Conjugate beam Problem no:6
Example 5: determine the force F, so the displacement at C will be zero assuming EI constant over the beam length?
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.
To draw M/EI, we need to determine A and B's reaction for the real beam.
So the shear and moment diagram will be as shown in figure no:4.
Now, we will take section B-C. to determine FB using the equilibrium equation(MC=0).
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.
apply triangle similarities, and you will get