Derivation of Supports Moments Coefficients for Prismatic Continuous Beams by Elastic Analysis

Research Area: Volume 4,Issue 4, July 2015 Year: 2015
Type of Publication: Article Keywords: Continuous Beams, Elastic Analysis, Moment Coefficients, Moment Distribution Method
  • Fathelrahman M. Adam
  • A. E. Hassaballa
  • H. E. M. Sallam
Journal: IJEIR Volume: 4
Number: 4 Pages: 613-622
Month: July
In this paper an elastic analysis was adopted in order to calculate the negative moment coefficients for the continuous beams of different number of spans form 2-spans to 10-spans and with different span lengths. The difference of spans adopted on the bases of spans ratio between the longest span to the shortest span on the continuous beam. The lengths of spans were taken in sequences starting with shortest span and the subsequent spans increase by constant rate. Eleven ratios were taken starting from 1.0 (equal spans) to 2.0 by constant rate of 0.1. The method of analysis used here is the moment distribution methods used to analyze ninety nine models of continuous beams gained by a combination between the different number of spans and the different spans ratios and all calculations were done using spreadsheets. A uniformly distributed load full spans was applied throughout all the models. The coefficients of negative moments have been calculated according to the negative moments at supports obtained for the various models and a comprehensive data were gained according to that. These data were analyzed and summarized by taking the average of the convergent values controlled and measured using standard deviation. The final filtered values of coefficients were listed in Tables and also explained graphically. A modification for the values of moment coefficients has been done for beams of 3-spans, 4-spans and 5-spans in order to consider the case of difference in spans lengths take place randomly differ than the adopted for the models taking into consideration the modification limited to the span ratio for the adjacent spans not more than 1.5.A verification has been done for the values of coefficients calculated by comparing the moment calculated using these coefficients with the moments gained by using PROKON software program, these all done for different examples taking on different spans numbers with different spans ratios. percentages differences between the two values for each moment were calculated as errors and most of the errors values fall less than 3%. Few of the errors increases than 3% to 9% in limited cases and these values as generally considered acceptable as these moments considered as approximate moments and as the larger errors always coincide with the larger span ratio between adjacent spans and this case is a rare practically.

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