Unequal Heights Research Articles

Approximating Lateral Stiffness of Stories in Elastic Frames

Despite advances in the computer analysis of frame buildings for lateral loads, there remains a need for simple models that provide accurate estimates of response. The concept of lateral stiffness is reviewed, and it is concluded that a single value can be used to represent the stiffness of a story in an elastic, rectangular frame with fixed base that is subjected to regular distributions of lateral load. Three existing expressions for approximating the lateral stiffness of stories are compared, but it is concluded that these are applicable only for uniform frames with girders that are flexurally stiffer than columns. An expression is proposed that includes three numerically derived factors that greatly improve the accuracy of stiffness estimates for regular and moderately irregular frames. The proposed expression simulates: (1) The effect of unequal heights for adjacent stories; (2) the influence of top and bottom boundaries; and (3) the stiffening effect of the fixed base in low-rise frames.

Climate Sensitivity: The Significance of the Altitude-mass-balance Feedback on Glaciers and Ice Sheets

An ice mass increasing its extent will generally also increase its mean surface elevation (anything else being unchanged). Since temperature drops rapidly with height this often implies a more positive mass balance and thus further growth. This powerful feedback loop is at least as important as the temperature-albedo feedback. In this work, we present a general study of the nature of the altitude-mass-balance feedback, with special attention for the role of differences in the bedrock geometry. One- and two-dimensional experiments on various bedrock topographies are run, using a numerical ice-sheet model based on plane shear flow of ice. Different climates are simulated by lowering or raising uniformly the mass-balance distribution over the ice sheet.These studies were first done on steady state ice sheets. They show that some geometries can largely enhance this altitude mass-balance feedback. On an island, for instance, it is possible to have two different stable steady states under the same climatic environment: no ice sheet, or a large one over the whole island. When the geometry of the island becomes more complex, for instance with two hills of unequal heights, four different equilibria can be found for the same climatic conditions: no ice sheet, one small one, two small ones or a very large one. Which will develop depends entirely on the history of the mass-balance fluctuations.

The interaction among adiabatic shear bands in simple and dipolar materials

The effect of average strain-rate on the interaction among shear bands in nonpolar and dipolar thermoviscoplastic materials has been investigated. The uniform temperature and stress fields in a block undergoing simple shearing deformations are perturbed when the body just starts deforming plastically and the governing nonlinear coupled partial differential equations are solved numerically. The temperature perturbations introduced are symmetric about the centerline of the block, and have two bumps of unequal heights on each side of the centerline. For nonpolar materials one band on either side of the centerline eventually emerges, the location of the center of the band and its width depend upon the overall strain-rate. For dipolar materials only one band situated at the center of the block forms irrespective of the applied strain-rate. The initiation of the band is significantly delayed in dipolar materials, especially at the higher overall strain-rate studied.

Climate Sensitivity: The Significance of the Altitude-mass-balance Feedback on Glaciers and Ice Sheets

An ice mass increasing its extent will generally also increase its mean surface elevation (anything else being unchanged). Since temperature drops rapidly with height this often implies a more positive mass balance and thus further growth. This powerful feedback loop is at least as important as the temperature-albedo feedback. In this work, we present a general study of the nature of the altitude-mass-balance feedback, with special attention for the role of differences in the bedrock geometry. One- and two-dimensional experiments on various bedrock topographies are run, using a numerical ice-sheet model based on plane shear flow of ice. Different climates are simulated by lowering or raising uniformly the mass-balance distribution over the ice sheet. These studies were first done on steady state ice sheets. They show that some geometries can largely enhance this altitude mass-balance feedback. On an island, for instance, it is possible to have two different stable steady states under the same climatic environment: no ice sheet, or a large one over the whole island. When the geometry of the island becomes more complex, for instance with two hills of unequal heights, four different equilibria can be found for the same climatic conditions: no ice sheet, one small one, two small ones or a very large one. Which will develop depends entirely on the history of the mass-balance fluctuations.

Interfacial Band Structure of Platinum‐Loaded CdS Powder and Its Correlation with the Photocatalytic Activity

The band structure near the surface of the Pt‐loaded photocatalyst has been discussed. The height of the energy barrier existing at the interface was experimentally derived by analyzing the temperature dependence of the cathodic current flowing in the Pt‐loaded sinter electrode. The barrier at the interface was obtained from the measurement of the flatband potential of electrodes. It turned out that these two barriers have unequal heights, which are advantageous for the photocatalytic reactions. The pH and the temperature effects on the photocatalytic hydrogen evolution from aqueous solutions of sodium sulfite are discussed using this band model. Marked enhancement of the reaction rate by addition of a small amount of EDTA to the solution has been reported. This is concluded to be due to the shift of the flatband potential of toward the negative potential.

