Deflection of Beams

Deflection of Beams

The deformation of a beam is usually expressed in terms of its deflection from its original unloaded position. The deflection is measured from the original neutral surface of the beam to the neutral surface of the deformed beam.

Slope of a Beam:

Slope of a beam is the angle between deflected beam to the actual beam at the same point.

Deflection of Beam: 

Deflection is defined as the vertical displacement of a point on a loaded beam. There are many methods to find out the slope and deflection at a section in a loaded beam.

The maximum deflection occurs where the slope is zero.  The position of the maximum deflection is found out by equating the slope equation zero.  Then the value of x is substituted in the deflection equation to calculate the maximum deflection

Cantilever Beam Deflection:

Cantilever beams are special types of beams that are constrained by only one support, as seen in the above example. These members would naturally deflect more as they are only supported at one end. To calculate the deflection of cantilever beam you can use the below equation, where W is the force at the end point, L is the length of the cantilever beam, E = Young's Modulus and I = Moment of Inertia.

Simply Supported Beam Deflection

Another example of deflection is the deflection of a simply supported beam. These beams are supported at both ends, so deflection of a beam is generally left and follows a much different shape to that of the cantilever. Under a uniform distributed load (for instance the self weight), the beam will deflect smoothly and toward the midpoint:

Fixed beam deflection:

Fixed beam is a beam in which both the ends are fixed and deflection occur from the center portion. Deflection is maxi from the center and mini from the points that are closed to the fixed ends.

Beam Deflection Formula

Cantilever Beams:

Simply supported Beams: