## Problem 653 | Beam Deflection by Conjugate Beam Method

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. ## Solution to Problem 665 | Deflections in Simply Supported Beams

Problem 665
Replace the concentrated load in Prob. 664 by a uniformly distributed load of intensity wo acting over the middle half of the beam. Find the maximum deflection.

## Solution to Problem 664 | Deflections in Simply Supported Beams

Problem 664
The middle half of the beam shown in Fig. P-664 has a moment of inertia 1.5 times that of the rest of the beam. Find the midspan deflection. (Hint: Convert the M diagram into an M/EI 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 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.
3. A simple support for the real beam remains simple support for the conjugate beam.
4. A fixed end for the real beam becomes free end for the conjugate beam.
5. The point of zero shear for the conjugate beam corresponds to a point of zero slope for the real beam.
6. The point of maximum moment for the conjugate beam corresponds to a point of maximum deflection for the real beam.