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9th Edition

Barry J. Goodno + 1 other

Publisher: Cengage Learning

ISBN: 9781337093347

Chapter 9, Problem 9.7.4P

Textbook Problem

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**-4 **A simple beam *ABCD *has moment of inertia I near the supports and moment of iertia 2I in the middle region, as shown in the figure. A uniform load of intensity q acts over the entire length of the beam.

Determine the quations of the deflection curve for the left-hand half of the beam. Also, find the angle of rotation

To determine

The equations of the deflection curve for the left-hand half of the beam, the angle of rotation

**Given Information: **

We have the simple beam ABCD with moment of inertia I near supports and moment of inertia 2I in the middle region as per below figure:

For the given simple beam below is the free body diagram.

For the above diagram, applying the force equilibrium in horizontal direction, we will get,

At the point A, we are applying moment equilibrium,

Again we are applying the force equilibrium but in vertical direction,

Now we are taking a section which is at distance of x from point A where

In above section, we are applying moment equilibrium,

We can get the slope equation after integrating the above equation.

Once again taking integration on both sides, we can determine the deflection equation,

Now we are taking a section which is at distance of x from point A where

In above section, we are applying moment equilibrium,

We can get the slope equation after integrating the above equation.

Once again taking integration on both sides, we can determine the deflection equation,

The exaggerated elastic curve for the simple beam ABCD can be represented as below diagram:

The boundary condition is applied for deflection equation for

This concludes that the slope contains value as zero when the maximum deflection of the beam

Now applying boundary condition to deflection equation

We are applying the continuity of slope condition at point B by evaluating the slope equations for segments

Now we are applying the continuity of deflection condition at point B by evaluating the slope equations for segments

Mechanics of Materials (MindTap Course List)

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