(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the slope and deflection at the point x on the beam (attached image)

2. Relevant equations

Bending stiffness equation: EIV'' = M

where E = young's modulus, I = second moment of area, V = deflection, M = moment

3. The attempt at a solution

By taking moments about both supports I have determined the reactions at the left and right supports to be b/(a+b) and a/(a+b) respectively.

Cutting the beam between point x and the right hand support:

EIV'' = M = bx/(a+b) - <x-a> (where <> are macaulay brackets)

EIV' = bx^2/2(a+b) - (<x-a>^2)/2 + A

EIV = bx^3/6(a+b) - (<x-a>^3)/6 + Ax + B

Here's where I get confused:

Using V=0 at the boundary conditions (x=0 and x=a+b) to find the integration constants, B is found to be 0 but A always comes out as a complicated fraction that I can't seem to simplify to get anything sensible.

I know the final answers are supposed to be: V' = (ab/3)((a-b)/(a+b))

and V =-a^2b^2/3(a+b)

I have worked through the question several times and I can't figure out where I'm going wrong so any help would be much appreciated.

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

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Beam deflection problem

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