Ｘ線および中性子回折図形のＲｉｅｔｖｅｌｄ解析

A computer software package, RIETAN, has been developed for the Rietveld refinement of angle-dispersive X-ray and neutron data, and TOF neutron data. The program is written in FORTRAN 77 and of modular construction to facilitate changes. RIETAN incorporates data bases of information on space groups, atomic scattering factors, scattering lengths, and anomalous dispersion corrections. It can handle all space groups without additional programming and allows refinement of the diffraction data of samples containing two or more phases. A new profile shape function, which is the sum of a Gauss function and a Lorentz function with unequal peak heights and widths at one-half peak height, has been included for the analysis of angle-dispersive diffraction data. Three different algorithms for nonlinear least squares have been implemented: Gauss-Newton, Marquardt, and conjugate direction methods. One can easily change the method of least squares one after another during refinement. These three methods are combined with an exterior penalty function method so that objective functions can be minimized under equal and unequal constraints which may be linear and/or nonlinear functions with respect to parameters. The program can not only plot the results of Rietveld analysis but also simulate powder diffraction patterns by using user-supplied parameters.

Surgical Gems: Even Coaptation of Wound Edges of Unequal Thicknesses or Unequal Heights

The Journal of Dermatologic Surgery and OncologyVolume 5, Issue 11 p. 844-844 Feature Surgical Gems: Even Coaptation of Wound Edges of Unequal Thicknesses or Unequal Heights June K. Robinson M.D., June K. Robinson M.D.Dr. Robinson is Assistant Professor of Dermatology, Department of Dermatology, Northwestern University Medical School, Chicago, Illinois.Search for more papers by this author June K. Robinson M.D., June K. Robinson M.D.Dr. Robinson is Assistant Professor of Dermatology, Department of Dermatology, Northwestern University Medical School, Chicago, Illinois.Search for more papers by this author First published: November 1979 https://doi.org/10.1111/j.1524-4725.1979.tb00765.x Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume5, Issue11November 1979Pages 844-844 RelatedInformation

AK Herculis ? An atypical W UMa-type system

AK Herculis is a contact binary of spectral class F with a number of obvious peculiarities such as a displacement of secondary eclipse from phase 0 . P 500, unequal heights of the maxima, and a possibly sinusoidal (≃60 yr) period variation. The light curve is variable and shows erratic short-term behavior, although the latter effects are not unusual for a short period contact binary. Here we present new photoelectric light curves in theB andV passbands and derive several new times of minima. The new observations are compared graphically with seven earlier light curves. We analyzed the new observations and those by Bookmyer (1972) by the method of differential corrections. We find that the temperature difference between components is too large (≃1000 K) for AK Her to be considered a normal W UMa-system, but too small to allow a detached configuration obeying the mass-luminosity law. The solutions of both series of observations clearly indicate a contact configuration. Other unusual findings include a bolometric albedo greater than 2, and rather low values for the limb-darkening coefficients. We offer some possible reasons for these peculiarities. The mass ratio seems well determined from the photometry and is about 0.26, which is much lower than assumed in most earlier papers. The brightness and color of the known visual companion, ADS 10408B, were found by the differential corrections program. They agree, within observational error, with values found directly at the 200-in. telescope by Eggen, despite the fact that the B component contributes only a few percent of the light of the multiple system. The suggestion by Schmidt and Herczeg (1959) that a fourth body is responsible for the sinusoidal period variation seems stronger now than when first proposed. To encourage a search for this hypothetical component, we have tabulated expected values for its angular separation and relative mass with respect to the eclipsing pair, as well as the amplitude of the expected variable proper motion of the eclipsing pair. Discovery as a visual component seems impossible with present means, but the variable proper motion should be detectable. Thus we suggest that ADS 10408A (AK Her) be observed astrometrically. If a search for the predicted variable proper motion proves negative, mass transfer would remain the only plausible mechanism to explain the period change. We advance a different reason than did Schmidt and Herczeg to explain the phase lag of secondary eclipse.

Seepage of Steady Rainfall through Soil into Ditches of Unequal Water Level Heights

AbstractA theoretical solution and numerical results for the seepage of steady rainfall into soil laying above an impermeable layer and drained by ditches of unequal water level heights is obtained for the ditches just reaching or penetrating into the impermeable layer. This is done by using a finite series of orthonormal functions generated from products of trigonometric and hyperbolic functions. The theoretical solution gives the potential function and stream function for a range of water level heights, ditch spacings, and a range of ratios R/K of rainfall rate R to hydraulic conductivity K. If R/K is increased from 0 to 0.05, for 10‐m spacing of ditches and for 1 ditch having water maintained 1 m above the barrier and the other ditch 1.5 m; then the maximum water table height in the soil will increase from 1.50 m to 1.82 m. Also, as R/K increases, the position of the maximum water table height will approach a position midway between the ditches. Flow nets and other results computed for a number of geometries from the theory bring out additional information.

