Determining reaction of indeterminate beam structure

[thundersword181]

Homework Statement

Homework Equations

The Attempt at a Solution

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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:

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:

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:

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

 

[KataKoniK]

,Thank you for your detailed response and for sharing your work with us. Your process seems to be correct and you have accounted for the necessary variables in your calculations. However, I would recommend double-checking your work and equations to ensure accuracy. It is also important to consider any assumptions or simplifications you may have made in your approach.

Additionally, I would suggest seeking guidance from a colleague or professor to review your work and provide feedback. Sometimes, a fresh pair of eyes can catch any errors or offer new insights.

Overall, I commend your effort and dedication in solving this problem. Keep persevering and I am sure you will find the correct solution. Best of luck!