Moment area method

From StructuralWiki
Jump to: navigation, search

The method for finding deflections in a framed structure by use of the moment area curve.

Contents

First Theorem

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.


\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx

where

  • M moment
  • EI flexural rigidity
  • \theta_{AB} ... 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 M/EI diagram between points A and B computed about point A (the point on the elastic curve), where the deviation t_{A/B} is to be determined.


t_{A/B} = {\int_A}^B \frac{M}{EI} \bar{x} \;dx

where

  • M moment
  • EI flexural rigidity
  • t_{A/B} ... deviation of tangent at point B with respect to the tangent at point A
  • \bar{x} ... 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

 

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
Personal tools
Namespaces

Variants
Actions
Navigation
administration
Toolbox
Related Sites
Excel for Engineers at ExcelCalcs.com
Advertising
HSE Contractors
  

TOPlist