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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 8, Problem 58P

Textbook Problem

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Draw the influence line for the vertical deflection at point *B* of the cantilever beam of Problem 8.5. *EI =* constant. See Fig. P8.5.

FIG. P8.5, P8.58

To determine

Sketch the influence line for the vertical deflection at the point *B* of the given cantilever beam.

**Given information:**

**Calculation:**

Consider a point load is acting at a distance *x* from the fixed end of the given cantilever beam.

Show the loading on the cantilever beam as shown in Figure 1.

Refer Figure 1.

Consider the beam portion ranges from

Show the expression for the deflection of the cantilever beam due to point load *P* acting at a distance *a* from the fixed end as follows:

Here, *E* is modulus of elasticity of the beam, *I* is the moment of inertia.

Calculate the deflection *B* due to the unit point load acting at a distance *x* from the fixed end.

Substitute 1 for *P* and *a* in Equation (1).

Consider the load is acting at a distance *x* as

Calculate the deflection at *B* as follows:

Substitute *x* in Equation (2).

Similarly, calculate the deflection at point *B* due to different position of the point load and tabulate the values as shown in Table 1.

x (ft) | |

2 | |

6 | |

10 | |

14 |

Structural Analysis

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