Deflection of Cantilevers beam. / Part - 22

Deflection of Cantilevers

◾ Introduction:

        We see that whenever a cantilever is loaded, it deflects from its original position. The amount, by which a beam deflects, depends upon its cross-section and the bending moment. In modern design offices, following are the two design criteria for the deflection of a cantilever:

1. Strength.

2. Stiffness.

   As per the strength criterion of the beam design, it should be strong enough to resist bending moment and shear force. Or in other words, the beam should be strong enough to resist the bending stresses and shear stresses. And as per the stiffness criterion of the beam design, which is equally important, it should be stiff enough to resist the deflection of the beam. Or in other words, the beam should be stiff enough not to deflect more than the permissible limit under the action of the loading. In actual practice, some specifications are always laid to limit the maximum deflection of a cantilever or a beam to a small fraction of its span.

◾ Watch this video for more details:

◾ Methods for Slope and Deflection at a Section:

    Though there are many methods for the slope and deflection at a Section in a loaded cantilever, yet the following are important from the subject point of view:

1. Double integration method.

2. Moment area method.

1. Double integration method for Slope and Deflection:

     The double integration method for finding out the slope and deflection at any section of a beam. We shall use the same method for finding out the slope and deflection in cantilever also.

1. Cantilever with a point load at its free end:

   

2. Cantilever with a point load not at the free end:

3. Cantilever with a uniformly distributed load :

4. Cantilever partially loaded with a uniformly distributed load:

5. Cantilever loaded from the free end:

6. Cantilever with a gradually varying load:

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