# superposition method

## Problem 715 | Distributed loads placed symmetrically over fully restrained beam

**Problem 12**

Determine the moment and maximum EIδ for the restrained beam shown in Fig. RB-012. (Hint: Let the redundants be the shear and moment at the midspan. Also note that the midspan shear is zero.)

## Problem 713 | Fully restrained beam with symmetrically placed concentrated loads

**Problem 713**

Determine the end moment and midspan value of EIδ for the restrained beam shown in Fig. PB-010. (Hint: Because of symmetry, the end shears are equal and the slope is zero at midspan. Let the redundant be the moment at midspan.)

## Problem 712 | Propped beam with initial clearance at the roller support

## Problem 711 | Cantilever beam with free end on top of a simple beam

**Problem 711**

A cantilever beam BD rests on a simple beam AC as shown in Fig. P-711. Both beams are of the same material and are 3 in wide by 8 in deep. If they jointly carry a load P = 1400 lb, compute the maximum flexural stress developed in the beams.

## Problem 708 | Two Indentical Cantilever Beams

**Problem 708**

Two identical cantilever beams in contact at their ends support a distributed load over one of them as shown in Fig. P-708. Determine the restraining moment at each wall.

## 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.