Design control (Beams: EC3 Eurocode)
Principles
There are multiple check lengths to deal with (LTB, y-y buckling and z-z buckling) all of which can be contained within or overlapped by their associated lengths. Consequently, a 'hierarchy' of checks is defined. In the approach taken the LTB segment length is taken as the driver and the other lengths whether overlapping or contained by this segment are mapped to it.
Design example
The following example illustrates how the checks are applied to I- and H-sections with equal flanges.
The beam (span) is 10.2 m long and has torsional restraints at each end. The top flange is restrained out-of-plane at 0.7m, 4.2m and 6.6 m – these provide restraint to the top flange for LTB and to the beam as a whole for out-of-plane strut buckling. The bottom flange has one restraint at mid-span and this restrains the bottom flange for LTB and the beam as a whole for in-plane strut buckling. (This is probably difficult to achieve in practice but is useful for illustration purposes.)
Note that the top flange LTB restraints and z-z restraints are coincident in this example but will not always be coincident.
Tekla Structural Designeridentifies the following lengths and checks. (in this example all the effective length factors are assumed to be 1.0 for simplicity.)
LTB Segment | Equation | In-plane strut segment | Out-of-plane strut segment |
---|---|---|---|
length (m) | length (m) | length (m) | |
Top flange 0 – 4.2 (first restraint ignored since top flange is in tension at this point) |
6.61 | 0 – 5.1 | 0 – 0.7 |
6.62 | 0 – 5.1 | 0 – 0.7 | |
6.61 | 0 – 5.1 | 0.7- 4.2 | |
6.62 | 0 – 5.1 | 0.7- 4.2 | |
Top flange 4.2 – 6.6 |
6.61 | 0 – 5.1 | 4.2 – 6.6 |
6.62 | 0 – 5.1 | 4.2 - 6.6 | |
6.61 | 5.1 - 10.2 | 4.2 - 6.6 | |
6.62 | 5.1 - 10.2 | 4.2 - 6.6 | |
Top flange 6.6 - 10.2 |
6.61 | 5.1 - 10.2 | 6.6 - 10.2 |
6.62 | 5.1 -10.2 | 6.6 - 10.2 | |
Bottom flange 0 – 10.2 |
6.61 | 0 – 5.1 | 0 – 0.7 |
6.62 | 0 – 5.1 | 0 – 0.7 | |
6.61 | 0 – 5.1 | 0.7- 4.2 | |
6.62 | 0 – 5.1 | 0.7- 4.2 | |
6.61 | 0 – 5.1 | 4.2 - 6.6 | |
6.62 | 0 – 5.1 | 4.2 - 6.6 | |
6.61 | 5.1 - 10.2 | 4.2 - 6.6 | |
6.62 | 5.1 - 10.2 | 4.2 - 6.6 | |
6.61 | 5.1 - 10.2 | 6.6 - 10.2 | |
6.62 | 5.1 - 10.2 | 6.6 - 10.2 |