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Section 8.2 Sign Conventions

When talking about internal loads our standard sign convention for forces and moments is not good enough. We can't, for instance, just call a vertical shear force positive if it points up and negative if it points down, because internal forces always occur in pairs so at any given point a shear force is both up and down. The direction of the internal force at a point depends on which side of the cut you’re looking at.

So to define the state of internal loads at a point we need a better sign convention. Although the choice is somewhat arbitrary, agreeing on a standard sign convention allows us to have consistency across our calculations and to communicate the internal state clearly to others. The standard sign conventions defined here are used for internal loadings at a point and also for the shear and bending moment diagrams which are discussed in Section 8.4.

Be aware that although this new sign convention applies all internal loads, it doesn't change the sign convention for the equations of equilibrium at all, so you will continue to solve them in the same way you alway have.

The standard sign convention used for shear force, normal force, and bending moment is shown below.

  • Positive Shear.

    Positive shear forces tends to rotate the object counterclockwise, i.e. the shear forces act down when looking towards the cut from the right, and up when looking from the left.

  • Positive Normal Force.

    Positive normal forces tends to stretch the object.

  • Positive Bending Moment.

    Positive bending moments tends to deform the object with an upward curvature.

Question 8.2.1.

We have defined positive internal loads by looking at the “front” side of the object. Would the results change if you walked around the object and analyzed it from the other side?