Local Coordinate System for Beam Elements
A local coordinate system for each element, as shown below, is defined as follows:
The local X-axis XL is oriented in the direction from element begin to element end. The angle α2 (angle in plan) is defined as the angle between the global XG-axis and the normal projection of the element on the XG-ZG-plane (plan). The angle α1 (angle of elevation) is defined as the angle between the XG-ZG-plane and the element axis XL. α1 is positive if the local X-axis XL has a positive YG-component (left-hand turning), α2 is positive when measured from XG-towards ZG (right-hand turning). A 3rd angle, denoted b, describes the deviation of the principal inertia planes from the default. The local coordinate system may be derived from the global system by applying three rotations in the correct order (a2, a1 and b).
α1 and α2 are automatically derived from the location of the element begin and end defined in the input. The orientations of the local axes YL and ZL (forming the 1st and 2nd principal inertia planes with XL respectively) are defined by the angle β. The input for the β-angle must be given by the user if the default axes Y'L, Z'L are not suitable. The definition of the angle β for deck elements and pier elements respectively is shown below. The angle ß is positive if turning to the left around the xL axis.
