Lateral force method

Lateral Force Method. Lateral forces are obtained at low scan velocity while the temperature is increased. Tg is determined as the increase in the lateral force or friction coefficient (19). 

From our results, we can exclude any large hydrostatic pressure effects induced by contact mechanical SPM approaches such as lateral force or shear modulation methods. The lateral force method has strong potential for heterogeneous surfaces. On homogeneous surfaces, however, the shear modulation mode is much more reliable without die difficulties of calibrating the load and scan velocity dependence. In figure 4, tip response vs. tenq>erature measurements on thick (476 nm) PS (M 90 k) films are presented for various loads. As the temperature is increased, we see a distinct increase in the ancqplitude response. We identify Tc as the intersection between the two line fits. The precision of the value is estimated to 2 K. At an applied load of... 

At the turn of the nineteenth to twentieth century, Riki Sano was getting his PhD from the University of Tokyo on Seismic Design Concept for Building Structures, along with Tachu Naito, his student Sano was to be instrumental in the development of the Japanese equivalent lateral force method. Their work came to fruition after the 1923 Great Kanto or Tokyo Earthquake of 1923, when the 1924 Urban Building Law Enforcement Regulations were passed. It used a 10 % lateral force factor (shindo) applied... 

Equivalent Static Elastic Lateral Force Method... 

The equivalent static lateral force method is a simplified technique to substitute the effect of dynamic loading of an expected earthquake by a static force distributed laterally on a stmcture for design purposes. The total applied seismic force V is generally evaluated in two horizontal directions parallel to the main axes of the building (Fig. 1). It assumes that the budding responds in its fundamental lateral mode. For this to be true, the building must be low rise and must be fairly symmetric to avoid torsional movement under ground motions. The stmcture must be able to resist effects caused by seismic forces in either direction, but not in both directions simultaneously. 

The simplest way to do so is using the equivalent static lateral force method, even though its uses are limited by various conditions, related to the site and the stmcture itself and which are acknowledged and detailed below. Within this method, a seismic coefficient is applied to the mass of the stmcture to produce the lateral force that is approximately equivalent in effect to the dynamic loading of the expected earthquake. 

The equivalent static lateral force method is a simplified technique to substitute the effect of dynamic loading of an expected earthquake by a static force distributed laterally on a structure for design purposes. The total applied seismic force V is generally evaluated in two horizontal directions parallel to the main axes of the building. 

Lateral force method Modal analysis Modal response spectrum analysis Modal superposition Response spectrum Seismic performance assessment... 

Eurocode 8, linear elastic analysis can be performed either with (a) the lateral force method of analysis for buildings meeting specific conditions or (b) with the modal response spectrum analysis, applicable to all types of builduigs and being the reference method for obtaining seismic response estimates. 

According to the lateral force method of analysis, a lateral load pattern that follows the first mode is applied (e.g., Eq. 35). In Eurocode 8, the method is applicable only if the fundamental period of vibration is less than 2s or 4Tc, where Tc is the comer period of the design spectrum. A second condition that also has to be satisfied is that the stiucture should meet the criteria for regularity in plan. Different criteria may be found in other codes. The modal response spectrum analysis is reconunended for all other cases, with the only exception of buildings with seismic isolation provided by highly nmilinear devices. Practically every design code in the world uses these two methods for linear elastic analysis and recommends criteria to determine if their applicable. 

Regarding the method of analysis, according to ASCE/AWEA RP2011 a fully coupled time-domain analysis and decoupled analyses based on equivalent lateral force method or modal response spectrum method are acceptable, as permitted by the local building code. For the specific implementation of each method of analysis, the local building code or ASCE/SEl 7-05 is referred to. In particular, if the equivalent lateral force procedure is used, the vertical distribution of seismic forces should be calculated based on the procedure given in ASCE/SEl 7-05,... 

