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Coordinate Axis Convention

The right-hand rule states that if you take the vector cross product of X cross Y, the result is in the Z direction.  This is what is used to establish the positive Z direction if you know the positive X and Y directions.  It applies to the Global Coordinate Axis system and the member local coordinate axis system in the 2-D Frame Analysis module,  in the 2-D Frame Analysis module.

The Global Coordinate Axis system is oriented such that X points to the right, Y points upward, and Z is perpendicular to the screen in the 2-D Frame Analysis module.

The member local coordinate axis system is established as follows.  A vector from the I node to the J node establishes the member local x axis.  The vector cross product of local x cross Global Y produces the member local z direction.  This works for all member orientations except for vertically oriented members, because it is not possible to take the vector cross product of two parallel vectors.  So in those cases the module adopts the convention that the member local z axis will be parallel to the Global Z axis.  These are just mathematical rules that establish that member local z will be perpendicular to the screen (unless you have specified that the member is working in weak axis bending).  The local z axis is perpendicular to the web of a wide flange section.  It typically represents the “strong” axis of a member.  Finally, we need to establish the orientation of the local y axis.  Vector cross product rules for a right-hand coordinate system also state that local z cross local x produces local y.  So this pins down the orientation of the local y axis.  The local y axis of a wide flange member lies in the plane of the web and is mutually perpendicular to the local x and local z axes.  For a horizontally oriented beam member, the local y axis points straight up, parallel to the Global Y axis.

 

Result Sign Convention

Now for the sign conventions of the various results that are available.

 

Joint Displacements

Joint Displacements are reported with respect to the Global Coordinate Axis system.  A positive displacement indicates a displacement in the direction of the positive corresponding axis.  A positive rotation indicates a positive rotation about the Global Z axis.  (Using the thumb of the right hand, point the thumb in the direction of the positive Global Z axis, and the natural curl of the right fingers will indicate the direction of a positive rotation.)

 

Reactions

Reactions are also reported with respect to the Global Coordinate Axis system.  A positive force reaction indicates a force in the direction of the positive corresponding axis.  A positive moment reaction indicates a positive moment about the Global Z axis.  (Using the thumb of the right hand, point the thumb in the direction of the positive Global Z axis, and the natural curl of the right fingers will indicate the direction of a positive moment.)

 

Member End Forces

Member End Forces are reported with respect to the member local coordinate axis system.  A positive value of axial load at the I end of the member means that the force acts in the member local x direction, so it is pushing into the starting end of the member, so it represents a compressive force.  Likewise, a negative value of axial load at the J end of the member means that the force acts in the member local -x direction, so it is pushing into the ending end of the member, so again this represents a compressive force.

Shears are also reported with respect to the member local coordinate axis system.  A positive value of shear at the I end of the member means that the force acts in the member local y direction.  Likewise, a negative value of shear at the J end of the member means that the force acts in the member local -y direction.

A positive value of moment at either end of the member means that the moment acts in the member local z direction.  (Using the thumb of the right hand, point the thumb in the direction of the positive Global Z axis, and the natural curl of the right fingers will indicate the direction of a positive moment.)  

 

Member Forces at Sections

The physical sense of the member forces at sections can best be established by relating to the physical sense of the member end forces at the starting end of the member as described above.  

 

Deflections (Relative to member ends)

The deflections relative to member ends are measured parallel to the member local y axis and are referenced from the straight-line chord connecting the undeflected end node locations.  Positive values represent deflections in the positive local y axis direction from that straight-line chord.