Thursday, 25 May 2017

SLOPE AND DEFLECTION OF BEAMS

SLOPE AND DEFLECTION OF BEAMS


Now we will start here, in this post, another important topic i.e. Deflection of beams and its various terms. If a beam will be loaded with point load or uniformly distributed load, beam will be bent or deflected from its initial position.

We will first discuss here the terminologies and various terms used in deflection of beam with the help of this post and after that we will see the amount by which beam will be deflected from its initial state and also slope of the deflected beam under the action of load in our next post.

 
So let us come to the main topic without wasting the time and let us see here various terms used in the concept of deflection of beam. Because without understanding the terms used in the deflection of beams, we will not be able to secure the amount by which beam will be deflected from its initial state and also slope of the deflected beam under the action of load.

Let us consider a beam AB of length L is simply supported at A and B as displayed in following figure. Let us think that one load P is acting at the midpoint of the beam. 
As beam is loaded with load P at the center of the beam and therefore beam will be subjected with bending moment and hence beam will be bent or deflected from its initial position under this load P.

Deflection

As we have seen above that beam is loaded with a load P at the midpoint of the beam and hence beam will be subjected with a bending moment and therefore beam will be bent in the form of a curvature or in to a circular arc.

We have shown the initial position of the beam i.e. before loading as ACB and deflected position of the beam i.e. after loading as ADB.

Now the vertical distance CD will be termed as the deflection of the beam under the action of the load P.

 

Let us define the deflection of the beam

Deflection of beam is basically defined as the vertical distance of beam measured before and after loading. Deflection of beam will be denoted by “y” and its unit of measurement will be mm.

Elastic curve

As we have seen above that beam is loaded with a load P at the midpoint of the beam and hence beam will be subjected with a bending moment and therefore beam will be bent in the form of a curvature or in to a circular arc.

Curvature or circular arc of the beam, formed under the action of load, will be termed as elastic curve.

Therefore, curvature ADB of the beam will be termed here as elastic curve.

Slope

Slope in deflection of beam will be defined as the angle turned by the beam under the action of load and hence under the action of bending moment.

 
Slope in deflection of beam will be basically defined as the angle made between the tangent drawn at the elastic curve and original axis of the beam.

Slope will be measured in radian and will be indicated by dy/dx or θ.


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Reference:

Strength of material, By R. K. Bansal
Image Courtesy: Google

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