# Deflection of Beams

## Continuous Beam With a Gap and a Zero Moment in Interior Support

**Situation**

A beam of uniform cross section whose flexural rigidity *EI* = 2.8 × 10^{11} N·mm^{2}, is placed on three supports as shown. Support *B* is at small gap Δ so that the moment at *B* is zero.

1. Calculate the reaction at *A*.

A. 4.375 kN | C. 5.437 kN |

B. 8.750 kN | D. 6.626 kN |

2. What is the reaction at *B*?

A. 4.375 kN | C. 5.437 kN |

B. 8.750 kN | D. 6.626 kN |

3. Find the value of Δ.

A. 46 mm | C. 34 mm |

B. 64 mm | D. 56 mm |

## Problem 731 | Cantilever beam supported by cable at the free-end

**Problem 731**

The beam shown in Fig. P-731 is connected to a vertical rod. If the beam is horizontal at a certain temperature, determine the increase in stress in the rod if the temperature of the rod drops 90°F. Both the beam and the rod are made of steel with E = 29 × 10^{6} psi. For the beam, use I = 154 in.^{4}

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

## Problem 704 | Solution of Propped Beam

**Problem 704**

Find the reactions at the supports and draw the shear and moment diagrams of the propped beam shown in Fig. P-704.

## 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.

## Problem 658 | Beam Deflection by Conjugate Beam Method

**Problem 658**

For the beam shown in Fig. P-658, find the value of EIδ at the point of application of the couple.

## Problem 657 | Beam Deflection by Conjugate Beam Method

**Problem 657**

Determine the midspan value of EIδ for the beam shown in Fig. P-657.