Partial instability mode: boundary conditions

In case the Partial instability mode is used, boundary conditions as rotational stiffness Cr1 and Cr2 should be defined, to take into account the relation of the member and its environment, like connecting members and supports.

Rotational stiffness Cr1 and Cr2

 

There are 2 ways to define this rotational stiffness:

  • Geometrical stiffness analysis of the connecting members (EI, Length, member-end springs) and support springs:
Geometrical stiffness analysis of the connecting members and support springs

 

  • Force stiffness analysis by the ratio of bending moment and rotation: Cr=M/φ:
Force stiffness analysis as the ratio of bending moment and rotation

 

As the 1st one (Geometrical) is limited in functional way, in MatrixFrame® the 2nd method (Force) is implemented. In case of the Force stiffness analysis, a L.E. analysis should be performed with specific loads in a way that the resulting deformations are affine with the buckling curvature, to get the proper values for M and φ.