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Section 1
1-11
1.5.3 Relationship Between Global & Local
Coordinates
Since the input for member loads can be provided in the local and
global coordinate system and the output for member-end-forces is
printed in the local coordinate system, it is important to know the
relationship between the local and global coordinate systems. This
relationship is defined by an angle measured in the following
specified way. This angle will be defined as the beta (β) angle.
For offset members the beta angle/reference point specifications
are based on the offset position of the local axis, not the joint
positions.
Beta Angle
When the local x-axis is parallel to the global Vertical axis, as in
the case of a column in a structure, the beta angle is the angle
through which the local z-axis (or local Y for SET Z UP) has been
rotated about the local x-axis from a position of being parallel and
in the same positive direction of the global Z-axis (global Y axis
for SET Z UP).
F
or input,
see section
5.26
When the local x-axis is not parallel to the global Vertical axis,
the beta angle is the angle through which the local coordinate
system has been rotated about the local x-axis from a position of
having the local z-axis (or local Y for SET Z UP) parallel to the
global X-Z plane (or global X-Y plane for SET Z UP)and the local
y-axis (or local z for SET Z UP) in the same positive direction as
the global vertical axis. Figure 1.7 details the positions for beta
equals 0 degrees or 90 degrees. When providing member loads in
the local member axis, it is helpful to refer to this figure for a
quick determination of the local axis system.