An important consideration for the direct physical measurement of adhesion via pull-off measurements is the influence of the precise direction of the applied force. In AFM the cantilever does not usually lie parallel to the surface, due to the risk that another part of the cantilever chip or chip holder will make contact with the surface before the tip. Another problem relates to the fact that the spot size in the optical beam deflection method is usually larger than the width of the lever. This can result in an interference effect between the reflection from the sample and the reflection from the cantilever. This is reduced if the cantilever and sample are not parallel. Most commercial AFM systems use an angle in the range of 10°-15° between the sample and the cantilever. Depending on this angle and the extent to which the cantilever is bent away from its equilibrium position, there can be a significant fraction of unintentional lateral forces applied to the contact. 

In 1987 Mate et al. [468] used, for the first time, an atomic force microscope (AFM) to measure friction forces on the nanometer scale (review Ref. [469]). This technique became known as friction force microscopy (FFM) or lateral force microscopy (LFM). To measure friction forces with the AFM, the fast scan direction of the sample is chosen perpendicular to the direction of the cantilever. Friction between the tip and the sample causes the flexible cantilever to twist (Fig. 11.7). This torsion of the cantilever is measured by using a reflected beam of light and a position-sensitive detector in the form of a quadrant arrangement of photodiodes. This new method made it possible for the first time to study friction and lubrication on the nanometer scale. 

Fig. 5. a Schematic representation of the SFM set-up using the optical beam deflection method, b When the tip interacts with the sample surface, the cantilever exhibits deflection perpendicular to the surface as well as torsion parallel to the surface plane. The normal force Fn and the lateral force FL corresponds to the force components which cause the deflection and torsion, respectively. Both responses are monitored simultaneously by the laser beam which is focused on the back side of the cantilever and reflected into a four-quadrant position sensitive detector (PSD)... 

Abstract. Quantitative measurements of lateral force required for displacement of SWNTs bundle on the surface of highly oriented pyrolytic graphite with the help of atomic force microscope (AFM) were performed in real time . New method of quantitative calibration of lateral forces was used for interpretation results of lateral force microscopy (LFM). It allows us to receive numerical values of adhesion force of bundle to substrate easy and without specific equipment. 

Atomic force microscopy [6, 7] is one of the most suitable methods for research carbon nanotubes. AFM allows to receive not only a relief of the studied sample, but also distribution of mechanical characteristics, electric, magnetic and other properties on its surface. With the help of AFM, controllable manipulation of individual CNTs and CNTs bundles became possible. In this paper we report our approach to manipulating SWCNTs bundles with lateral force microscopy. LFM gives possibility to study lateral forces that probe acts upon bundles. In spite of good visualization of LFM, its lack is absence of reliable techniques of quantitative interpretation of results. The new way of calibration developed ourselves has allowed to pass from qualitative estimations to quantitative investigations [8], The given calibration technique is much more exact, than others known till now [9, 10], and does not assume simplification. With the help of new technique we may study adhesion of bundles to substrate and adhesion of CNTs in bundle qualitatively in real time more easy way. This result will provide new possibilities for nanotube application. 

To define absolute value of force acted during the experiment we need recalculate DFL and LF signals measured in nA into normal load force and lateral force using natural force units (nN). Method of normal load calibration is well known ... 

Calculation of the critical lateral force is more complicated because traditional LFM does not provide us with easy method to translate current units into force ones. There is no way to define the factor of proportionality until calibration algorithm was developed recently by ourselves [8], The required coefficient depends on design of a microscope, adjustment of the optical system, torsion force constant kL of cantilever and tip height lnp. 

Methods of AFM, by means of a new method of calibration of lateral forces, allow to quantitavely investigate various mechanical characteristics of nanotubes. We have demonstrated one of applications of this method and determined critical lateral force that displace bundle of nanotubes over HOPG surface. The advantage of the work is possibility of real time observation of moment of nanotubes displacement, so relatively exact value of the lateral force caused such event can be estimated. 

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