moment diagram

Properties of Conjugate Beam

Engr. Christian Otto Mohr

1. The length of a conjugate beam is always equal to the length of the actual beam.
2. The load on the conjugate beam is the M/EI diagram of the loads on the actual beam.

Problem 655
Find the value of EIδ under each concentrated load of the beam shown in Fig. P-655.
 

Problem 654
For the beam in Fig. P-654, find the value of EIδ at 2 ft from R₂. (Hint: Draw the reference tangent to the elastic curve at R₂.)
 

Problem 653
Compute the midspan value of EIδ for the beam shown in Fig. P-653. (Hint: Draw the M diagram by parts, starting from midspan toward the ends. Also take advantage of symmetry to note that the tangent drawn to the elastic curve at midspan is horizontal.)
 

Problem 632
For the beam loaded as shown in Fig. P-632, compute the value of (Area_AB) barred(X)_A. From this result, is the tangent drawn to the elastic curve at B directed up or down to the right? (Hint: Refer to the deviation equations and rules of sign.)
 

Problem 631
Determine the value of the couple M for the beam loaded as shown in Fig. P-631 so that the moment of area about A of the M diagram between A and B will be zero. What is the physical significance of this result?
 

Problem 630
For the beam loaded as shown in Fig. P-630, compute the value of (Area_AB)barred(X)_A . From the result determine whether the tangent drawn to the elastic curve at B slopes up or down to the right. (Hint: Refer to the deviation equations and rules of sign.)
 

Problem 629
Solve Prob. 628 if the sense of the couple is counterclockwise instead of clockwise as shown in Fig. P-628.
 

Problem 628
For the beam loaded with uniformly varying load and a couple as shown in Fig. P-628 compute the moment of area of the M diagrams between the reactions about both the left and the right reaction.
 

Problem 627
For the beam loaded as shown in Fig. P-627compute the moment of area of the M diagrams between the reactions about both the left and the right reaction. (Hint: Resolve the trapezoidal loading into a uniformly distributed load and a uniformly varying load.)