# Simple Beam with Overhang

**Situation**

The total length of the beam shown below is 10 m and the uniform load $w_o$ is equal to 15 kN/m.

1. What is the moment at midspan if *x* = 2 m?

A. 37.5 kN·m | C. -187.5 kN·m |

B. -37.5 kN·m | D. 187.5 kN·m |

2. Find the length of overhang *x*, so that the moment at midspan is zero.

A. 2.5 m | C. 2.4 m |

B. 2.6 m | D. 2.7 m |

3. Find the span *L* so that the maximum moment in the beam is the least possible value.

A. 5.90 m | C. 5.92 m |

B. 5.88 m | D. 5.86 m |

## Influence Lines for Beams

A downward concentrated load of magnitude 1 unit moves across the simply supported beam *AB* from *A* to *B*. We wish to determine the following functions:

- reaction at
*A* - reaction at
*B* - shear at
*C*and - moment at
*C*

when the unit load is at a distance *x* from support *A*. Since the value of the above functions will vary according to the location of the unit load, the best way to represent these functions is by influence diagram.

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