# Beam Deflection

## Simply Supported Beam with Support Added at Midspan to Prevent Excessive Deflection

**Situation**

A simply supported beam has a span of 12 m. The beam carries a total uniformly distributed load of 21.5 kN/m.**1.** To prevent excessive deflection, a support is added at midspan. Calculate the resulting moment (kN·m) at the added support.

A. 64.5 | C. 258.0 |

B. 96.8 | D. 86.0 |

**2.** Calculate the resulting maximum positive moment (kN·m) when a support is added at midspan.

A. 96.75 | C. 108.84 |

B. 54.42 | D. 77.40 |

**3.** Calculate the reaction (kN) at the added support.

A. 48.38 | C. 161.2 |

B. 96.75 | D. 80.62 |

## Limit the Deflection of Cantilever Beam by Applying Force at the Free End

**Situation**

A cantilever beam, 3.5 m long, carries a concentrated load, *P*, at mid-length.

**Given:**

*P*= 200 kN

Beam Modulus of Elasticity,

*E*= 200 GPa

Beam Moment of Inertia,

*I*= 60.8 × 10

^{6}mm

^{4}

**1.** How much is the deflection (mm) at mid-length?

A. 1.84 | C. 23.50 |

B. 29.40 | D. 14.70 |

**2.** What force (kN) should be applied at the free end to prevent deflection?

A. 7.8 | C. 62.5 |

B. 41.7 | D. 100.0 |

**3.** To limit the deflection at mid-length to 9.5 mm, how much force (kN) should be applied at the free end?

A. 54.1 | C. 129.3 |

B. 76.8 | D. 64.7 |

## Support Added at the Midspan of Simple Beam to Prevent Excessive Deflection

**Situation**

A simply supported steel beam spans 9 m. It carries a uniformly distributed load of 10 kN/m, beam weight already included.

**Given Beam Properties:**

Area = 8,530 mm

^{2}

Depth = 306 mm

Flange Width = 204 mm

Flange Thickness = 14.6 mm

Moment of Inertia,

*I*= 145 × 10

_{x}^{6}mm

^{4}

Modulus of Elasticity,

*E*= 200 GPa

1. What is the maximum flexural stress (MPa) in the beam?

A. 107 | C. 142 |

B. 54 | D. 71 |

2. To prevent excessive deflection, the beam is propped at midspan using a pipe column. Find the resulting axial stress (MPa) in the column

**Given Column Properties:**

Outside Diameter = 200 mm

Thickness = 10 mm

Height = 4 m

A. 4.7 | C. 18.8 |

B. 9.4 | D. 2.8 |

3. How much is the maximum bending stress (MPa) in the propped beam?

A. 26.7 | C. 15.0 |

B. 17.8 | D. 35.6 |

## 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 |