Continuous beam deflection (structural)

[psyclone]

Homework Statement

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: R_b = 685 N]

Homework Equations

d²v/dx²=-M(x)/ (IE)

The Attempt at a Solution

please find attached

[edit: please find revised attachment]

 

[SteamKing]

Homework Statement

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: R_b = 685 N]

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.

 

[psyclone]

Thank-you for your post.

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?

Your thoughts.

[edit] Please let me know if you need more information [edit]