SUMMARYA simple method which can be applied in seismic codes to determine the critical angle of seismic incidence and the corresponding peak response of structures subjected to two horizontal components applied along any arbitrary directions and to the vertical component of earthquake ground motion, is proposed in this paper. The seismic components are given in terms of response spectra that may be equal or have different spectral shapes. The structures are discrete, linear systems with viscous damping. The method, which is based on the response spectrum method of analysis, requires the solution of standard cases of seismic analysis and therefore can be easily implemented in standard computer programs. For the general case of three arbitrary response spectra, the method requires the solution of five seismic loading cases, two for each horizontal component and one for the vertical component. If the horizontal response spectra have the same shape or if there is only one horizontal component, it is then required to solve just two seismic loading cases for the horizontal components and one for the vertical component. It can be shown that the formulas derived for the critical angles and the peak response are essentially identical to the ones obtained earlier by Smeby and Der Kiureghian using random vibration theory.The application and the accuracy of the method is illustrated by means of numerical analysis of buildings, comparing the results with those obtained using other proposed methods. For the specific case of two horizontal spectra with identical shape and an arbitrary vertical spectra, the critical angle neither depends on the spectral ratio of the two horizontal components nor on the vertical spectrum. For the special case of equal horizontal spectra, the structural response does not vary with the angle of incidence and it is an upper bound for all possible responses.

SUMMARYThis paper aims to develop an improved understanding of the critical response of structures to multicomponent seismic motion characterized by three uncorrelated components that are deÿned along its principal axes: two horizontal and the vertical component. An explicit formula, convenient for code applications, has been derived to calculate the critical value of structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. The critical response is deÿned as the largest value of response for all possible incident angles. The ratio rcr=rsrss between the critical value of response and the SRSS response-corresponding to the principal components of ground acceleration applied along the structure axes-is shown to depend on three dimensionless parameters: the spectrum intensity ratio between the two principal components of horizontal ground motion characterized by design spectra A(Tn) and A(Tn); the correlation coe cient of responses rx and ry due to design spectrum A(Tn) applied in the x-and y-directions, respectively; and ÿ = ry=rx. It is demonstrated that the ratio rcr=rsrss is bounded by 1 and (2=1 + 2 ). Thus the largest value of the ratio is √ 2, 1.26, 1.13 and 1.08 for = 0, 0.5, 0.75 and 0.85, respectively. This implies that the critical response never exceeds √ 2 times the result of the SRSS analysis, and this ratio is about 1.13 for typical values of , say 0.75. The correlation coe cient depends on the structural properties but is always bounded between −1 and 1. For a ÿxed value of , the ratio rcr=rsrss is largest if ÿ = 1 and = ± 1. The parametric variations presented for one-storey buildings indicate that this condition can be satisÿed by axial forces in columns of symmetric-plan buildings or can be approximated by lateral displacements in resisting elements of unsymmetrical-plan buildings.

The paper in discussion [1] presents an interesting comparison of various combination rules for maximum response calculation under two-component horizontal earthquake motions. The authors should be commended for their contribution, in particular for the error bounds they have presented for each of the combination rules examined.The purpose of this discussion is to bring to the authors' attention some past pertinent work by the writer [2], who addressed not the same but a similar problem 20 years ago, and also to suggest one way for making the critical response approach compatible with current codes and design practices. Apparently that publication has escaped the attention of the authors.In that work, eight modal-spatial combination rules were examined, including those by the authors, with the exception of the CQC rule, which had just appeared in a 1979 Berkeley report. However, the double summation rule, very similar to the CQC, had been considered, but gave results very close to the SRSS rule, since the structures examined had no close lower modes.While the present paper addresses the problem of maximum value of any response parameter under two-component horizontal motions acting along the worst possible direction for the parameter, Reference [2] deals with the more traditional problem of peak response under three component earthquake motions acting along three principal structural axes. Although maximum member response, considering all possible earthquake incident angles is certainly of practical interest, a structure should not be designed with each of its members sized to such maximum forces, as this would lead to an over-designed but not necessarily safer structure. The structure would be safer if its response remained elastic. However, under design level earthquakes the structure will respond inelastically and its safety margins will be determined by capacity design procedures requiring consistent sets of member forces. Thus, before the useful concept of critical response is introduced into practice, it should be made compatible with capacity design procedures.The comparisons in Reference [2] were carried out using results from time history analyses with 30 real, three-component earthquake motions, acting on three di erent structures. In addition, the problem of maximum stresses, which requires proper combination of maximum member forces, thus introducing a third level of uncertainty beyond the modal and spatial * Correspondence to:

INTRODUCCIÓN. Con el advenimiento de la tecnología, el uso de redes sociales se ha convertido en la principal vía para realizar anuncios publicitarios y llegar al consumidor o cliente final, sin embargo, en Ecuador pocas empresas aprovechan estos nuevos canales de publicidad. OBJETIVO. Este artículo describe un estudio documental exploratorio sobre Marketing Digital y dentro de esta área el uso de las redes sociales por pequeñas y medianas empresas (Pymes). MÉTODO. El estudio inició con una revisión bibliográfica en bases de datos científicas sobre estrategias de Marketing Digital. Posteriormente, se buscaron sitios web con observatorios y cifras comerciales en el ámbito de las redes sociales. Finalmente, se identificaron las estadísticas sobre el uso de redes sociales en las Pymes. RESULTADOS. Los resultados reflejaron que el 82% de las Pymes del Ecuador accede a Internet, pero su uso se limita a enviar correos y tareas administrativas. Se identificó que las grandes corporaciones, al disponer de más recursos o equipos responsables de la comunicación aprovechan las redes sociales con verdaderas campañas publicitarias. En este contexto hasta finales de 2017 las redes sociales más utilizadas fueron: Facebook, WhatsApp, Instagram, Twitter y YouTube. DISCUSIÓN Y CONCLUSIONES. El evidente crecimiento de usuarios en estas redes sociales en el Ecuador es quizás, un nuevo reto, que exigirá una reorientación interna y el planteamiento de nuevas formas de relacionarse con sus clientes.

This paper aims to investigate the response spectra characteristics of the principal components of seismic motion, which are required for accurate multicomponent structural analysis. Mean spectra were determined for the three principal uncorrelated acceleration components for an ensemble of 97 earthquake records. The average inclination of the quasi-vertical component from the vertical axis is found to be 11.4°, with a standard deviation of 9.9°. The ratio of the minor and the major quasi-horizontal spectra varies between 0.63 and 0.81, which are lower than the value of 1 commonly used in design codes. Greater differences are found for near-fault motions in the intermediate-period range. The ratio of the quasi-vertical and the major quasi-horizontal spectra varies between 0.34 and 0.69 for far-fault and between 0.3 and 1.33 for near-fault motions, depending on vibration period. Smoothed spectra of the three principal components that can be used in modern multicomponent structural analysis methods are presented.