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Conjugate beam Problem no:5

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Example 5: determine the displacement at C and the slope at point B for the beam shown in figure no: 1 considering EI a constant?

Figure 1

 

The support at A for this beam will allow the rotation but no movement, so it is considered a pin, and it will stay the same in the conjugate beam. While the support at B will allow the movement in horizontal direction and rotation, it will be similar to the roller, and it will stay the same in the conjugate beam. So the real beam will be as in figure no:2. And the conjugate beam will be as shown in figure no:3.

Figure 2

Figure 3





To determine the displacement at point C and the slope at B, we need to determine the moment at point C and the shear at point B in the conjugate beam. The conjugate beam will be loaded with M/EI of the real beam, so we need to draw M/EI for the real beam. To draw the M/EI diagram, we need to determine the reaction at point A and point B.

From the symmetry we can know that the reaction FA=FB=P. so the shear moment diagram will be as shown in the figure no:4.

Figure 4



So the conjugate beam will be loaded as shown in the figure no:5. 
Figure 5


From the symmetry the reaction FA=FB. So



 







To determine the displacement at point C, we need to determine the moment, we will take the section A-C. so using the equilibrium equations





















Figure 6

Figure 7




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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)