Engineering Mathematics
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moment diagram

Conjugate Beam Method | Beam Deflection

Slope on real beam = Shear on conjugate beam
Deflection on real beam = Moment on conjugate beam

 

Properties of Conjugate Beam

Otto Mohr
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.

Solution to Problem 655 | Deflections in Simply Supported Beams

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

Simple Beam with Two Concentrated Loads

 

Solution to Problem 654 | Deflections in Simply Supported Beams

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.)
 

Simple beam subjected to rectangular loading

 

Solution to Problem 653 | Deflections in Simply Supported Beams

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.)
 

Simple beam with symmetrically placed rectangular load

 

Solution to Problem 632 | Moment Diagrams by Parts

Problem 632
For the beam loaded as shown in Fig. P-632, compute the value of (AreaAB) 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.)
 

Overhang beam with point and rectangular loads

 

Solution to Problem 631 | Moment Diagrams by Parts

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?
 

Overhang beam with moment load at free end

 

Solution to Problem 630 | Moment Diagrams by Parts

Problem 630
For the beam loaded as shown in Fig. P-630, compute the value of (AreaAB)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.)
 

Overhang beam with point load at free end

 

Solution to Problem 629 | Moment Diagrams by Parts

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

Simple beam loaded with triangular and moment loads

 

Solution to Problem 628 | Moment Diagrams by Parts

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.
 

Simple beam loaded with triangular and moment loads

 

Solution to Problem 627 | Moment Diagram by Parts

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.)
 

627-uniformly-varying.gif

 

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