Sign Conventions

General Stress Sign Convention

• Positive normal stress acts outward from all faces.
• Positive shear stress points towards the positive axis direction in a positive face.
• Positive shear stress points towards the negative axis direction in a negative face.

Axial (Normal) Stress

• Tension: \( \sigma > 0 \)
• Compression: \( \sigma < 0 \)

• Displacement of points in space: the movement of a point relative to its initial position in space (ex; \( \delta_B \) )
• Change in length of a segment: the relative displacement of a point with respect to another point (ex; \( \delta_{B/A} = \delta_B - \delta_A = \delta_1 \) ). This can be written multiple ways:

Sign Conventions for internal forces in a bar.

• \( F>0 \) : tension
• \( F<0 \) : compression
• \( \delta>0 \) : elongation
• \( \delta<0 \) : contraction

Torsion

• \( \phi > 0 \) : counter clockwise
• \( \phi < 0 \) : clockwise

Torque and angle of twist follow the right hand rule sign convention. When positive, using the right hand, the thumb points outward from the shaft and the fingers will curl in the direction of the positive twist/torque.

Shear and Moment Diagrams

For the purposes of drawing shear and moment diagrams, the adopted sign conventions for internal forces and moments are shown below. The internal shear force \( V \) and moment \( M \) in a beam are plotted with positive values when they act in the indicated directions with respect to internal surfaces in the beam. These conventions assume the analysis is conducted on a horizontal beam with positive \( x \) axis pointing to the right.