# slope of beam

## Problem 735 | Fixed-ended beam with one end not fully restrained

**Problem 735**

The beam shown in Fig. P-735 is perfectly restrained at A but only partially restrained at B, where the slope is w_{o}L^{3}/48EI directed up to the right. Solve for the end moments.

## Application of Double Integration and Superposition Methods to Restrained Beams

## Superposition Method

There are 12 cases listed in the method of superposition for beam deflection.

- Cantilever beam with...
- concentrated load at the free end.
- concentrated load anywhere on the beam.
- uniform load over the entire span.
- triangular load with zero at the free end
- moment load at the free end.

- Simply supported beam with...
- concentrated load at the midspan.
- concentrated load anywhere on the beam span.
- uniform load over the entire span.
- triangular load which is zero at one end and full at the other end.
- triangular load with zero at both ends and full at the midspan.
- moment load at the right support.
- moment load at the left support.

See beam deflection by superposition method for details.

## Conjugate Beam Method | Beam Deflection

Slope on real beam = Shear on conjugate beam

Deflection on real beam = Moment on conjugate beam

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.