# Plotting deflection of a beam

I have a formula to compute the deflection of a beam.

When I have computed the deflection I get a vector with non-negative elements representing the deflection in each position on the beam.

When I am plotting the deflection vector I get a downwards parabola since the elements are positive.

But now I found this plot somewhere else I guess the plot illustrates how the beam is bending at positions where loads are placed.

Is it correct to get negative deflections? I wonder if I need to multiply my elements in my deflection vector by -1 in order to obtain the same plot as shown here.

Deflection

A deflection is a movement in a direction. It is up to you to determine your frame of reference.

It sounds like the calculations that you have done yourself (all positive) are shown for a force also in the positive direction. This makes sense logically.

The deflections shown in the graph that you attached (all negative) may be in a different coordinate system where the force is acting in the negative direction. It is up to you to determine whether you are calculating in the frame reference of the force or from the outside.

Also remember that it is reasonable to get both positive or negative deflections in the same component. A beam with two supports and a cantilever could show negative deflection at the free end and positive deflection between the supports.

Example 1 - Gravity on a Beam Deflection is negative from the world-view but positive from the view of the force.

Example 2 - Cantilever Deflection is opposite for the free end (right side) when compared to the portion under the arrow.

• Thank you. It is for a programming exercise and I'm not told whether the forces are inputted as negative or positive numbers. Would you choose to keep my normal reference system with positive deflections and positive y-axis, and assume the user inputs negative forces, or instead multiplying the deflection vector with -1? Can I limit the forces to positive or negative numbers? I what situation can a load have opposite direction? Apr 27 '15 at 20:39
• @Jamgreen I would say always make it so that a positive force gives a positive deflection. Changing things around internally will just add confusion. There are many situations where a load can be either positive or negative (or alternate). If nothing else, picture yourself pulling on a post in either direction.
– hazzey
Apr 27 '15 at 20:55