Calculate reaction in hyper static beam

[PythagoreLove]

Homework Statement

Calculate the reaction M_A

http://alkaspace.com/is.php?i=134123&img=E-3.1.jpg

Homework Equations

The Attempt at a Solution

First I have put the reaction B_y as an hyper static force. Then I found the deflection in B with the force B_y as a variable.

v_b= $\frac{w}{24EI}$(3L⁴-4a³L+a⁴) - $\frac{B_{y}L^{3}}{3EI}$

Then I know that v_b=0 because it is on a reaction. With that I find that
B_y= $\frac{w}{8L^{3}}$[3L⁴-4a³L+a⁴]

Now I just have to calculate the moment with
M_b=(a+b/2)bw-LB_y

My final answer is $\frac{wb^{2}}{8L^{2}}[2L^{2}+6L^{4}-b^{2}]$

In the book, the final answer is $\frac{wb^{2}}{8L^{2}}[2L^{2}-b^{2}]$.

I only have a 6L⁴ that isn't supposed to be here. Please help.


PytLov

 

[pongo38]

If the answer in the book is "In the book, the final answer is wb28L2[2L2−b2].", what is the question, exactly?

 

[pongo38]

Sorry, I should have added: If you put b=L, in the book answer, you get the wrong answer wL^2/8

 

[PythagoreLove]

The question is "what are the reactions" and I gave you the answer of the moment at point A. Maybe the book answer is wrong, it's a book from 1992. But I still don't know if I have the good answer, and I think that hyper static structure is really hard. If someone knows the good answer that would be really nice !


PytLov

 

[pongo38]

Sorry again. If you put b=L then the book is correct. If you could show all your working or references to formulas, then maybe someone would see an algebraic error.

 

[PythagoreLove]

Well, I was writing my solution, and now I get the good answer... no idea what was my mistake. But thank you anyway.

PytLov