ANALYSIS OF INTERNAL SUPPORT MOMENTS OF CONTINUOUS BEAMS OF EQUAL SPANS USING SIMPLIFIED MATHEMATICAL MODEL APPROACH

Okonkwo, V.O., Aginam, C.H., and Chidolue, C. A.

Department of Civil Engineering

Nnamdi Azikiwe University, Awka

ABSTRACT

This paper developed the mathematical Model for the evaluation of the internal support moments of a uniformly loaded continuous beam of equal span and the number of spans, taking the uniformly distributed load on the beam to be equal for all spans. The internal support moments of a continuous beam with unit uniformly distributed load (UDL) and unit span length were evaluated at different number of spans (n). The result showed that the values of the internal support moments oscillate (alternately increase and decrease) with rapidly diminishing magnitude at every unit increase in the number of spans (n) of the continuous beam. This showed that it is possible to express the values of the internal support moments with a model. The Euler method for linear interpolation was applied repeatedly between subsequent values of the moments at each internal support for different values of number of spans (n) and each internal moment expressed as a series comprising the sum of their initial values and the subsequent increases and decreases to their values as a result of an increase in the number of spans of the continuous beam. The results obtained showed perfect and close comparison with that obtained using Clapeyron’s Method as depicted on the graphs shown in the appendix.

Keywords: Continuous beams, equal Spans, Internal Support moment, Mathematical Model.