Calculate reaction in hyper static beam

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Discussion Overview

The discussion revolves around calculating the reaction forces in a hyperstatic beam, specifically focusing on the reaction at point A (MA) and the moment at point B. Participants are examining their calculations and comparing them to a reference answer from a textbook.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents their calculations for the reaction By and the moment Mb, noting a discrepancy with the textbook answer.
  • Another participant questions the clarity of the original question and the context of the textbook answer.
  • A participant points out that substituting b=L into the textbook answer yields an incorrect result, suggesting a potential issue with the book's answer.
  • One participant expresses uncertainty about their own answer and the complexity of hyperstatic structures, seeking confirmation from others.
  • Another participant suggests that showing all calculations might help identify any algebraic errors in the original post.
  • A later reply indicates that the participant has resolved their confusion and found the correct answer, though they are unsure of their previous mistake.

Areas of Agreement / Disagreement

Participants express uncertainty about the correctness of their answers and the textbook answer, with no consensus reached on the validity of the calculations or the reference material.

Contextual Notes

There are unresolved issues regarding the assumptions made in the calculations, the definitions of variables, and the potential for algebraic errors in the participants' work.

PythagoreLove
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Homework Statement


Calculate the reaction MA

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 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}].

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


PytLov
 
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If the answer in the book is "In the book, the final answer is wb28L2[2L2−b2].", what is the question, exactly?
 
Sorry, I should have added: If you put b=L, in the book answer, you get the wrong answer wL^2/8
 
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
 
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.
 
Well, I was writing my solution, and now I get the good answer... no idea what was my mistake. But thank you anyway.

PytLov
 

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