# cantilever beam

## 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 |

## Problem 733 | Cantilever beam with moment load at the free end and supported by a rod at midspan

**Problem 733**

The load P in Prob. 732 is replaced by a counterclockwise couple M. Determine the maximum value of M if the stress in the vertical rod is not to exceed 150 MPa.

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

## 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.

## Method of Superposition | Beam Deflection

The slope or deflection at any point on the beam is equal to the resultant of the slopes or deflections at that point caused by each of the load acting separately.

## Solution to Problem 648 | Deflection of Cantilever Beams

**Problem 648**

For the cantilever beam loaded as shown in Fig. P-648, determine the deflection at a distance x from the support.

## Solution to Problem 647 | Deflection of Cantilever Beams

**Problem 647**

Find the maximum value of EIδ for the beam shown in Fig. P-647.

## Solution to Problem 646 | Deflection of Cantilever Beams

**Problem 646**

For the beam shown in Fig. P-646, determine the value of I that will limit the maximum deflection to 0.50 in. Assume that E = 1.5 × 10^{6} psi.