NIEUWE BLIK OP KIP EN KNIK - Bouwen met Staal

H 1a Summary
n * =
20
total deformation
nd
2 order part of deformation
Distinction is made between the deformation in the two main directions normal to the
beam-column axis.
The determination of n z* (due to the displacement in the ‘weak’ direction) is the key to
calculating 2 nd order effects in an efficient and well-organized manner.
Very important is the 'alerting function' that n* can fulfil when judging the stability of
beam-columns. While this is known, it is not found in rules for flexural-torsional buckling
in the design codes reviewed.
Beam-column types and load cases
Considered
straight members:
- on two simple supports
- cantilevers
Loaded by a: - constant moment or:
- a uniformly distributed load or:
- a point load
Iteration method
whether or not supported
laterally
in all cases combined with a
compressive normal force
In Chapter 5 an iteration procedure is proposed, in which nine steps are passed through in
each cycle:
1 - choice of the shape and magnitude of the deflection in the weak direction,
2 - determination of the twisting moment,
3 - determination of the rotation,
4 - from this deduction of 2 nd order moments,
5 - determination of the member curvature,
6 - from this deduction of magnitude and shape of the 2 nd order displacements,
7 - calculating of the total displacements by superposition,
8 - comparing the results with the choices made in step 1,
9 - if in agreement, determination of n z*.
The iteration procedure is done for all discussed load cases in a spreadsheet program.
Hereafter a general formula for n z* is presented, which in a simple way is valid for the study
of all load cases. The factors in this formula (differing per load case) are derived from a
spreadsheet calculation.