## Continuous Beams with Fixed Ends

Assume the fixed end to be equivalent to an imaginary span with imaginary loading. In three-moment equation, all the terms that refer to the imaginary span have zero values.

In the following problems, the ends of the beams are assumed to be perfectly fixed by the walls against rotation. All supports are assumed to remain at the same level.

## Problem 725 | Propped beam with partially restrained wall and settling simple support

Problem 725
If the support under the propped beam in Problem 724 settles an amount $\delta$, show that the propped reaction decreases by $3EI\delta / L^3$.

## Problem 724 | Propped beam with partially restrained wall support

Problem 724
The beam shown in Fig. P-724 is only partially restrained at the wall so that, after the uniformly distributed load is applied, the slope at the wall is $w_oL^3 / 48EI$ upward to the right. If the supports remain at the same level, determine $R$.

## Problem 723 | Propped beam with uniform load over half the span

Problem 723
Find the reaction R and the moment at the wall for the propped beam shown in Fig. P-723.