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The sign convention used in the beam section is defined in the following illustrations. Notice that unlike some publications on this subject, the loading term P(x) points to the same direction as y-axis. Please refer to the Euler-Bernoulli beam theory for more details.

Loading and deflection sign convention

The loading P and deflection y directions indicated are positive


bending moment sign convention

The bending moment M direction indicated is positive


shear force sign convention

The shear force V direction indicated is positive.