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Conjugate beam Problem no:6

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 Example 5: determine the force F, so the displacement at C will be zero assuming EI constant over the beam length?

Figure 1

The first step is to draw the M/EI diagram for the real beam. The conjugate beam will be loaded with M/EI diagram for the real beam. The pin at A will stay the same for the conjugate beam while the internal roller at B will change to an internal pin for the conjugate beam. The free end at point C will become a fixed end. So the conjugate beam will be as shown in figure no:2. 
Figure 2


To draw M/EI, we need to determine A and B's reaction for the real beam.

Figure 3

So the shear and moment diagram will be as shown in figure no:4.
Figure 4





Now, we will take section B-C. to determine FB using the equilibrium equation(MC=0).













Figure 5

Now, we will take section A-B. to determine FB using the equilibrium equation. The FB computed from section A-B will be equaled to Fb calculated from section B-C to determine F related to P.










To calculate a1 and a2, we will use the triangle similarity.

a2=a1-a 

apply triangle similarities, and you will get
Figure 6



Substitute a1 and a2 in the previous equation and rearrange it. You will get 3 order equation:


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My name is Mohammad Hamdan, and I am a Civil/bridge Engineer with extensive professional background and experience in the field of construction. I have 10+ years of experience in the construction field. During my professional career, my emphasis has been placed on structural projects, mainly bridges, infrastructure and roads. Reading and practicing the design of structures is my passion.i was lucky to be a part of a big team that executed major highway interchanges. I believe in spreading the knowledge, thus, i compose these courses to share my experience and knowledge. My course focuses on the practical side of construction field. On other word, i am sharing some of what new engineers need to know about construction field. Beside working on construction field, i love writing some articles on my website ( curious civil engineer) Moreover, i wrote some engineering papers, you can check them  by searching my name on Google (Mohammad mamon Hamdan)