# Global and Local Coordinate Systems in START-PROF

## Global Coordinate System

START-PROF uses a right coordinate system. Coordinate systems are considered right if the Y axis is formed by rotating the X axis counter-clockwise when looking from the end of the Z axis at a 90 degree angle. In this global coordinate system, the Z axis is always directed upward. Gravity acts along the Z axis in the opposite direction (fig. 1).

All forces and linear displacements are input as projections on the global coordinate axes,  Х, Y, Z. Positive directions correspond with axes directions. Rotation angles and moments are positive if they are counter-clockwise when looking from the end of the axis around which they act.

Fig. 1. Global coordinate system in START-PROF and positive directions of forces, moments, linear displacement and rotation angles

## Local Coordinate System

Support loads, node displacement, expansion joint deformation and  internal forces can be model in local coordinates, Xm, Ym, Zm, connected to element axes (fig. 2).

Local axis Xm is always along the pipe element axis from start node to the end node, Zm is perpendicular to the element axis and is in the vertical plane with the angle between the global Z axis and local Zm axis of 900 or less (fig. 1.a). Ym is perpendicular to Zm and Xm, forming a right trio. For vertical elements, Xm lies along the Z axis, Ym – along the X axis, and  Zm – along the Y axis (fig. 1.b).

Fig. 2. Global coordinate system  (X, Y, Z) and local coordinate system connected to element axes (Xm, Ym, Zm)

## Local Coordinate System for Supports

Axes directions are selected as follows:

• along the axis - along the pipe axis projection on the horizontal plane (Xmm)

• transverse - transverse to the pipe axis in the horizontal plane (Ymm)

• vertical (Zmm)

Local pipe coordinate axes do not correspond to local coordinate axes of elements adjoining the support! Pipe axes are always in the horizontal and vertical planes. In other words, the local coordinate system remains constant regardless of the pipe's slope.