# Shear and moments

rsq_a
I can't seem to wrap my head around the signs of shears and moments when applied to beams. Consider a cantilever beam that goes from x = 0 to x = L (with positive deflection, or y(x), corresponding to a deflection upwards).

The standard equations tell us that

$$\text{Moment} = EI \frac{d^2 y}{dx^2}$$

$$\text{Shear} = EI \frac{d^3 y}{dx^3}$$

$$\text{Load} = EI \frac{d^4 y}{dx^4}$$

Now consider what happens when we change $$x = -x$$ (that is, we put our coordinate system so that the beam begins at x = 0 and goes to x = -L).

Why does that change the shear to negative, but keep the sign of the moments and loads the same?

$$\text{Curvature} = EI \frac{d^1 y}{dx^1}$$