Transcription of The Three-Moment Equation for Continuous-Beam Analysis
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The Three-Moment Equation for Continuous-Beam Analysis
The Three-Moment Equation forContinuous-Beam AnalysisCEE 201L. Uncertainty, Design, and OptimizationDepartment of Civil and Environmental EngineeringDuke UniversityHenri P. GavinSpring, 2009 Consider a continuous beam over several supports carrying arbitrary loads,w(x).Using the moment -Area Theorem, we will analyze two adjoining spans of thisbeam to find the relationship between the internal moments at each of thesupports and the loads applied to the beam. We will label the left, center,and right supports of this two-span segmentL,C, andR. The left span haslengthLLand flexural rigidityEIL; the right span has lengthLRand flexuralrigidityEIR(see figure (a)).
To apply the three-moment equation numerically, the lengths, moments of inertia, and applied loads must be specified for each span. Two commonly applied loads are point loads and uniformly distributed loads. For point loads P L and P R acting a distance x L and x R from the left and right supports,
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