Moment area method
From StructuralWiki
The method for finding deflections in a framed structure by use of the moment area curve.
Contents |
First Theorem
.gif)
Picture illustrating the 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
Picture illustrating the 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
| Home > Topics > Traditional Analysis Methods e | |
| Fundamentals | Traditional analysis methods · Section properties · Mohr's Circle · Interaction diagram |
| Theory | Elasticity equations |
| Forces and Stresses | Torsion · Flexure · Shear · Principal stress |
| Basic Statics | Beam equations · Moment area method · Vereschagin's rule · Stiffness matrix · Fixed end moments · Determinate statics · Indeterminate statics · Maxwell's theorem of reciprocal displacements · Betti's law |
| Influence lines · Muller-Breslau principle | |
| Basic Dynamics | Damping · Mass matrix · Damping matrix |
| Energy Methods | External work and strain energy · Principle of work and energy · Virtual work method · Unit load method · Castigliano's Theorem |
| Approximate Methods | Moment distribution method |
| Graphical | Cremona Diagram |
| See Also | Computational analysis methods |
| Related Categories | Traditional Analysis Methods |
