Moment area method
From StructuralWiki
The method for finding deflections in a framed structure by use of the moment area curve.
Contents |
First Theorem
Theorem 1: The change in slope between any two points on the elastic curve equals the area of the M/EI diagram between these two points.
where
- M moment
- EI flexural rigidity
- ... change in slope between points A and B
- A, B ... points on the elastic curve
Second Theorem
Theorem 2: The deviation of the tangent at point B on the elastic curve with respect to the tangent at point A equals the "moment" of the diagram between points A and B computed about point A (the point on the elastic curve), where the deviation is to be determined.
where
- M moment
- EI flexural rigidity
- ... deviation of tangent at point B with respect to the tangent at point A
- ... centroid of M/EI diagram measured horizontally from point A
- A, B ... points on the elastic curve
References
- Russel C. Hibbeler: Structural Analysis, 3rd Edition, Prentice Hall, 1995, chapter 8, p. 354-569, ISBN 0-02-354041-9
External links
- Deflection of Cantilever Beam by Area Moment Method
- Deflection of Simply Supported Beam by Area Moment Method
- Colin Caprani: Structural Analysis III The Moment Area Method – Mohr’s Theorems (lecture notes), 2007
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