# double integration method

## Problem 707 | Propped Beam with Moment Load

## Problem 706 | Solution of Propped Beam with Decreasing Load

**Example 03**

The propped beam shown in Fig. P -706 is loaded by decreasing triangular load varying from w_{o} from the simple end to zero at the fixed end. Find the support reactions and sketch the shear and moment diagrams

## Problem 705 | Solution of Propped Beam with Increasing Load

**Problem 705**

Find the reaction at the simple support of the propped beam shown in Fig. P-705 and sketch the shear and moment diagrams.

## 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.