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.
for the BaSICS investigators and the BRICNet members IMPORTANCE Slower intravenous fluid infusion rates could reduce the formation of tissue edema and organ dysfunction in critically ill patients; however, there are no data to support different infusion rates during fluid challenges for important outcomes such as mortality.OBJECTIVE To determine the effect of a slower infusion rate vs control infusion rate on 90-day survival in patients in the intensive care unit (ICU). DESIGN, SETTING, AND PARTICIPANTS Unblinded randomized factorial clinical trial in 75 ICUs in Brazil, involving 11 052 patients requiring at least 1 fluid challenge and with 1 risk factor for worse outcomes were randomized from May 29, 2017, to March 2, 2020. Follow-up was concluded on October 29, 2020. Patients were randomized to 2 different infusion rates (reported in this article) and 2 different fluid types (balanced fluids or saline, reported separately).INTERVENTIONS Patients were randomized to receive fluid challenges at 2 different infusion rates; 5538 to the slower rate (333 mL/h) and 5514 to the control group (999 mL/h). Patients were also randomized to receive balanced solution or 0.9% saline using a factorial design.
MAIN OUTCOMES AND MEASURESThe primary end point was 90-day survival.RESULTS Of all randomized patients, 10 520 (95.2%) were analyzed (mean age, 61.1 years [SD, 17.0 years]; 44.2% were women) after excluding duplicates and consent withdrawals. Patients assigned to the slower rate received a mean of 1162 mL on the first day vs 1252 mL for the control group. By day 90, 1406 of 5276 patients (26.6%) in the slower rate group had died vs 1414 of 5244 (27.0%) in the control group (adjusted hazard ratio, 1.03; 95% CI, 0.96-1.11; P = .46). There was no significant interaction between fluid type and infusion rate (P = .98).CONCLUSIONS AND RELEVANCE Among patients in the intensive care unit requiring fluid challenges, infusing at a slower rate compared with a faster rate did not reduce 90-day mortality. These findings do not support the use of a slower infusion rate.
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