Fundamental Difference Between Slope and Deflection

After reading this article you will understand fundamental difference between slope and deflection. 

Slope is the angle formed by the tangent of the curve to the horizontal axis. 


For example the slope of the line.

2x + y = 3   Slope is -2.

While deflection is the translational movement of the beam from its original position. Maximum Y coordinate of the curve. 

Deflection can be calculated by finding minimum and maximum points for a curve by using differentiation?

Slope defines the direction in which the curvature of the deflection is heading.

If we have a cable and load it with a point load, we get a deflected shape of cable will be as shown in fig. below

In the image above, the deflection of the cable is linearly increasing as you go towards the midpoint of the span, but the slope is constant, just because cables do not have any out-of-plane stiffness. The entire action of a cable is governed by tension.

But this is not the case in beam. Let us take a look at what happens in a beam.

As you can see in the image above, deflection is stiff increasing in the beam as we move towards the midpoint, but the rate of increase in deflection along with span is not linear but parabolic.

δmax = PL348EI

Now, the slope of the beam as seen from the fig. is varying from support to center of the beam which is reflected by the tangent slope. It is maximum at the end while zero at the center of the beam.

The difference between beam and cable is, beam has out of plane stiffness which causes bending moments in the beam. While cable does not have out of plane stiffness so there is no bending moment.

They both rely on each other. Basically by differentiating the deflection equation, you will get the slope for the beam.