Joint connections M-Phi diagram

M-Phi diagram for steel joint connections

It is possible to perform a not linear (NL) analysis for steel joint connections in case the degrees of freedom are defined by using a M-Phi diagram (M - moment [kNm], Phi - angle of rotation [mRad]). For the M-Phi diagram angular rotation Phi has a global meaning.


The M-Phi diagram in absolute units:

M-Phi diagram in absolute units


The M-Phi diagram in relative units:

M-Phi diagram in relative units


Requirements for M-Phi diagram input

1. diagram may not have discontinuity points (according to continuous function definition)

2. diagram may not be defined in II and IV quadrants

3. diagram must be increasing without vertical (dX=0) or horizontal (dZ=0) branches

  • Vertical branch (dX=0) not allowed:
Joint connections M-Phi diagram: dX=0 not allowed


  • Horizontal branch (dZ=0) not allowed:
Joint connections M-Phi diagram: dZ=0 not allowed


  • The diagram must be only increasing: any part of the diagram can't be directed down as:
Joint connections M-Phi diagram: only increasing


4. zero point [0;0] is absolutely necessary:

  • The diagram without zero point can not be defined:

Joint connections M-Phi diagram with zero point     Joint connections M-Phi diagram without zero point


After calculation is performed and the M-Phi diagram of joint connections is created, MatrixFrame® provides a feedback to not linear (NL) releases to recalculate the updated not linear spring releases.