# Sign convention for deflection and slope of beam?

What is the sign convention for deflection and slope of a beam as shown in the diagram below? When I derive the formula using Euler-Bernoulli for deflection and slope myself, I end up with - deflection at y, - slope at A and + slope at B.

However, using formula I found, for the same scenario:

$$y=\frac{Px}{12EI}\ \left(\frac{3l^2}{4}-x^2\right)$$

$$θ1=θ2=\frac{Pl^2}{16EI}\$$

Gives + deflection at y, + slope at A and + slope at B.

What is the convention here?

• Are those the exact equations you found? If theta 1 = theta 2 from the get go, you'll never have a different sign. They could just express the magnitude only of the deflection angle. As for your deflection at y you need to use negative P since it is acting in the negative y direction. – jko Apr 17 at 13:39
• @jko yes, those are retyped exactly as I found them and you make a good point. Perhaps both equations are just calculating magnitude and ignoring direction. – FEA42 Apr 17 at 13:45
• Yes, that is what they are doing, plus using an approximation for small angles. When you get into more complicated systems, you tend to have two sketches. One shows the angles as you tend to think about them, and the second has a consistent set of angles all measured CC from the positive X axis that let you get the signs correct. Just get in the habit of making two sketches and always calculate from a consistent drawing. – Phil Sweet Apr 17 at 19:46