Equivalent lateral force

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... 

In the 2003 NEHRP Recommended Provisions (BSSC 2004) for buildings with passive dampers, and for the equivalent lateral force (ELF) analysis (linear static analysis) specifically, the response is defined by two modes the fundamental mode and the residual mode, which is used to approximate the combined effects of higher modes. For response spectrum analysis, higher modes are... 

Whittaker AS, Constantinou MC, Oscar MR, Johnson MW, Chrysostomou CZ (2003) Equivalent lateral force and modal analysis procedures of the 2000 NEHRP provisions for buildings with damping systems. Earthq Spectra 19(4) 959-980... 

The analysis of isolated buildings is generally conducted by one of three possible methods equivalent lateral force (static) analysis, response spectmm analysis, and response history analysis. 

Equivalent Lateral Force Procedure The simplest analysis procedure is the equivalent lateral force (ELF) procedure, which is analogous to the static design procedures for conventional structures. In this procedure, the 5 % damped design spectral acceleration for a site at a period of 1 s, Sjji, represents the design input. 

Some destmctive earthquakes motivated several communities to adopt codes with different percentages for the seismic coefficient C. Later the equivalent static lateral force was based on the seismic zone factor, building period, building weight, and lateral resisting system type. These factors are still being refined and used to estimate the equivalent lateral force (Mitchell et al. 2010). 

The classification of a structure as regular or irregular affects several aspects of the design and analysis such as the permission to use the equivalent lateral force, the behavior factor, and the type of models for analysis. 

The maximum displacement and the equivalent lateral force of the jth storey will be... 

Alternatively, the maximum values of the member forces due to the nth mode can be obtained by static analysis by loading the structure with the maximum equivalent lateral forces of Eq. 19. The calculation would be... 

Another approach to obtain the modal displacements is through applying the equivalent lateral forces of Eq. 20. For the first mode, the calculation will be... 

The equivalent lateral forces are applied on the structure to the yield the modal displacements ... 

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,... 

Fig. 17 Typical lateral force-temperature curves for the PMMA brush (Mn = 45400, Mw/Mn <1.2, a = 0.8 chains nm ) and an equivalent spin-coated film at the scanning rate of 10" nms . Reproduced with permission from [148] (Copyright 2003 The Society of Polymer Science, Japan)...

Figure 11.9 Friction force microscope pictures (a, b) of a graphite(OOOl) surface as obtained experimentally with FFM and results of simulations (c, d) of the stick-slip friction using a two-dimensional equivalent of the Tomlinson model. The friction force parallel to the scan direction (a, c) and the lateral force perpendicular to the scan direction (b, d) are shown. The scan size is 20 Ax 20 A. Pictures taken from Ref. [481] with kind permission from R. Wiesendanger.

Equation 5.128 expresses a condition for equivalence between the membrane and detailed models with respect to the lateral force. To derive the normal force balance we consider a parcel of unit area from the film surface in the detailed approach. Because the pressure in the outer phase Pq is larger than the pressure inside the liquid, P the mechanical equilibrium at the film surface is ensured by the action of an additional disjoining pressure, U h), representing the surface force per unit area of the film surfaces ... 

In a direct attack upon the radial migration problem in essentially its full generality, Cox and Brenner (C18) succeeded in obtaining a first-order solution of the Navier-Stokes and continuity equations for the motion of a rigid spherical particle immersed in a Poiseuille flow within a circular tube of finite radius. No couple acts on the particle, so it is free to rotate. It is presumed in the analysis that the sphere center moves parallel to the tube axis. The lateral force required to maintain the sphere at a fixed distance from the axis is computed and converted into an equivalent radial migration velocity by application of Stokes law to this sidewise motion. 

The origin of lateral force has not been completely understood yet because the lateral force reflects many properties of sample surface. The results of LFM measurement do not al vays have intuitive explanation, the counterintuitive results in the asymmetric LFM measurement have been obtained in the system of thiolipid monolayer ( ). In the case of PE single crystal, the molecular tilt direction was equivalent in four sectors of one HDPE lamellar single crystal (4). However, the folding direction of HDPE chain on the surface in adjacent sectors of HDPE single crystal seems to be different. Therefore, it is reasonable to consider that the anisotropy of the lateral force in our experiment was due to the difference in folding direction of HDPE chain. 

Equivalent Static Elastic Lateral Force Method... 

Equivalent seismic force Lateral seismic force Seismic base shear, Seismic design Seismic force distribution... 

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. 

Equivalent Static Analysis of Structures Subjected to Seismic Actions, Fig. 1 Equivalent lateral shear force... 

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