# Continuous beam deflection (structural)

1. Apr 14, 2015

### psyclone

1. The problem statement, all variables and given/known data

Using continuous beam theory, constructing BM diagram from points b to c, to calculate the max deflection. I only found a have a single solution, though the BM digram show two points of zero bending. I can provide the solution.

[edit: Rb = 685 N]

2. Relevant equations

d2v/dx2=-M(x)/ (IE)

3. The attempt at a solution

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Last edited: Apr 14, 2015
2. Apr 14, 2015

### SteamKing

Staff Emeritus
The point of max. deflection within a span will not occur where the BM is zero, it will occur close to where the BM is a maximum.

If you had a single beam which was fixed at both ends with an evenly distributed load applied, there would be two points where the BM = 0, but obviously, the maximum deflection would occur in the center of the beam.

If you were to make a rough sketch the deflected shape of this beam with its loading, you would see that there should be only one point in each span where the deflection will be a maximum or minimum.

3. Apr 14, 2015

### psyclone

Obviously, max deflection can not occur at BM = 0. In this case the fixed moments are not equal, therefore it won't occur at centre of beam.

Given, I've used 'three moment equation(s)' to arrive at the given moments at b and c, and reaction at b (reaction b is under the support b).

My question is, given the manner in which I've formulated the M(x) equation. Is it correct- given I have fixed unequal (in this case) BM's at points b and c, with a free moment due to dist load?