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Determining reaction of indeterminate beam structure

  1. Nov 30, 2017 #1
    1. The problem statement, all variables and given/known data

    ewmbHA.png

    2. Relevant equations


    3. The attempt at a solution

    As this is an indeterminate structure with degree of redundancy 2, I have released support B & C. I then draw the BMD M0 of the Primary structure as well as BMD m1 and m2 of unit load system acting on B & C as follow:
    zM5myh.jpg
    I have also written the compatibility equation which I will need to find out the values in order to solve for reactions at B & C.

    Next up I forms formula that calculate the bending moment on diagram M0, m1 and m2 with x running from 0 to 12 (left to right), as shown, this is derived using free body diagram to determine moment:

    26wTrb.jpg
    Here I look to make the formula strictly gives positive value, knowing that when I do product integrals of M0m1 and M0m2 I need to multiply them by -1 due to one BM being in sagging and another being hogging. m1^2, m2^2 and m1m2 should give positive values as both BMD are on the same side.

    Next up is my calculation process to determine all the necessary variables that lead to the simultaneous equations to solve for reactions at B & C, as shown at the bottom of the right page:

    NaltN7.jpg

    This entire process leads to reaction at B being 0.01784 kN and C being 18.598 kN. This result does not make me feel confident at all because I feel the reaction at B is too low even when taking into account the effect of settlement.

    Are my process correct? Have I made any mistakes? Please help me out (I have worked on this problem for a week and it is killing me...)

    Thank you very much,

    Sincerely
     
  2. jcsd
  3. Dec 6, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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