## Sign conventions

- Global axis system: The origin of the global axis system is located at the upstream end of the foundation. The global axis system allows the coordinates of any point in space to be located with reference to the longitudinal axis X (upstream-downstream), vertical axis Y and transverse axis Z (cross-stream direction).
- Local axis system: All lift joints, including the base joint, have a local axis system where its origin is at the upstream point and the longitudinal axis of the joint (L) follows the inclination of the joint.
- Positive Forces and Moments: The sign convention adopted for the positive direction of forces and moments are illustrated in Figure 7. Positive forces follow the positive direction of global and local axes. The positive directions of the moments use the right-hand rule as shown in Figure 7.

Figure 7

The sign convention for stresses and pressures is illustrated in Figure 8.

Figure 8

Positive direction of inertia forces: According to dâ€™Alembert principle, the inertia forces, induced by an earthquake are opposed to the direction of the base acceleration (Figure 9). A positive acceleration results in a negative inertia force.

Figure 9