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## Main Question or Discussion Point

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

[tex]

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

[/tex]

[tex]

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

[/tex]

[tex]

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

[/tex]

Now consider what happens when we change [tex]x = -x[/tex] (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?

The standard equations tell us that

[tex]

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

[/tex]

[tex]

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

[/tex]

[tex]

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

[/tex]

Now consider what happens when we change [tex]x = -x[/tex] (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?