# Calculate reaction in hyper static beam

1. Feb 24, 2012

### PythagoreLove

1. The problem statement, all variables and given/known data
Calculate the reaction MA

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

2. Relevant equations

3. The attempt at a solution
First I have put the reaction By as an hyper static force. Then I found the deflection in B with the force By as a variable.

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

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

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

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

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

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

2. Relevant equations

3. The attempt at a solution

2. Feb 24, 2012

### pongo38

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

3. Feb 24, 2012

### pongo38

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

4. Feb 24, 2012

### 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

5. Feb 24, 2012

### 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.

6. Feb 24, 2012

### 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