# Homework Help: Elastic curve of cantilever beam

1. Apr 9, 2010

### chris54

1. The problem statement, all variables and given/known data
Using method of integration, determine the elastic curve for the beam and calculate the total deflection at a point A (end) of the beam. Use EI as a constant.
See word document attached with diagram.

2. Relevant equations
EIV''(x) = - M(x)

3. The attempt at a solution
I know how to integrate to get the deflection formula but I'm not sure how to calculate M(x) with the moment at the free end.
Is it M(x) = -w/2(L-x)^2 + M(a)(x/L)
or M(x) = -w/2(L-x)^2 + M(a)

Why do some problems in my textbook (Mechanics of materials, Gere) include the support reactions in M(x) and others don't? Do I need to include the support the reactions?

Also will my answer be in meters e.g. v = 100m/EI ?

Any help is much appreciated.
Thanks.

#### Attached Files:

• ###### Cantilever beam.doc
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2. Apr 9, 2010

If there's a moment on the free end of the beam, the moment diagram M(x) is constant, right? You can set your coordinate system with a positive direction from the free end to the fixed end, and then use integration to determine w(x). You need a boundary condition to find the constant of integration, which actually equals the deflection at the free end.

3. Apr 9, 2010