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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 7, Problem 21P

Textbook Problem

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7.20 and 7.21 Use the virtual work method to determine the slope and deflection at point *B* of the beam shown.

FIG. P7.21, P7.23, P7.58

To determine

Find the slope and deflection at point *B* of the beam using virtual work method.

Given information:

The beam is given in the Figure.

The value of *E* is 70 GPa and *I* is

Calculation:

Consider the real system.

Sketch the real system of the beam as shown in Figure 1.

Refer Figure 1.

Consider the section at *x* distance from the end *B*.

Calculate the moment *M* as follows:

Consider the virtual system.

Remove all the real loads and apply a unit couple at the point on the beam where the slope is desired.

Sketch the virtual system of the beam with unit couple at point *B* as shown in Figure 2.

Let an equation expressing the variation of bending moment due to virtual couple be

Refer Figure 2.

Find the slope at *B* using the virtual work expression:

Here, *L* is the length of the beam, *E* is the Young’s modulus, and *I* is the moment of inertia.

Substitute *L*, and

Substitute 70 GPa for *E* and *I*.

Therefore, the slope at point *B* of the beam is

Structural Analysis

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