatively unaffected by the near-fault shaking effects.

In the past, implementing delivered pricing has been perceived as unrealistic because of practical difficulties in distinguishing between customers, determining an individual’s willingness to pay, and setting different prices to individuals. The rise of e-commerce has introduced the possibility of doing all three. Competitive location with delivered pricing was studied by Lederer and Hurter (1986) but only with inelastic customer demand. This paper extends the literature by allowing price elastic demand. A Nash equilibrium with inelastic demand always exists but examples show that it may not with price elasticity. General sufficient conditions guaranteeing existence of a Nash equilibrium are developed despite the fact that even with these conditions a firm’s profit function is generally not concave, quasi-concave, supermodular or even continuous in location choices. Examples demonstrate how violation of sufficient conditions result in lack of existence. Given price elasticity, equilibrium locations demonstrate properties unlike the inelastic case, for example, as transportation cost rises or firms’ production costs rise, each firm locates closer to its competitor. Given our sufficient conditions for equilibrium’s existence, the interval spanning firms’ ordered equilibrium locations always contains a social welfare optimum pair and a social welfare optimum pair is always contained by an ordered equilibrium.

A computational study of path-based methods for optimal traffic assignment with both inelastic and elastic demand

As for the inelastic displacement demand of a single-degree-of-freedom system, previous studies usually focus on the strength reduction factor, R, or the inelastic displacement ratio, C. Only a little literature reports the direct statistical results of the mean inelastic displacement spectra, Sd. Based on 308 earthquake records selected from three types of site soil, differences between the direct mean Sd and the indirect ones that respectively derived from mean R and mean Cμ are investigated, in which Cμ refers to the constant ductility inelastic displacement ratio. It is found the indirect Sd will introduce errors for using mean R and mean Cμ, while the dispersion of the direct spectra need to be reduced before putting into practice. Two methods, the period normalized method and the spectra-matching method, are employed to address the dispersion problem, and the latter one that modified a record to make its acceleration response spectra compatible with the specified standard, Chinese highway bridge seismic design guidelines in this study, works with more acceptable performance. Finally, a comprehensive equation is proposed to characterize the spectra-matching mean Sd, the practicality and efficiency of the identified parameters in the equation are verified. It is advisable to use the proposed equation to assess the inelastic displacement demand of Chinese highway bridges characterized by single-degree-of-freedom bilinear system, and the procedures to obtain the displacement spectra can also be utilized for other corresponding researches.

A compliant tuned liquid damper for controlling seismic vibration of short period structures