# moment diagram

## Conjugate Beam Method | Beam Deflection

Deflection on real beam = Moment on conjugate beam

### Properties of Conjugate Beam

Engr. Christian Otto Mohr

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

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## 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.

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## 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 R_{2}. (Hint: Draw the reference tangent to the elastic curve at R_{2}.)

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## 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.)

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## Solution to Problem 632 | Moment Diagrams by Parts

**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.)

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## 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?

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## Solution to Problem 630 | Moment Diagrams by Parts

**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.)

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## 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.

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## 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.

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## 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.)

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