Puente sobre el tramo inferior del Elba, Hamburgo

This bridge joins to Hamburg-Hannover and the Hamburg-Lubeck roadways. It is 411 m long, 30.74 m wide, and has five spans. The main span is 172 m long, and is suspended by cables from two towers, rising 53 m above the bridge pavement. The stiffening; structure of this suspended span consists of a central box and two lateral full web girders, with a uniform depth of 2 ms. The towers support two sets of cables, which rest on supports situated at unequal heights with respect to each other. These supports are so arranged that thermal deformations shall not be excessive nor cause large secondary moments. Most of the bridge elements have been manufactured in the workshops and taken to the site by river transport. The main span has been built by successive overhangs, till the two sides have met together at the crown.

Seepage of leaching water into drainage ditches of unequal water level heights

The theory is developed, and numerical examples are worked out for the seepage of ponded water into equally spaced ditches in homogeneous soil overlying a barrier. Two general cases are solved: (a) unequal depth of water in the drainage ditches and (b) equal depth. For both (a) and (b) the problem is solved for zero depth of ponded water and for finite depth of ponded water; these solutions are quite different. Curves are supplied showing the surface inflow seepage velocity as it varies with distance from a ditch. Near ditches the seepage inflow rate is very high compared with that between ditches, which helps explain why, many times, crops do better when near ditches than when removed from them in reclaimed saline soil.

Mutual Impedance between Vertical Antennas of Unequal Heights

An expression is derived for the resistive and reactive components of the mutual impedance between vertical antennas of unequal heights, located above a perfectly conducting ground. Mutual-impedance curves for typical combinations of antenna heights are plotted for spacings between 0.1 and 1.0 wavelength.

Heat losses due to load current in direct-current armature windings

Designers of alternating-current machinery have long been able to make rapid estimates, by means of published curves, of the heating effect due to current displacement in slot-wound conductors. The wave-shape of the current in the windings of direct-current armatures is complex, since it is rich in harmonics. The estimation of the heating effect due to current displacement in direct-current armatures has hitherto necessitated laborious calculation, for each case on its own merits. The busy designer rarely has the time to carry out such a long process, and it is probable that in most cases guesswork is resorted to.In this paper an attempt is made to provide curves, by the use of which the heating of direct-current armatures may be estimated rapidly. It is believed that results are obtainable with fair accuracy, and with almost the same rapidity as is associated with the estimation of the loss in an alternating-current machine. It is not possible to construct one curve for use in all cases; a “standard” curve is given, which refers to a single-turn full-pitch winding, having 15 slots per pole and 45 commutator segments per pole. Two additional curves give coefficients which enable other full-pitch single-turn windings to be dealt with. The heating ratios so obtained do not differ from those obtained from individual calculations by more than 2 per cent in any practical case. Curves are also given for windings which differ from the standard winding in having (a) two turns per coil, (b) three turns per coil, (c) chording. The question of the critical height of conductor, and the question of the use of unequal heights for the two layers in a slot, are alsotouched upon.It is, perhaps, not generally realized that current displacement is present at all times in a direct-current armature winding; it is not confined to the period of commutation. A set of current-distribution curves has been calculated for one case, to show this.The author hopes to deal with the problem of the rotary convertor, and the problem of unusual winding arrangements designed to reduce heating losses, in a subsequent paper.

Sag calculations for transmission lines

A set of sag formulas is presented, in the form of convergent series which give accurately the results of the hyperbolic catenary formulas. The series are useful for calculating almost any practical transmission line span, long or short. Trial and error methods are not used. First, the sag or deflection is calculated for a given maximum tension in the cable. Then, changes in temperature corresponding to changes in deflection and loading are computed. This procedure is followed whether the supports are at equal heights or at unequal heights. A formula is presented for the deflection from the line joining the supports, when the elevations are unequal. This is useful in sighting from tower to lower, as shown in Fig. 2. A few examples are worked out and some derivations of formulas are given. In the last appendix instructions are given with regard to allowing for the change in weight per ft. with change in length of cable.

Sag Calculations for Transmission Lines

A set of sag formulas is presented, in the form of convergent series which give accurately the results of the hyperbolic catenary formulas. The series are useful for calculating almost any practical transmission line span, long or short. Trial and error methods are not used. First, the sag or deflection is calculated for a given maximum tension in the cable. Then, changes in temperature corresponding to changes in deflection and loading are computed. This procedure is followed whether the supports are at equal heights or at unequal heights. A formula is presented for the deflection from the line joining the supports, when the elevations are unequal. This is useful in sighting from tower to tower, as shown in Fig. 2. A few examples are worked out and some derivations of formulas are given. In the last appendix instructions are given with regard to allowing for the change in weight per ft. with change in length of cable.