Assumptions

Situation

Questions

Answers

  • No nodal rotations in results

 

The calculated frame:

Calculated frame

 

where nodal displacements are presented as:

Nodal displacements

1. Why nodal rotation angle Ry in node N6 is equal to zero, while in Node N7 has some value?

2. Why nodal rotation angle Ry in node N1 is equal to zero, while in Node N7 has some value?

1. In mathematical approach every fixed degree of freedom is making correction in stiffness matrix by some value, what is drawing near to infinity as:

Stiffness matrix

By solving this linear problem is seen, that ith degree of freedom is equal to zero, while ui=Fi / ∞.

Similar situation is happen for node N6, where rotational degree of freedom was set to zero while, at least while fixed support was applied. Node N7 hasn't stiffness correction in rotational degree of freedom for infinite value, that’s why there rotation angle is calculated.

 

2. Kind of similar problem like #1. Explanation of this problem is described in the book of: Blaauwendraat Johan, "Eindige-Elementen Methode voor Staafconstructies", Academic service, 2000, p. 154-155.