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Area-Moment Method Calculate Deflections in Beams

Beam, Deflection, Stress, Strain Equation and Calculators
Strength Mechanical of Materials

Area-Moment Method To Calculate Deflections in Beams

Calculation of deflections and redundant reactions for beams on two supports can be made by the use of the area–moment method. Area– moment method is a semigraphical solution that relates slopes and deflections of the elastic curve to the area under the “M/EI” diagram, and the moment of the area of the “M/EI” diagram respectively.

This method is particularly useful when deflection at a specific point on the beam is required. When deflection and slope curves for the entire length of the beam are desired, the graphical method described by Graphical Integration Analysis Method may be more suitable to use.

Specifically, the slope θ at point A with respect to a tangent line at point B on a beam deflection curve See Beloow) is the area under the “M/EI” diagram between the two points. Expressed mathematically:

Curve and M/EI Diagram Deflection

Example Calculation:

Find:

Calculate the slope and deflection at the free end of a constant EI cantilever beam.

Given:

Solution:

First, by integration:

and deflection at A,

Second

By graphical: Area-Moment Method: