Rules of signs for bending

Rules of signs of forces and moments in bending

In the case of plane transverse bending, an internal transverse force Q and an internal bending moment M arise in the beam sections.

For their calculation and the subsequent construction of the diagrams, the following rule of signs is adopted:

Signs of transverse forces

The internal transverse force Q is assumed to be positive (ie, Q> 0) if it tends to rotate the cut off part of the beam clockwise.

The rule of signs for transverse force

The rule of signs for transverse force

When compiling the equilibrium equations for the cut off parts of the beam, the rule of signs for external loads (for example, the concentrated force F) is defined similarly.

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In other words, external forces and distributed loads striving to rotate the cut off part of the beam relative to the cross-section in question along the clockwise direction are considered positive, and vice versa.

Signs of bending moments

The internal bending moment M is assumed to be positive (that is, M> 0) if it tends to compress the upper layers of the cut off part of the beam in the section under consideration.

The rule of signs for a bending moment

The rule of signs for a bending moment

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For external concentrated moments and moments of forces, the rule of signs is analogous, i.e. Positive external moments, concentrated forces and distributed loads compressing the upper layers of the beam are considered positive.

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