# deviation from tangent

## 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 735 | Fixed-ended beam with one end not fully restrained

**Problem 735**

The beam shown in Fig. P-735 is perfectly restrained at A but only partially restrained at B, where the slope is w_{o}L^{3}/48EI directed up to the right. Solve for the end moments.

## Problem 734 | Restrained beam with uniform load over half the span

**Problem 734**

Determine the end moments for the restrained beams shown in Fig. P-734.

## 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 722 | Propped beam with moment load on the span by area-moment method

**Problem 722**

For the beam shown in Fig. P-722, compute the reaction R at the propped end and the moment at the wall. Check your results by letting b = L and comparing with the results in Problem 707.

**Solution**

## Problem 707 | Propped beam with moment load at simple support by moment-area method

## Problem 721 | Propped beam with decreasing load by moment-area method

**Problem 721**

By the use of moment-are method, determine the magnitude of the reaction force at the left support of the propped beam in Fig. P-706.

## Problem 720 | Propped beam with increasing load by moment-area method

**Problem 720**

Find the reaction at the simple support of the propped beam shown in Fig. P-705 by using moment-area method.

## Problem 704 | Propped beam with some uniform load by moment-area method

**Problem 704**

Find the reaction at the simple support of the propped beam shown in Figure PB-001 by using moment-area method.

## Application of Area-Moment Method to Restrained Beams

See deflection of beam by moment-area method for details.

Rotation of beam from A to B

Deviation of B from a tangent line through A