Moment area method: Difference between revisions
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The method for finding [[deflection|deflections]] in a framed structure by use of the [[moment area|moment area curve]]. | The method for finding [[deflection|deflections]] in a framed structure by use of the [[moment area|moment area curve]]. | ||
== First Theorem == | |||
<tex> | |||
\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx | |||
</tex> | |||
'''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. | |||
== Second Theorem == | |||
<tex> | |||
t_{A/B} = {x} {\int_A}^B \frac{M}{EI}\;dx | |||
</tex> | |||
'''Theorem 2:''' The deviation of the tangent at point B on the elatic curve with respect to the tangent at point A equals the "moment" of the <tex>M/EI</tex> diagram between points A and B computed about point A (the point on the elastic curve), where the deviation <tex>t_{A/B}</tex> is to be determined. | |||
== References == | |||
[[Category:Glossary]] | [[Category:Glossary]] | ||
[[Category:Analysis and Design Methods]] | [[Category:Analysis and Design Methods]] | ||
Revision as of 05:22, 20 March 2009
The method for finding deflections in a framed structure by use of the moment area curve.
First Theorem
<tex> \theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx </tex>
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.
Second Theorem
<tex> t_{A/B} = {x} {\int_A}^B \frac{M}{EI}\;dx </tex>
Theorem 2: The deviation of the tangent at point B on the elatic curve with respect to the tangent at point A equals the "moment" of the <tex>M/EI</tex> diagram between points A and B computed about point A (the point on the elastic curve), where the deviation <tex>t_{A/B}</tex> is to be determined.